* Hoover et al. (2022) Hoover, D. J., Seligman, D. Z., & Payne, M. J. 2022, PSJ, 3, 71, doi: 10.3847/PSJ/ac58fe
  * Hotokezaka et al. (2013) Hotokezaka, K., Kiuchi, K., Kyutoku, K., et al. 2013, PhRvD, 87, 024001
  * Howard et al. (2010) Howard, A. W., Marcy, G. W., Johnson, J. A., et al. 2010, Science, 330, 653, doi: 10.1126/science.1194854
  * Howard et al. (2012) Howard, A. W., Marcy, G. W., Bryson, S. T., et al. 2012, ApJS, 201, 15, doi: 10.1088/0067-0049/201/2/15
  * Hsieh & Jewitt (2006) Hsieh, H. H., & Jewitt, D. 2006, Science, 312, 561, doi: 10.1126/science.1125150
  * Hsieh et al. (2018) Hsieh, H. H., Ishiguro, M., Kim, Y., et al. 2018, AJ, 156, 223, doi: 10.3847/1538-3881/aae528
  * Hsieh et al. (2021) Hsieh, H. H., Chandler, C. O., Denneau, L., et al. 2021, ApJ, 922, L9, doi: 10.3847/2041-8213/ac2c62
  * Hsieh, H. H. (2009) Hsieh, H. H. 2009, A&A, 505, 1297, doi: 10.1051/0004-6361/200912342
  * Hu et al. (2023) Hu, M., Wang, L., Wang, X., & Wang, L. 2023, MNRAS, 525, 246, doi: 10.1093/mnras/stad2340
  * Huang et al. (2021) Huang, C.-K., Lehner, M. J., Granados Contreras, A. P., et al. 2021, PASP, 133, 034503, doi: 10.1088/1538-3873/abd4bc
  * Huang & Ormel (2022) Huang, S., & Ormel, C. W. 2022, MNRAS, 511, 3814, doi: 10.1093/mnras/stac288
  * Huber et al. (2011) Huber, D., Bedding, T. R., Stello, D., et al. 2011, ApJ, 743, 143, doi: 10.1088/0004-637X/743/2/143
  * Huber et al. (2013) Huber, D., Chaplin, W. J., Christensen-Dalsgaard, J., et al. 2013, ApJ, 767, 127, doi: 10.1088/0004-637X/767/2/127
  * Humphreys & Davidson (1994) Humphreys, R. M., & Davidson, K. 1994, PASP, 106, 1025, doi: 10.1086/133478
  * Humphreys et al. (2016) Humphreys, R. M., Weis, K., Davidson, K., & Gordon, M. S. 2016, ApJ, 825, 64, doi: 10.3847/0004-637X/825/1/64
  * Jewitt (2009) Jewitt, D. 2009, AJ, 137, 4296, doi: 10.1088/0004-6256/137/5/4296
  * Jewitt (2012) —. 2012, AJ, 143, 66, doi: 10.1088/0004-6256/143/3/66
  * Jewitt et al. (2015) Jewitt, D., Agarwal, J., Weaver, H., Mutchler, M., & Larson, S. 2015, ApJ, 798, 109, doi: 10.1088/0004-637X/798/2/109
  * Ji et al. (2022) Ji, J.-H., Li, H.-T., Zhang, J.-B., et al. 2022, Research in Astronomy and Astrophysics, 22, 072003, doi: 10.1088/1674-4527/ac77e4
  * Jian et al. (2024) Jian, M., Matsunaga, N., Jiang, B., Yuan, H., & Zhang, R. 2024, A&A, 682, A59, doi: 10.1051/0004-6361/202347911
  * Jiang et al. (2023) Jiang, H.-X., Mizuno, Y., Fromm, C. M., & Nathanail, A. 2023, MNRAS, 522, 2307, doi: 10.1093/mnras/stad1106
  * Jiang et al. (2017) Jiang, J.-A., Doi, M., Maeda, K., et al. 2017, Nature, 550, 80, doi: 10.1038/nature23908
  * Johansen et al. (2019) Johansen, A., Ida, S., & Brasser, R. 2019, A&A, 622, A202, doi: 10.1051/0004-6361/201834071
  * Kaasalainen & Torppa (2001) Kaasalainen, M., & Torppa, J. 2001, Icarus, 153, 24, doi: 10.1006/icar.2001.6673
  * Kaasalainen et al. (2001) Kaasalainen, M., Torppa, J., & Muinonen, K. 2001, Icarus, 153, 37, doi: 10.1006/icar.2001.6674
  * Kaib & Volk (2022) Kaib, N. A., & Volk, K. 2022, arXiv e-prints, arXiv:2206.00010, doi: 10.48550/arXiv.2206.00010
  * Kanagawa et al. (2018) Kanagawa, K. D., Tanaka, H., & Szuszkiewicz, E. 2018, ApJ, 861, 140, doi: 10.3847/1538-4357/aac8d9
  * Kasen et al. (2013) Kasen, D., Badnell, N. R., & Barnes, J. 2013, ApJ, 774, 25
  * Kasliwal (2012) Kasliwal, M. M. 2012, PASA, 29, 482, doi: 10.1071/AS11061
  * Kelley et al. (2023) Kelley, M. S. P., Hsieh, H. H., Bodewits, D., et al. 2023, Nature, 619, 720, doi: 10.1038/s41586-023-06152-y
  * Kempton et al. (2023) Kempton, E. M. R., Zhang, M., Bean, J. L., et al. 2023, Nature, 620, 67, doi: 10.1038/s41586-023-06159-5
  * Kervella et al. (2019) Kervella, P., Arenou, F., Mignard, F., & Thévenin, F. 2019, A&A, 623, A72, doi: 10.1051/0004-6361/201834371
  * Kipping et al. (2016) Kipping, D. M., Torres, G., Henze, C., et al. 2016, ApJ, 820, 112, doi: 10.3847/0004-637X/820/2/112
  * Knevitt et al. (2014) Knevitt, G., Wynn, G. A., Vaughan, S., & Watson, M. G. 2014, MNRAS, 437, 3087, doi: 10.1093/mnras/stt2008
  * Knight et al. (2023) Knight, M. M., Kokotanekova, R., & Samarasinha, N. H. 2023, arXiv e-prints, arXiv:2304.09309, doi: 10.48550/arXiv.2304.09309
  * Krolik et al. (1991) Krolik, J. H., Horne, K., Kallman, T. R., et al. 1991, ApJ, 371, 541, doi: 10.1086/169918
  * Kupfer et al. (2018) Kupfer, T., Korol, V., Shah, S., et al. 2018, MNRAS, 480, 302, doi: 10.1093/mnras/sty1545
  * Kupfer et al. (2021) Kupfer, T., Prince, T. A., van Roestel, J., et al. 2021, MNRAS, 505, 1254, doi: 10.1093/mnras/stab1344
  * Kupfer et al. (2023) Kupfer, T., Korol, V., Littenberg, T. B., et al. 2023, arXiv e-prints, arXiv:2302.12719, doi: 10.48550/arXiv.2302.12719
  * Law et al. (2009) Law, N. M., Kulkarni, S. R., Dekany, R. G., et al. 2009, PASP, 121, 1395, doi: 10.1086/648598
  * Li et al. (2023a) Li, G., Hu, M., Li, W., et al. 2023a, arXiv e-prints, arXiv:2311.14409, doi: 10.48550/arXiv.2311.14409
  * Li et al. (2023b) Li, J.-Y., Hirabayashi, M., Farnham, T. L., et al. 2023b, Nature, 616, 452, doi: 10.1038/s41586-023-05811-4
  * Li & Paczyński (1998) Li, L.-X., & Paczyński, B. 1998, ApJ, 507, L59
  * Li et al. (2021) Li, W., Wang, X., Bulla, M., et al. 2021, ApJ, 906, 99, doi: 10.3847/1538-4357/abc9b5
  * Li et al. (2023) Li, Y., Wang, C., Qu, M., et al. 2023, StarGLM, https://github.com/Yu-Yang-Li/StarGLM
  * Liang et al. (2023) Liang, H., Shi, J., Ma, Y., Xu, R., & Li, J. 2023, Icarus, 401, 115605, doi: 10.1016/j.icarus.2023.115605
  * Lin & Papaloizou (1986) Lin, D. N. C., & Papaloizou, J. 1986, ApJ, 309, 846, doi: 10.1086/164653
  * Lin et al. (2019) Lin, J., Yan, Z., Han, Z., & Yu, W. 2019, ApJ, 870, 126, doi: 10.3847/1538-4357/aaf39b
  * Lin et al. (2022) Lin, J., Wang, X., Mo, J., et al. 2022, MNRAS, 509, 2362, doi: 10.1093/mnras/stab2812
  * Lin et al. (2023a) Lin, J., Wu, C., Wang, X., et al. 2023a, Nature Astronomy, 7, 223, doi: 10.1038/s41550-022-01783-z
  * Lin et al. (2023b) Lin, J., Wang, X., Mo, J., et al. 2023b, MNRAS, 523, 2172, doi: 10.1093/mnras/stad994
  * Lin et al. (2024) Lin, J., Wu, C., Xiong, H., et al. 2024, Nature Astronomy, doi: 10.1038/s41550-023-02188-2
  * Lin et al. (2021) Lin, Y.-C., Matsumoto, Y., & Gu, P.-G. 2021, ApJ, 907, 81, doi: 10.3847/1538-4357/abd0f3
  * Lithwick et al. (2012) Lithwick, Y., Xie, J., & Wu, Y. 2012, ApJ, 761, 122, doi: 10.1088/0004-637X/761/2/122
  * Liu et al. (2022) Liu, B., Johansen, A., Lambrechts, M., Bizzarro, M., & Haugbølle, T. 2022, Science Advances, 8, eabm3045, doi: 10.1126/sciadv.abm3045
  * Lovis & Fischer (2010) Lovis, C., & Fischer, D. 2010, in Exoplanets, ed. S. Seager, 27–53
  * LSST Science Collaboration et al. (2017) LSST Science Collaboration, Marshall, P., Anguita, T., et al. 2017, arXiv e-prints, arXiv:1708.04058, doi: 10.48550/arXiv.1708.04058
  * Luo et al. (2016) Luo, J., Chen, L.-S., Duan, H.-Z., et al. 2016, Classical and Quantum Gravity, 33, 035010, doi: 10.1088/0264-9381/33/3/035010
  * Luu (1993) Luu, J. X. 1993, PASP, 105, 946, doi: 10.1086/133260
  * Lyu & Yang (2023) Lyu, X., & Yang, M. 2023, ApJ, 943, L7, doi: 10.3847/2041-8213/acb056
  * Madau & Rees (2001) Madau, P., & Rees, M. J. 2001, ApJ, 551, L27, doi: 10.1086/319848
  * Madhusudhan (2019) Madhusudhan, N. 2019, ARA&A, 57, 617, doi: 10.1146/annurev-astro-081817-051846
  * Madhusudhan et al. (2023) Madhusudhan, N., Sarkar, S., Constantinou, S., et al. 2023, ApJ, 956, L13, doi: 10.3847/2041-8213/acf577
  * Maeder (2009) Maeder, A. 2009, Physics, Formation and Evolution of Rotating Stars, doi: 10.1007/978-3-540-76949-1
  * Mamajek (2017) Mamajek, E. 2017, Research Notes of the American Astronomical Society, 1, 21, doi: 10.3847/2515-5172/aa9bdc
  * Marty (2012) Marty, B. 2012, Earth and Planetary Science Letters, 313, 56, doi: 10.1016/j.epsl.2011.10.040
  * Marzari et al. (2003) Marzari, F., Tricarico, P., & Scholl, H. 2003, Icarus, 162, 453, doi: 10.1016/S0019-1035(03)00026-5
  * Masci et al. (2018) Masci, F. J., Laher, R. R., Rusholme, B., et al. 2018, Publications of the Astronomical Society of the Pacific, 131, 018003, doi: 10.1088/1538-3873/aae8ac
  * Matsumura et al. (2017) Matsumura, S., Brasser, R., & Ida, S. 2017, A&A, 607, A67, doi: 10.1051/0004-6361/201731155
  * Mayor & Queloz (1995) Mayor, M., & Queloz, D. 1995, Nature, 378, 355, doi: 10.1038/378355a0
  * Mayor et al. (2011) Mayor, M., Marmier, M., Lovis, C., et al. 2011, arXiv e-prints, arXiv:1109.2497.  https://arxiv.org/abs/1109.2497
  * Mazeh et al. (2016) Mazeh, T., Holczer, T., & Faigler, S. 2016, A&A, 589, A75, doi: 10.1051/0004-6361/201528065
  * McNally et al. (2019) McNally, C. P., Nelson, R. P., Paardekooper, S.-J., & Benítez-Llambay, P. 2019, MNRAS, 484, 728, doi: 10.1093/mnras/stz023
  * McQuillan et al. (2014) McQuillan, A., Mazeh, T., & Aigrain, S. 2014, The Astrophysical Journal Supplement Series, 211, 24, doi: 10.1088/0067-0049/211/2/24
  * McWhirter & Lam (2022) McWhirter, P. R., & Lam, M. C. 2022, MNRAS, 511, 4971, doi: 10.1093/mnras/stac291
  * Metzger et al. (2018) Metzger, B. D., Beniamini, P., & Giannios, D. 2018, ApJ, 857, 95
  * Metzger et al. (2008) Metzger, B. D., Piro, A. L., & Quataert, E. 2008, MNRAS, 390, 781
  * Metzger et al. (2010) Metzger, B. D., Martínez-Pinedo, G., Darbha, S., et al. 2010, MNRAS, 406, 2650
  * Micheli et al. (2018) Micheli, M., Farnocchia, D., Meech, K. J., et al. 2018, Nature, 559, 223, doi: 10.1038/s41586-018-0254-4
  * Miller & Hamilton (2002) Miller, M. C., & Hamilton, D. P. 2002, MNRAS, 330, 232, doi: 10.1046/j.1365-8711.2002.05112.x
  * Montet et al. (2014) Montet, B. T., Crepp, J. R., Johnson, J. A., Howard, A. W., & Marcy, G. W. 2014, ApJ, 781, 28, doi: 10.1088/0004-637X/781/1/28
  * Morgan et al. (2022) Morgan, J. V., Bralower, T. J., Brugger, J., & Wünnemann, K. 2022, Nature Reviews Earth and Environment, 3, 338, doi: 10.1038/s43017-022-00283-y
  * Moriya et al. (2023) Moriya, T. J., Mazzali, P. A., Ashall, C., & Pian, E. 2023, MNRAS, 522, 6035, doi: 10.1093/mnras/stad1386
  * Morton (2012) Morton, T. D. 2012, ApJ, 761, 6, doi: 10.1088/0004-637X/761/1/6
  * Mosby et al. (2020) Mosby, G., Rauscher, B. J., Bennett, C., et al. 2020, Journal of Astronomical Telescopes, Instruments, and Systems, 6, 046001, doi: 10.1117/1.JATIS.6.4.046001
  * Mulders et al. (2015) Mulders, G. D., Ciesla, F. J., Min, M., & Pascucci, I. 2015, ApJ, 807, 9, doi: 10.1088/0004-637X/807/1/9
  * Mumma & Charnley (2011) Mumma, M. J., & Charnley, S. B. 2011, ARA&A, 49, 471, doi: 10.1146/annurev-astro-081309-130811
  * Mustill & Wyatt (2011) Mustill, A. J., & Wyatt, M. C. 2011, MNRAS, 413, 554, doi: 10.1111/j.1365-2966.2011.18201.x
  * Nagasawa et al. (2000) Nagasawa, M., Tanaka, H., & Ida, S. 2000, AJ, 119, 1480, doi: 10.1086/301246
  * Nelemans et al. (2001) Nelemans, G., Portegies Zwart, S. F., Verbunt, F., & Yungelson, L. R. 2001, A&A, 368, 939, doi: 10.1051/0004-6361:20010049
  * Nesvorný et al. (2002) Nesvorný, D., Ferraz-Mello, S., Holman, M., & Morbidelli, A. 2002, in Asteroids III, 379–394
  * Newton et al. (2018) Newton, E. R., Mondrik, N., Irwin, J., Winters, J. G., & Charbonneau, D. 2018, The Astronomical Journal, 156, 217, doi: 10.3847/1538-3881/aad73b
  * Nielsen et al. (2019) Nielsen, E. L., De Rosa, R. J., Macintosh, B., et al. 2019, AJ, 158, 13, doi: 10.3847/1538-3881/ab16e9
  * O’Brien et al. (2014) O’Brien, D. P., Walsh, K. J., Morbidelli, A., Raymond, S. N., & Mandell, A. M. 2014, Icarus, 239, 74, doi: 10.1016/j.icarus.2014.05.009
  * Ogihara et al. (2023) Ogihara, M., Genda, H., & Sekine, Y. 2023, PSJ
  * Ogihara & Kobayashi (2013) Ogihara, M., & Kobayashi, H. 2013, ApJ, 775, 34, doi: 10.1088/0004-637X/775/1/34
  * Ogihara et al. (2018) Ogihara, M., Kokubo, E., Suzuki, T. K., & Morbidelli, A. 2018, A&A, 615, A63, doi: 10.1051/0004-6361/201832720
  * Ogihara et al. (2015) Ogihara, M., Morbidelli, A., & Guillot, T. 2015, A&A, 584, L1, doi: 10.1051/0004-6361/201527117
  * Oró (1961) Oró, J. 1961, Nature, 190, 389, doi: 10.1038/190389a0
  * Ou et al. (2019) Ou, J.-W., Yang, M., Liu, H.-G., Liang, E.-S., & Zhou, J.-L. 2019, MNRAS, 487, 2455, doi: 10.1093/mnras/stz1475
  * Owen & Wu (2013) Owen, J. E., & Wu, Y. 2013, ApJ, 775, 105, doi: 10.1088/0004-637X/775/2/105
  * Owen & Wu (2017) —. 2017, ApJ, 847, 29, doi: 10.3847/1538-4357/aa890a
  * Paardekooper (2014) Paardekooper, S. J. 2014, MNRAS, 444, 2031, doi: 10.1093/mnras/stu1542
  * Paardekooper et al. (2011) Paardekooper, S. J., Baruteau, C., & Kley, W. 2011, MNRAS, 410, 293, doi: 10.1111/j.1365-2966.2010.17442.x
  * Palle et al. (2023) Palle, E., Biazzo, K., Bolmont, E., et al. 2023, arXiv e-prints, arXiv:2311.17075, doi: 10.48550/arXiv.2311.17075
  * Pastorello & Fraser (2019) Pastorello, A., & Fraser, M. 2019, Nature Astronomy, 3, 676, doi: 10.1038/s41550-019-0809-9
  * Pastorello et al. (2004) Pastorello, A., Zampieri, L., Turatto, M., et al. 2004, MNRAS, 347, 74, doi: 10.1111/j.1365-2966.2004.07173.x
  * Pastorello et al. (2019) Pastorello, A., Mason, E., Taubenberger, S., et al. 2019, A&A, 630, A75, doi: 10.1051/0004-6361/201935999
  * Patra et al. (2020) Patra, K. C., Winn, J. N., Holman, M. J., et al. 2020, The Astronomical Journal, 159, 150, doi: 10.3847/1538-3881/ab7374
  * Piani et al. (2020) Piani, L., Marrocchi, Y., Rigaudier, T., et al. 2020, Science, 369, 1110, doi: 10.1126/science.aba1948
  * Pietrukowicz et al. (2017) Pietrukowicz, P., Dziembowski, W. A., Latour, M., et al. 2017, Nature Astronomy, 1, 0166, doi: 10.1038/s41550-017-0166
  * Pinamonti et al. (2022) Pinamonti, M., Sozzetti, A., Maldonado, J., et al. 2022, A&A, 664, A65, doi: 10.1051/0004-6361/202142828
  * Poleski et al. (2021) Poleski, R., Skowron, J., Mróz, P., et al. 2021, AcA, 71, 1, doi: 10.32023/0001-5237/71.1.1
  * Pollack et al. (1996) Pollack, J. B., Hubickyj, O., Bodenheimer, P., et al. 1996, Icarus, 124, 62, doi: 10.1006/icar.1996.0190
  * Portegies Zwart et al. (2018) Portegies Zwart, S., Torres, S., Pelupessy, I., Bédorf, J., & Cai, M. X. 2018, MNRAS, 479, L17, doi: 10.1093/mnrasl/sly088
  * Portegies Zwart & McMillan (2002) Portegies Zwart, S. F., & McMillan, S. L. W. 2002, ApJ, 576, 899, doi: 10.1086/341798
  * Pravec et al. (2002) Pravec, P., Harris, A. W., & Michalowski, T. 2002, in Asteroids III, 113–122
  * Pravec et al. (2006) Pravec, P., Scheirich, P., Kušnirák, P., et al. 2006, Icarus, 181, 63, doi: 10.1016/j.icarus.2005.10.014
  * Pravec et al. (2012) Pravec, P., Scheirich, P., Vokrouhlický, D., et al. 2012, Icarus, 218, 125, doi: 10.1016/j.icarus.2011.11.026
  * Price et al. (2021) Price, E. M., Cleeves, L. I., Bodewits, D., & Öberg, K. I. 2021, ApJ, 913, 9, doi: 10.3847/1538-4357/abf041
  * Ragazzoni et al. (2016) Ragazzoni, R., Magrin, D., Rauer, H., et al. 2016, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 9904, Space Telescopes and Instrumentation 2016: Optical, Infrared, and Millimeter Wave, ed. H. A. MacEwen, G. G. Fazio, M. Lystrup, N. Batalha, N. Siegler, & E. C. Tong, 990428, doi: 10.1117/12.2236094
  * Rao, Suvrat et al. (2021) Rao, Suvrat, Pezzotti, Camilla, Meynet, Georges, et al. 2021, A&A, 651, A50, doi: 10.1051/0004-6361/202039965
  * Rauer et al. (2014) Rauer, H., Catala, C., Aerts, C., et al. 2014, Experimental Astronomy, 38, 249, doi: 10.1007/s10686-014-9383-4
  * Raymond & Izidoro (2017a) Raymond, S. N., & Izidoro, A. 2017a, Icarus, 297, 134, doi: 10.1016/j.icarus.2017.06.030
  * Raymond & Izidoro (2017b) —. 2017b, Icarus, 297, 134, doi: 10.1016/j.icarus.2017.06.030
  * Refsdal (1964) Refsdal, S. 1964, MNRAS, 128, 295, doi: 10.1093/mnras/128.4.295
  * Rest et al. (2018) Rest, A., Garnavich, P. M., Khatami, D., et al. 2018, Nature Astronomy, 2, 307, doi: 10.1038/s41550-018-0423-2
  * Rhodes et al. (2023) Rhodes, L., Bright, J. S., Fender, R., et al. 2023, MNRAS, 521, 389, doi: 10.1093/mnras/stad344
  * Ricker et al. (2014) Ricker, G. R., Winn, J. N., Vanderspek, R., et al. 2014, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 9143, Space Telescopes and Instrumentation 2014: Optical, Infrared, and Millimeter Wave, ed. J. Oschmann, Jacobus M., M. Clampin, G. G. Fazio, & H. A. MacEwen, 914320, doi: 10.1117/12.2063489
  * Rigby et al. (2023) Rigby, J., Perrin, M., McElwain, M., et al. 2023, PASP, 135, 048001, doi: 10.1088/1538-3873/acb293
  * Roberts et al. (2011) Roberts, L. F., Kasen, D., Lee, W. H., & Ramirez-Ruiz, E. 2011, ApJ, 736, L21
  * Rosswog (2005) Rosswog, S. 2005, ApJ, 634, 1202
  * Rowan et al. (2016) Rowan, D., Meschiari, S., Laughlin, G., et al. 2016, ApJ, 817, 104, doi: 10.3847/0004-637X/817/2/104
  * Rowan et al. (2023) Rowan, D. M., Jayasinghe, T., Stanek, K. Z., et al. 2023, MNRAS, 523, 2641, doi: 10.1093/mnras/stad1560
  * Rowan et al. (2022) Rowan, D. M., Jayasinghe, T., Stanek, K. Z., et al. 2022, Monthly Notices of the Royal Astronomical Society, 517, 2190, doi: 10.1093/mnras/stac2520
  * Sabotta et al. (2021) Sabotta, S., Schlecker, M., Chaturvedi, P., et al. 2021, A&A, 653, A114, doi: 10.1051/0004-6361/202140968
  * Sadowski et al. (2016) Sadowski, A., Tejeda, E., Gafton, E., Rosswog, S., & Abarca, D. 2016, Monthly Notices of the Royal Astronomical Society, 458, 4250, doi: 10.1093/mnras/stw589
  * Safronov (1969) Safronov, V. 1969, NASA TTF-677 (1972)(Nauka, Moscow)(Russian)
  * Sako et al. (2018) Sako, S., Ohsawa, R., Takahashi, H., et al. 2018, 18, doi: 10.1117/12.2310049
  * Schleicher & Farnham (2004) Schleicher, D. G., & Farnham, T. L. 2004, in Comets II, ed. M. C. Festou, H. U. Keller, & H. A. Weaver, 449
  * Schwab et al. (2016) Schwab, C., Rakich, A., Gong, Q., et al. 2016, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 9908, Ground-based and Airborne Instrumentation for Astronomy VI, ed. C. J. Evans, L. Simard, & H. Takami, 99087H, doi: 10.1117/12.2234411
  * Shi et al. (2019) Shi, J., Ma, Y., Liang, H., & Xu, R. 2019, Scientific Reports, 9, 5492, doi: 10.1038/s41598-019-41880-0
  * Showman et al. (2020) Showman, A. P., Tan, X., & Parmentier, V. 2020, SSRv, 216, 139, doi: 10.1007/s11214-020-00758-8
  * Shporer et al. (2010) Shporer, A., Brown, T., Lister, T., et al. 2010, Proceedings of the International Astronomical Union, 6, 553–555, doi: 10.1017/s1743921311021193
  * Smith & WASP Consortium (2014) Smith, A. M. S., & WASP Consortium. 2014, Contributions of the Astronomical Observatory Skalnate Pleso, 43, 500
  * Smith et al. (2011) Smith, N., Li, W., Silverman, J. M., Ganeshalingam, M., & Filippenko, A. V. 2011, MNRAS, 415, 773, doi: 10.1111/j.1365-2966.2011.18763.x
  * Solheim (2010) Solheim, J. E. 2010, PASP, 122, 1133, doi: 10.1086/656680
  * Sozzetti & de Bruijne (2018) Sozzetti, A., & de Bruijne, J. 2018, Space Astrometry Missions for Exoplanet Science: Gaia and the Legacy of Hipparcos, ed. H. J. Deeg & J. A. Belmonte (Cham: Springer International Publishing), 1205–1228, doi: 10.1007/978-3-319-55333-7_81
  * Spiro et al. (2014) Spiro, S., Pastorello, A., Pumo, M. L., et al. 2014, MNRAS, 439, 2873, doi: 10.1093/mnras/stu156
  * Stevenson (1987) Stevenson, D. J. 1987, Annual Review of Earth and Planetary Sciences, 15, 271, doi: 10.1146/annurev.ea.15.050187.001415
  * Sun et al. (2023) Sun, X.-Y., Zuo, Z.-Y., Yang, T.-Z., & García Hernández, A. 2023, ApJ, 955, 80, doi: 10.3847/1538-4357/ace905
  * Swift et al. (2015) Swift, J. J., Bottom, M., Johnson, J. A., et al. 2015, Journal of Astronomical Telescopes, Instruments, and Systems, 1, 027002, doi: 10.1117/1.JATIS.1.2.027002
  * Tanaka & Hotokezaka (2013) Tanaka, M., & Hotokezaka, K. 2013, ApJ, 775, 113
  * Team et al. (2024) Team, J., Liu, C., Zu, Y., et al. 2024, Astronomical Techniques and Instrument, 1, 1, doi: 10.61977/ati2024008
  * Tsiganis et al. (2005) Tsiganis, K., Gomes, R., Morbidelli, A., & Levison, H. F. 2005, Nature, 435, 459, doi: 10.1038/nature03539
  * Tu et al. (2021) Tu, Z.-L., Yang, M., Wang, H. F., & Wang, F. Y. 2021, ApJS, 253, 35, doi: 10.3847/1538-4365/abda3c
  * Tu et al. (2020) Tu, Z.-L., Yang, M., Zhang, Z. J., & Wang, F. Y. 2020, ApJ, 890, 46, doi: 10.3847/1538-4357/ab6606
  * Turner et al. (2021) Turner, J. D., Ridden-Harper, A., & Jayawardhana, R. 2021, The Astronomical Journal, 161, 72, doi: 10.3847/1538-3881/abd178
  * Ulrich et al. (1997) Ulrich, M.-H., Maraschi, L., & Urry, C. M. 1997, ARA&A, 35, 445, doi: 10.1146/annurev.astro.35.1.445
  * Valenti et al. (2009) Valenti, S., Pastorello, A., Cappellaro, E., et al. 2009, Nature, 459, 674, doi: 10.1038/nature08023
  * Valiante et al. (2018) Valiante, R., Schneider, R., Graziani, L., & Zappacosta, L. 2018, MNRAS, 474, 3825, doi: 10.1093/mnras/stx3028
  * Valsecchi et al. (2015) Valsecchi, F., Rappaport, S., Rasio, F. A., Marchant, P., & Rogers, L. A. 2015, ApJ, 813, 101, doi: 10.1088/0004-637X/813/2/101
  * Vick et al. (2019) Vick, M., Lai, D., & Anderson, K. R. 2019, MNRAS, 484, 5645, doi: 10.1093/mnras/stz354
  * Vigan et al. (2021) Vigan, A., Fontanive, C., Meyer, M., et al. 2021, A&A, 651, A72, doi: 10.1051/0004-6361/202038107
  * Vissapragada et al. (2021) Vissapragada, S., Stefánsson, G., Greklek-McKeon, M., et al. 2021, AJ, 162, 222, doi: 10.3847/1538-3881/ac1bb0
  * Vogt et al. (2014) Vogt, S. S., Radovan, M., Kibrick, R., et al. 2014, PASP, 126, 359, doi: 10.1086/676120
  * Volonteri et al. (2008) Volonteri, M., Lodato, G., & Natarajan, P. 2008, MNRAS, 383, 1079, doi: 10.1111/j.1365-2966.2007.12589.x
  * Walsh et al. (2011) Walsh, K. J., Morbidelli, A., Raymond, S. N., O’Brien, D. P., & Mandell, A. M. 2011, Nature, 475, 206, doi: 10.1038/nature10201
  * Wang et al. (2021) Wang, B., Chen, W.-C., Liu, D.-D., et al. 2021, MNRAS, 506, 4654, doi: 10.1093/mnras/stab2032
  * Wang et al. (2015) Wang, J., Fischer, D. A., Horch, E. P., & Huang, X. 2015, ApJ, 799, 229, doi: 10.1088/0004-637X/799/2/229
  * Ward et al. (1976) Ward, W. R., Colombo, G., & Franklin, F. A. 1976, Icarus, 28, 441, doi: 10.1016/0019-1035(76)90117-2
  * Watson et al. (2006) Watson, C. L., Henden, A. A., & Price, A. 2006, Society for Astronomical Sciences Annual Symposium, 25, 47
  * Weiss et al. (2018) Weiss, L. M., Marcy, G. W., Petigura, E. A., et al. 2018, AJ, 155, 48, doi: 10.3847/1538-3881/aa9ff6
  * Wheatley et al. (2017) Wheatley, P. J., West, R. G., Goad, M. R., et al. 2017, Monthly Notices of the Royal Astronomical Society, 475, 4476, doi: 10.1093/mnras/stx2836
  * Whipple (1950) Whipple, F. L. 1950, ApJ, 111, 375, doi: 10.1086/145272
  * Wimarsson et al. (2020) Wimarsson, J., Liu, B., & Ogihara, M. 2020, MNRAS, 496, 3314, doi: 10.1093/mnras/staa1708
  * Wittenmyer et al. (2020) Wittenmyer, R. A., Wang, S., Horner, J., et al. 2020, MNRAS, 492, 377, doi: 10.1093/mnras/stz3436
  * Wright et al. (2010) Wright, E. L., Eisenhardt, P. R. M., Mainzer, A. K., et al. 2010, AJ, 140, 1868, doi: 10.1088/0004-6256/140/6/1868
  * Wright et al. (2012) Wright, J. T., Marcy, G. W., Howard, A. W., et al. 2012, ApJ, 753, 160, doi: 10.1088/0004-637X/753/2/160
  * Wu & Li (2018) Wu, T., & Li, Y. 2018, MNRAS, 478, 3871, doi: 10.1093/mnras/sty1347
  * Xiao et al. (2023) Xiao, G.-Y., Liu, Y.-J., Teng, H.-Y., et al. 2023, Research in Astronomy and Astrophysics, 23, 055022, doi: 10.1088/1674-4527/accb7e
  * Xie (2014) Xie, J.-W. 2014, ApJS, 210, 25, doi: 10.1088/0067-0049/210/2/25
  * Xin et al. (2024) Xin, Y., Shi, J., & Ma, Y. 2024, MNRAS, 527, 10309, doi: 10.1093/mnras/stad3883
  * Xiong et al. (2022) Xiong, H., Casagrande, L., Chen, X., et al. 2022, A&A, 668, A112, doi: 10.1051/0004-6361/202244571
  * Yahalomi et al. (2023) Yahalomi, D. A., Angus, R., Spergel, D. N., & Foreman-Mackey, D. 2023, AJ, 166, 258, doi: 10.3847/1538-3881/ad05cc
  * Yang (2022) Yang, M. 2022, Universe, 8, 614, doi: 10.3390/universe8120614
  * Yang et al. (2013) Yang, M., Liu, H.-G., Zhang, H., Yang, J.-Y., & Zhou, J.-L. 2013, ApJ, 778, 110, doi: 10.1088/0004-637X/778/2/110
  * Yang et al. (2015) Yang, M., Zhang, H., Wang, S., et al. 2015, ApJS, 217, 28, doi: 10.1088/0067-0049/217/2/28
  * Yang et al. (2018) Yang, T., Esamdin, A., Song, F., et al. 2018, ApJ, 863, 195, doi: 10.3847/1538-4357/aad241
  * Yang & Esamdin (2019) Yang, T.-Z., & Esamdin, A. 2019, ApJ, 879, 59, doi: 10.3847/1538-4357/ab23f3
  * Yang et al. (2021a) Yang, T.-Z., Sun, X.-Y., Zuo, Z.-Y., & Liu, H.-W. 2021a, AJ, 161, 27, doi: 10.3847/1538-3881/abcb8b
  * Yang et al. (2021b) Yang, T.-Z., Zuo, Z.-Y., Li, G., et al. 2021b, A&A, 655, A63, doi: 10.1051/0004-6361/202142198
  * Yang et al. (2022) Yang, T.-Z., Zuo, Z.-Y., Sun, X.-Y., Tang, R.-X., & Esamdin, A. 2022, ApJ, 936, 48, doi: 10.3847/1538-4357/ac86c9
  * Yee et al. (2019) Yee, S. W., Winn, J. N., Knutson, H. A., et al. 2019, The Astrophysical Journal Letters, 888, L5, doi: 10.3847/2041-8213/ab5c16
  * Yee et al. (2022) Yee, S. W., Winn, J. N., Hartman, J. D., et al. 2022, AJ, 164, 70, doi: 10.3847/1538-3881/ac73ff
  * Young (1967) Young, A. T. 1967, AJ, 72, 747, doi: 10.1086/110303
  * Yuan et al. (2020) Yuan, X., Li, Z., Liu, X., et al. 2020, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 11445, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, 114457M, doi: 10.1117/12.2562334
  * Zhang et al. (2019) Zhang, H., Yu, Z., Liang, E., et al. 2019, ApJS, 240, 16, doi: 10.3847/1538-4365/aaec0c
  * Zhang et al. (2020) Zhang, J.-C., Wang, X.-F., Mo, J., et al. 2020, Publications of the Astronomical Society of the Pacific, 132, 125001, doi: 10.1088/1538-3873/abbea2
  * Zhu et al. (2018) Zhu, W., Petrovich, C., Wu, Y., Dong, S., & Xie, J. 2018, ApJ, 860, 101, doi: 10.3847/1538-4357/aac6d5


# A Service for Supporting Digital and Immersive Cultural Experiences

Karthik Vaidhyanathan  University of L’Aquila
<EMAIL_ADDRESS>Antonio Bruno  University of L’Aquila
<EMAIL_ADDRESS>Eleonora Mendola  University of L’Aquila
<EMAIL_ADDRESS>Filippo Mignosi
University of L’Aquila
<EMAIL_ADDRESS>Mahyar T. Moghaddam  MMMI Institute - University of
Southern Denmark
<EMAIL_ADDRESS>Henry Muccini  University of L’Aquila
<EMAIL_ADDRESS>Monica Nesi University of L’Aquila
<EMAIL_ADDRESS>
###### Abstract

Cultural heritage sites in Italy typically attract a large number of tourists
every year. However, the lack of support for i) locating contents of interest;
ii) discovering information on specific contents; and iii) ease of navigation
within the heritage site; hinders the overall experience of the visitor. To
this end, in this work, we present a Digital Object Space Management service
developed as a part of the VASARI project. The service generates a digital
twin (with 3D visualization) of a given cultural heritage site and further
provides support for navigation and localization, thereby providing an
immersive cultural experience to the visitor.

###### Index Terms:

Indoor Navigation, Digital Twin, Indoor Localization, Space Management, 3D
Visualization

##  I Introduction

Italy is known for the presence of rich cultural heritage sites, attracting
millions of visitors every year. As per the latest data from Statista, the
cultural heritage sites in Italy have attracted around 67 million visitors in
the last two years [1]. Although this is the case, the cultural tourism market
is evolving towards a dimension of complete satisfaction of the needs of the
tourist, enhancing, on the one hand, the centrality of the cultural aspect
using 360° experiences and on the other hand by creating customized visit
routes. The visitors are also showing a growing interest to play an active and
participatory role in the tourism experience, integrating the cultural content
of the visit with self-generated personal content and sharing them with the
community. However, cultural heritage in Italy, especially museums, is often
under-exploited and does not provide adequate supports for visitors in i)
locating contents of interest; ii) discovering information on specific
contents; iii) navigating within the heritage sites and iv) creating
customized visit routes based on interests. Thereby limiting the affecting the
overall experience of the visitor. To meet these needs, the VASARI
project111VASARI ARS01_00456 is co-funded by MIUR, with the support of EU
proposes a novel paradigm for sustaining on-site, immersive, inclusive, and
contextualized user experiences by exploiting several recent technologies,
such as IoT and mobile computing, semantics, big data processing, virtual and
augmented reality within an innovative infrastructure based on microservices
deployed in edge, fog and cloud nodes. It follows a User-Centered Paradigm
that aims to create an integrated virtual-physical space where sites, cultural
assets, and users coexist in the two spaces simultaneously.

In this work, we present the Digital Object Space Management Service (DOSM)
developed as a part of the VASARI project. It provides support for the
generation of a digital twin [2] that captures the physical space and the
cultural assets. Further, it leverages IoT devices to enable navigation and
localization support for visitors, thereby providing them with an immersive
visiting experience. In particular, the service caters to two main
stakeholders: i) The heritage site administrators/staff who can
add/modify/remove a digital representation of a given physical space,
add/modify or remove: the POI’s, cultural assets, and the position of objects,
etc. ii) visitors who can make use of this service on their mobile apps to get
real-time 3D visualization of the physical space, track their real-time
locations, locate cultural assets/POI’s, fetch detailed information of a
cultural asset, navigate to cultural assets/POI’s, generate customized
navigations routes based on interests, etc.

##  II Scenarios and Models

We envision several engaging scenarios where the VASARI DOSM service could be
used to provide an enhanced and immersive visiting experience. We describe
here three key scenarios. The first two scenarios concern the visitor before
the visit and during the visit, while the third concerns the
administrator/staff of the cultural heritage site: i) A prospective visitor
intends to visit a cultural heritage site, and before the visit, she may want
to use a mobile/web app that provides the 3D map of the heritage site, to go
through the list of assets (exhibits), read about them and mark her preferred
assets; ii) The visitor arriving at the museum can make use of the app on her
mobile/tablet to get a 3D immersive view of the heritage site, locate her
real-time position in the heritage site, generate a navigation path that
connects her preferred assets that she had marked provided prior to the visit,
get notification whenever she reaches near any asset, clicking on which gets
detailed information on the asset.

To support the above scenarios, the VASARI DOSM service provides mechanisms
that allow physical space to coexist with digital space through the definition
of views (realized at different levels of abstraction). These views provide a
mapping between the physical and digital space. The entities of the physical
space are the environments in the heritage site where the works are placed
(e.g., museum rooms associated with floors of buildings, areas in open spaces,
etc.). In effect, the service supports the generation of a digital twin of the
physical space, where the physical space corresponds to the digital
representation with a one-to-one relationship. In particular, the physical
space of interest is represented through 3D models, and the same types of
modeling are used for representing the works (cultural assets, artworks,
etc.). The result will be a cyber-physical space in which the physical space
is represented, enriched, and complemented by digital components. Further, the
use of sensor devices (BLE beacons, RFID readers, mobile devices of the
visitors, etc.) is leveraged for enabling support for navigation and
localization services for visitors to provide an immersive visiting
experience.

##  III Digital Object Space Management Service

The VASARI DOSM service provides two key functionalities i) Digital Twin
Generation ii) Navigation and Localization. In this section, we provide high-
level details on how these functionalities are accomplished by the DOSM
service.

###  III-A Digital Twin Generation

Generation of digital twin comprises of three processes, namely: i) Panoramic
Scanning, ii) 2D to 3D Conversion, and iii) POI Tagging. Panoramic scanning is
performed with the help of a camera by choosing a starting point in the
physical space. Following this, the camera is rotated to perform a 360 scan of
all the observable points with respect to the starting point. The choice of
the observable points needs to be done in such a manner that the time required
to scan the space is optimal such that no points are left uncovered. This can
be done with different types of devices such as high-resolution mobile
cameras, standard digital cameras, etc. This process results in a panoramic 2D
image composed of a set of 2D images that capture the 360 views of a given
physical space. The 2D panoramic image generated is then converted to a 3D
representation with the help of a 2D to 3D Conversion process. The process
achieves this by making use of Matterport technology222https://matterport.com/
along with an API layer provided by e-Building333https://www.e-building.it/.
The process converts the $x,y$ coordinates of the captured images into $x,y,z$
coordinates based on the panoramic scans performed. The starting point of the
panoramic scan is considered as origin $(0,0,0)$ and every scan made to left
or right is considered as the corresponding increase/decrease in $x,y$
respectively and the movement made towards or away from the physical space
during the scan becomes the $z$. This process generates a 3D digital map of
the physical space. Following this, the POI Tagging process allows heritage
administrators/staff to mark the POIs or cultural assets on the generated map.
This is performed using the concept of mattertags provided by Matterport. It
allows the assignment of dedicated tags with unique ID along with a
description for each of the cultural assets/POIs. Further, each such tag has
an associated position (x,y,z) in the 3D map of Matterport. This information
is further stored in a database. The above three processes generate a complete
digital representation of a physical space resulting in a digital twin.

###  III-B Navigation and Localization

The DOSM service achieves this with the help of three main processes, namely,
i) POI Device Mapping, ii) Visitor Tracking and iii) Path Generation. The POI
Device mapping involves mapping each of the cultural assets to an IoT device (
BLE Beacon in this work). The ID of the cultural asset, along with that of the
beacon, is stored in a database. This information is used by the Visitor
Tracking process. Whenever a visitor is in the vicinity of a particular
cultural asset, the service running on the visitor’s device receives the
signals from all the beacons. These signals are used in calculating the
distance between the visitor’s device and different beacons. Once these
distances have been obtained, the service uses a triangulation technique to
obtain the visitor’s position (relative to a cultural asset). The position
information is then appended on the Matterport 3D map to denote the visitor
location. Further, based on this position, the cultural asset closer to the
visitor is estimated, and this information is used by the service to display a
detailed description of the cultural asset. The Path Generation process
involves generating the navigation path for the visitor based on her
preferences by also considering her current location. This is performed by
generating a navigation graph that considers the different rooms, walls,
cultural assets, and other POI’s. Such information can be obtained by
associating a mattertag to each wall, room, etc. Further, the graph also
considers the visitor’s preferred cultural assets. Based on this, the process
uses a 2D Dijkstra algorithm to compute the shortest path that includes the
visitor’s preferred assets.

##  IV Conclusions

In this work, we presented the digital object space management service
developed as a part of the VASARI project. The service provides support for
generating a digital twin of a given cultural heritage site and further
leverages IoT devices to provide navigation and localization support for
visitors, thereby providing an immersive cultural experience.

## References

  * [1] Statista. 2021. Number of museum visitors Italy 2020 — Statista. [online] Available at: https://tinyurl.com/y468kp8x [Accessed 10 July 2021].
  * [2] Boschert, Stefan, and Roland Rosen. ”Digital twin—the simulation aspect.” In Mechatronic futures, pp. 59-74. Springer, Cham, 2016.


# LAGA: Layered 3D Avatar Generation and Customization via Gaussian Splatting

Jia Gong1,2† Shengyu Ji2† Lin Geng Foo1 Kang Chen2 Hossein Rahmani3 Jun Liu1‡
1Singapore University of Technology and Design 2Netease 3Lancaster University
<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>
<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

Creating and customizing a 3D clothed avatar from textual descriptions is a
critical and challenging task. Traditional methods often treat the human body
and clothing as inseparable, limiting users’ ability to freely mix and match
garments. In response to this limitation, we present LAyered Gaussian Avatar
(LAGA), a carefully designed framework enabling the creation of high-fidelity
decomposable avatars with diverse garments. By decoupling garments from
avatar, our framework empowers users to conviniently edit avatars at the
garment level. Our approach begins by modeling the avatar using a set of
Gaussian points organized in a layered structure, where each layer corresponds
to a specific garment or the human body itself. To generate high-quality
garments for each layer, we introduce a coarse-to-fine strategy for diverse
garment generation and a novel dual-SDS loss function to maintain coherence
between the generated garments and avatar components, including the human body
and other garments. Moreover, we introduce three regularization losses to
guide the movement of Gaussians for garment transfer, allowing garments to be
freely transferred to various avatars. Extensive experimentation demonstrates
that our approach surpasses existing methods in the generation of 3D clothed
humans. Project page: https://gongjia0208.github.io/LAGA/

Figure 1:  We present LAGA, a novel layered avatar generation framework based
on Gaussian Splatting (GS). With the layered structure, our generated clothed
avatar can be decomposed to a human body with multiple individual garments,
allowing users to assemble and edit specific garments to create new
variations.

††† Equal contribution; ‡ Corresponding author

##  1 Introduction

The generation of 3D avatars is an important task that holds immense
significance across various industries, including film, gaming, and fashion.
However, traditional methods for 3D avatar generation often rely on skilled
engineers employing specialized software tools [3] or require the usage of
scanners to scan specific actors [4], demanding considerable human effort and
resources. Benefited by the developments in generative models [6], several
research works have attempted to simplify the 3D avatar generation process
through large-scale 3D generative models [12, 39] or leveraging robust 2D
text-to-image priors to generate 3D humans from text prompts [31, 1, 15].
However, despite the significant progress, most works still treat the avatar
as a singular entity, lacking the capability to separate garments from the
avatar itself. This inherent limitation presents challenges in avatar
customization, particularly in scenarios where users want to decorate diverse
clothing and accessories for specific characters, such as in gaming or virtual
reality environments.

To address this challenge, a promising approach is to create a decomposable
avatar where the garments are separated from the human body. Specifically, a
straightforward way is to treat the human body and its garments as separate
meshes to generate a disentangled avatar [37, 2]. However, this approach not
only requires additional human effort to design garment mesh templates but
also encounter difficulties accommodating diverse clothing types due to the
inherent geometric constraints of meshes. In response to this challenge,
recent works [5, 40, 13] have explored modeling clothing using Neural Radiance
Fields (NeRF) [28], which provide better fidelity and flexibility in
representing various clothing types. Yet, due to their implicit
representation, NeRF-based approaches tend to struggle with complex and
inefficient rendering procedures, requiring multiple network forward passes
and/or complex calculations per pixel. Besides, NeRF-based approaches also
present challenges for applying deformations, making it difficult to transfer
the garment when the shape of the human body changes significantly [40].

Recently, 3D Gaussian Splatting (GS) [20] has provided a fresh perspective on
3D asset generation. This approach leverages 3D Gaussian points characterized
by color, opacity, and density parameters to represent 3D scenes. In
particular, we observe that the inherent flexibility of their point-cloud-like
representation makes GS suitable for generating diverse garments. Meanwhile,
the explicit nature of GS grants direct control over the Gaussians,
facilitating the customization of garments to suit different body shapes.
Building upon these insights, we introduce the LAyered Gaussian Avatar (LAGA)
framework to overcome the aforementioned challenges. Our framework enables the
generation of high-quality 3D avatars with diverse garments, including both
tight-fitting and loose clothings, while also allowing for effortless
adaptation of garments to different human shapes. Specifically, our approach
treats a clothed avatar to be comprising multiple layers, with each layer
corresponding to a specific component, such as the base avatar, garments, or
accessories. To control the location and scale of each component, we create
the stack of layers by progressively expanding the SMPL mesh [27] layer-by-
layer, initializing Gaussian points based on the expanded mesh and related
joints in each layer. Then, we can employ score distillation sampling (SDS) to
optimize the Gaussian points at each layer, tapping into the rich 2D knowledge
in the pre-trained diffusion model for 3D generation.

However, we find that there still exists three main challenges to achieve
effective generation of decomposable avatars with our pipeline: 1 Diverse
Garment Generation: Although initializing Gaussian points based on the SMPL
model provides a good basic structure for locating the avatar component’s
position and scale, it can potentially restrict the diversity of generated
garments, making it unsuitable for generating garments with shapes diverging
significantly from the human body. 2 Coherence of Generated Garments: Simply
optimizing Gaussian points via SDS loss may lead to garments lacking coherence
with other avatar components, detracting from the natural appearance of the
avatar. For example, generating a skirt independently can result in its
waistline not closely fitting the human avatar and parts of it occluding the
avatar’s upper garment, leading to a lower-quality clothed avatar when they
are combined together. 3 Difficulty of Garment Transfer: The dense and
unstructured nature of GS presents a unique challenge in adapting garments to
avatars with diverse body shapes. Unlike meshes, which offer well-defined
geometry properties for deformation, controlling thousands of Gaussian points
for garment transfer is challenging and requires a multifaceted approach.

To address the above challenges, we propose the following designs. 1 First, to
facilitate diverse garment generation, we propose a coarse-to-fine generation
strategy coupled with a density guidance loss. Specifically, we divide the
garment generation into two stages: a coarse stage to approximate the overall
shape of the target garment and a fine stage for high-quality garment
generation. Moreover, we introduce a density guidance loss to guide Gaussian
points to match well with the garment shape during optimization. 2 Second, to
ensure coherence between the garments in each layer and the rest of the
avatar, we introduce a dual-SDS loss. This loss optimizes local garment-only
images for high-quality garment generation while ensuring consistency with
other avatar parts through a global rendering containing all current garments.
3 Finally, we propose three regularization losses aimed at guiding the
movement of Gaussian points for garment transfer: a Human Fitting Loss to
encourage the garment to fit the contours of the human body, a Similarity Loss
to preserve the overall shape of the garment during adaptation, and a
Visibility Loss to prevent the garment from being obscured by the avatar’s
existing components. Overall, these losses help guide the thousands of
Gaussian points to properly adapt to the target avatar.

In summary, our contributions are as follows: 1) We introduce LAGA, a novel
decomposable avatar generation framework capable of producing high-quality
decomposable avatar with various garments and support easy garment adaptation
between various human body shapes. 2) Our method incorporates various
meticulously designed modules to facilitate layered avatar generation and
garment adaptation, enabling us to achieve superior quality. 3) Through
extensive qualitative and quantitative experiments, we validate the efficacy
of our approach. Our method consistently outperforms existing methods,
generating avatars of exceptional quality. Moreover, the generated avatars
demonstrate a remarkable level of consistency with the corresponding input
natural languages.

##  2 Related Work

#### Text-guided 3D Asset Generation.

Recent text-to-3D generation methods can generally be divided into two main
categories: 1) Direct 3D Generation Pipelines: These methods optimize models
to directly learn the distribution of 3D explicit representations [9, 30, 19,
42] or implicit representations [19, 44, 23]. However, due to the high
complexity of 3D data, these methods either struggle to generate complex 3D
assets or are restricted to specific categories. 2) 2D-to-3D Lifting
Pipelines: These methods generate a 3D scene matching the given prompt by
leveraging extensive 2D domain knowledge stored in 2D text-to-image
generators. Early approaches [16, 29] used the image-text retrieval model,
CLIP [32], to guide the image-text alignment in each camera view for 3D
generation. Recently, leveraging the powerful 2D generation ability of
diffusion-based text-to-image models [33, 34], several 3D generation
techniques [25, 36, 49] employ SDS [31], which stochastically distills the 2D
knowledge from diffusion models, to generate high-quality 3D assets. While the
above methods have achieved remarkable success in 3D generation, adopting them
for decomposable avatar generation remains challenging due to the high
complexity of the hierarchical avatar structure and the huge difficulties
involved in generating realistic textures.

#### Text-guided 3D Human Generation.

To facilitate text-to-3D human generation, most works adopt 2D-to-3D lifting
pipelines with various dedicated designs to incorporate human priors. For
instance, AvatarCLIP [11] pioneers the integration of a parametric human model
(SMPL [27]) with Neus [38], leveraging CLIP [32] for supervising the creation
of diverse 3D humans. More recently, various approaches [22, 1, 45] have
adopted score distillation sampling (SDS) for generating high-quality clothed
humans. Specifically, DreamHuman [22] introduces a pose-conditioned NeRF model
for animatable 3D clothed human generation. Both DreamAvatar [1] and
AvatarCraft [18] utilize the pose and shape parameters of SMPL as a guiding
prior for high-quality human synthesis. Further advancements address specific
challenges and enhance realism. DreamWaltz [15] tackles the Janus (multi-face)
problem by implementing an occlusion-aware SDS loss with skeleton-based
conditioning techniques. AvatarVerse [45] replaces human skeleton conditions
in conditional diffusion models with DensePose maps, enhancing view
consistency in 3D human generation. TADA [24] replaces the NeRF representation
with a deformable SMPL-X mesh and optimizes texture UV-maps for avatar
rendering, making the generated avatars more suitable for computer graphics
workflows. HumanNorm [14] refines diffusion models to generate normal maps,
enriching the geometric fidelity of the resulting avatars. Recently,
HumanGaussian [26] explores modeling avatars via 3D GS, generating high-
quality clothed humans with fast rendering speeds. However, these methods
focus on generating human models as a single entity, and thus lack the ability
to effectively decouple bodies and clothing. Moreover, in contrast to [26],
which primarily focuses on utilizing GS for better avatar rendering
performance, our key contribution lies in recognizing the high flexibility and
controllability of GS due to its explicit nature, which unlocks significant
potential for more flexible, layered avatar generation.

#### Layered Avatar Modeling.

Early methods for modeling layered avatars treat the human body and its
garments as two separate meshes to generate disentangled avatars [37, 2, 17,
43, 48]. However, this approach requires additional human effort to design
garment mesh templates and faces difficulties accommodating diverse clothing
types due to the inherent geometric constraints of meshes. In response to this
challenge, recent works [5, 40, 13] have explored modeling clothing using
NeRFs [28], which provide better fidelity and flexibility in representing
various clothing types. Specifically, HumanLiff [13] generates the avatar in a
layer-wise manner, presenting the human with clothing in each layer via a
triplane neural feature. However, the features of the human body and garments
are still not disentangled, limiting the ability for garment editing.
Conversely, other existing works [5, 40] model the human body and garments
separately, but due to their implicit representation, the garments generated
by these methods cannot be easily deformed, making them transferrable only
between avatars with similar human shapes [40]. In contrast, our method can
generate decomposable clothed avatars with diverse, replaceable garments and
supports garment transfer between avatars with various human shapes.

##  3 Method

Figure 2: Overview of the avatar component generation process in each layer.
As outlined in the green box, our generation process of each layer mainly
consists of three steps: (a) sparse initialization of Gaussian points, (b)
density guidance to obtain coarse garment, (c) densification to obtain fine
garment, In the beginning, based on the given layer’s text description, we
initialize a set of sparse Gaussian points using the parametric human model
(SMPL) and associated joints. Then, these points are refined to approximate
the broad shape of the target component in the coarse stage. Subsequently, in
the fine stage, we densify the Gaussians to capture finer details and sharper
features of the avatar component, aiming for high-quality results. To ensure
coherence with other generated avatar components, a dual-SDS loss (as
presented in the blue box) is introduced to optimize the Gaussian points in
both coarse and fine stages. This loss function optimizes Gaussians from both
local and global perspectives, enhancing the quality and coherence of the
generated avatar component.

We present LAyered Gaussian Avatar (LAGA), a method for generating
decomposable clothed avatars with diverse, interchangeable garments. First, to
facilitate better understanding, we introduce some important preliminaries
regarding SDS and 3D GS in Section 3.1. Subsequently, we introduce our method
in two parts: how to generate the decomposable avatar (covered in Section
3.2), and how to perform garment transfer (covered in Section 3.3).
Specifically, in Section 3.2 we present our avatar generation framework, which
includes a coarse-to-fine strategy for diverse garment generation and a dual-
SDS loss for coherent garment generation. Then, in Section 3.3, we introduce
three regularization losses to facilitate garment transfer. Our overall
framework is illustrated in Fig. 1.

###  3.1 Preliminaries

Score Distillation Sampling (SDS) is introduced in DreamFusion [31] for
refining 3D representations by leveraging a 2D pre-trained diffusion
generator. Specifically, a 3D scene, parameterized by $\theta$, is optimized
to render images that match with the data distribution of natural images
learned by diffusion model $\phi$ across various noise levels. In practical
implementation, DreamFusion employs a text-to-image diffusion model [34] as
the score estimator $\bm{\epsilon}_{\phi}(\mathbf{c}_{t};y)$, which predicts
the sampled noise $\bm{\epsilon}_{\phi}$ based on the noisy image
$\mathbf{c}_{t}$, text embedding $y$, and timestep $t$. SDS optimizes 3D
scenes ($\theta$) through gradient descent with respect to $\theta$ as
follows:

$\displaystyle\small\nabla_{\theta}\mathcal{L}_{\mathrm{SDS}}=\mathbb{E}_{\bm{\epsilon},t}\left[w_{t}\left(\bm{\epsilon}_{\phi}\left(\mathbf{c}_{t};y\right)-\bm{\epsilon}\right)\frac{\partial\mathbf{c}}{\partial\theta}\right],$
(1)

where $\bm{\epsilon}\sim\mathcal{N}(\mathbf{0},\mathbf{I})$ is Gaussian noise,
$\mathbf{c}_{t}=\alpha_{t}\mathbf{c}+\sigma_{t}\bm{\epsilon}$ is the noised
image; $\alpha_{t}$, $\sigma_{t}$, and $w_{t}$ are noise hyperparameters.

3D Gaussian Splatting (3D GS) [20] introduces an efficient yet effective
approach for 3D scene representation. 3D GS represents the scene using a
collection of anisotropic Gaussians defined by their center position $\mu$,
covariance $\Sigma$, color $c$, and opacity $\alpha$. During rendering, a ray
$r$ is cast from the center of the camera, and the color and density of the 3D
Gaussians that the ray intersects are computed along the ray. The rendering
process is as follows:

$\displaystyle\begin{aligned}
G\left(p,\mu_{i},\Sigma_{i}\right)=\exp(-\frac{1}{2}(p-\mu_{i})^{\mathsf{T}}\Sigma_{i}^{-1}(p-\mu_{i}))&,\\\
\mathbf{c}(r)=\sum_{i\in\mathcal{M}}c_{i}\sigma_{i}\prod_{j=1}^{i-1}\left(1-\sigma_{j}\right),{\text{where~{}~{}}}\sigma_{i}=\alpha_{i}G\left(p,\mu_{i},\Sigma_{i}\right)&,\end{aligned}$
(2)

where $\mathbf{c}(r)$ is the color value of the pixel in the 2D image
$\mathbf{c}$ contributed by the ray $r$; $p$ is the location of queried point
on the ray $r$; $\mu_{i}$, $\Sigma_{i}$, $c_{i}$, $\alpha_{i}$, and
$\sigma_{i}$ are the center position, covariance, color, opacity, and density
of the $i$-th Gaussian respectively; $G\left(p,\mu_{i},\Sigma_{i}\right)$ is
the value of the $i$-th Gaussian at point $p$; $\mathcal{M}$ denotes the set
of 3D Gaussians in this tile.

###  3.2 Layered Avatar Generation

In this section, we present our proposed approach for generating a
decomposable avatar in a layer-by-layer manner. As shown in Fig. 1, for an
avatar with $N-1$ garments described in the text prompt, we first create $N$
layers to represent the human body and garments independently. Then, we
sequentially generate the human body and garments, aiming to optimize the
Gaussian points in each layer to produce a component (i.e., human body or
garments) that matches its text description and integrates with other existing
avatar components seamlessly. However, there are two notable challenges: 1
Diverse Garment Generation: During initialization of the 3D avatar, although
initializing Gaussian points based on the SMPL model provides a good basic
structure for locating the avatar component’s position and scale, it can
potentially restrict the diversity of generated garments, making it unsuitable
for generating garments with shapes diverging significantly from the human
body. 2 Coherence of Generated Garments: During optimization, simply
optimizing Gaussian points via SDS loss may lead to garments lacking coherence
with existing avatar components, detracting from the natural appearance of the
avatar. To address the above challenges, we propose a Coarse-to-Fine
Generation Strategy and Dual-SDS Loss to tackle challenge 1 and challenge 2
respectively. We explain these two designs in detail below.

#### Coarse-to-Fine Strategy.

Facilitating diverse garment generation for clothed avatars (Challenge 1) is
challenging because we need to satisfy two requirements: 1) the garment should
be suitable for the target avatar; 2) yet, the 3D GS Gaussian points need to
be optimized towards a diverse range of garments. Notably, it is challenging
to simultaneously achieve both requirements. For instance, an intuitive
approach to the first problem is initializing the Gaussian points by sampling
points from the SMPL-X mesh, which provides a robust foundation for
determining the position and scale of the garment. However, this approach
makes the second problem harder to solve, as the shapes of many loose garments
(e.g., skirt) differ significantly from the human body, and an inappropriate
initialization of GS will lead to a significant performance drop [36, 20], as
shown in Fig. 5. Therefore, to address these challenges and achieve diverse
garment generation, we divide the garment generation process into two stages
as shown in Fig. 2, which we call Coarse-to-Fine Strategy. Specifically, in
the Coarse Stage, we initialize a sparse set of Gaussian points and optimize
them to approximate the overall shape of the target garment, allowing the
Gaussian points to be initialized in diverse shapes accordingly. Then, in the
Fine Stage, to capture sharper and more detailed garment features, we densify
the Gaussian points, allowing them to be more suitable for the target avatar.

In the Coarse Stage, we begin by initializing the Gaussian points at each
layer by sampling a small number of points (5,000 points) from the SMPL-X
mesh. To focus these points on the target garment at each layer, we query
relevant human joints to generate a 3D bounding box and remove Gaussian points
outside this box. By performing this initialization at each layer, we can
obtain the set of sparse Gaussian points at each $m$-th layer, which we denote
as $\mathbf{G}_{m}$.

Next, we aim to optimize $\mathbf{G}_{m}$ to approximate the coarse shape of
the $m$-th avatar component described in the text prompt. A straightforward
approach is to adopt the SDS loss (discussed in Section 3.1) to optimize
$\mathbf{G}_{m}$ to match the target garment. However, SDS loss primarily
focuses on optimizing $\mathbf{G}_{m}$ to produce a natural-looking 2D image
in each view independently, which is stochastic [35] and lacks strong geometry
constraints. There is no explicit regularization process to control the
density of Gaussian points throughout the avatar during SDS optimization, and
thus to model the avatar, SDS can often optimize the Gaussian points in
certain areas to be sparser but larger, especially for the areas where the
initialized Gaussian points were already sparse. However, this can be sub-
optimal, since the Gaussian points may turn out to be overly sparse at some
areas, which poses issues with modeling the coarse approximate shape of the
component (see Fig. 5 for visualization).

Therefore, to encourage the Gaussian points to be spread evenly for a better
coarse approximation of the component’s shape, we propose incorporating
density guidance into optimization to ensure the Gaussian points are more
evenly distributed to address this issue. Specifically, we regard the opacity
of each Gaussian point as its density in the 3D space and then render a 2D
opacity map of GS to represent the density distribution of $G_{m}$. Formally,
similar to Eq. 2, the opacity map of $\mathbf{G}_{m}$ is computed by
accumulating the opacity values along the ray $r$, as shown below:

$\displaystyle\mathbf{\alpha}_{m}(r)=\sum_{i\in\mathcal{M}}\sigma_{i}\prod_{j=1}^{i-1}\left(1-\sigma_{j}\right),\text{where}~{}\sigma_{i}=\alpha_{i}G\left(p,\mu_{i},\Sigma_{i}\right)$
, (3)

where $\mathbf{\alpha}_{m}(r)$ is the value of the 2D opacity map
$\mathbf{\alpha}_{m}$ contributed by the ray $r$; $r$ is a ray cast from the
center of the camera; $p$ is the location of queried point on the ray;
$\alpha_{i}$ is the opacity of $i$-th Gaussian and
$G\left(p,\mu_{i},\Sigma_{i}\right)$ is the value of the $i$-th Gaussian at
the queried point $p$ as defined in Eq. 2.

After that, we capture the areas occupied by the component by creating a
binary component mask $M_{m}$ via a segmentor [21] and then optimize the
density of Gaussians in these areas to be uniform as shown below:

$\displaystyle\begin{aligned}
\mathcal{L}_{d}=||M_{m}-f_{n}(M_{m}*\mathbf{\alpha}_{m})||^{2}_{2}\end{aligned}$
(4)

where $f_{n}$ is a normalization operation that adjusts the values of the
masked opacity map $(M_{m}*\mathbf{\alpha}_{m})$ to range between 0 and 1.
With this strategy, we can effectively control the sparse Gaussian points
$G_{m}$ to fit the coarse shape of the target garment, making it suitable for
generating diverse garments, including garments with shapes that are very
different from the human body.

In the Fine Stage, our goal is to refine $\mathbf{G}_{m}$ to obtain sharper
and more detailed garment features. To achieve this, we recurrently upsample
the Gaussian points and then optimize them to generate the high-quality avatar
component via SDS loss. During each upsampling step, instead of simply
duplicating $\mathbf{G}_{m}$ to create a denser distribution, we propose to
duplicate the Gaussian points $\mathbf{G}_{m}$ with several perturbations to
better capture the detailed variations in the local object area. Specifically,
we duplicate the existing Gaussian points $\mathbf{G}_{m}$ to create another
set of Gaussian points, denoted as $G_{d}$, and then perturb their positions
and colors as follows:

$\bm{\mu}_{d}^{\prime}=\bm{\mu}_{d}+\bm{\epsilon}_{d},\;\;\bm{c}_{d}^{\prime}=\bm{c}_{d}+\bm{\epsilon}_{c},$
(5)

where $\bm{\mu}_{d}$ and $\bm{c}_{d}$ are the original positions and colors of
the Gaussian points in ${G}_{d}$, $\bm{\mu}_{d}^{\prime}$ and
$\bm{c}_{d}^{\prime}$ are the updated positions and colors,
$\bm{\epsilon}_{d}$ is a small position noise sampled between -0.0005 and
0.0005, and $\bm{\epsilon}_{c}$ is the color noise sampled between 0 and 0.05.
Then, we obtain the denser set of Gaussian points by merging $\mathbf{G}_{d}$
into $\mathbf{G}_{m}$ and optimize the updated $\mathbf{G}_{m}$ via the SDS
loss (see Section 3.1) to generate a high-quality garment.

#### Dual-SDS Loss.

While our Coarse-to-Fine strategy above offers a good framework for
controlling the position and scale of each avatar component, optimizing each
component individually can sometimes lead to a lack of coherence with other
parts, resulting in an unnatural appearance. This issue (Challenge 2) arises
from the shape changes of each component during optimization and the inherent
geometric complexity of overlapping areas. For example, optimizing pants from
the standard SMPL-X model might not yield a suitable fit for a slender woman.
Similarly, independently creating a loose shirt and jeans can lead to issues
with occlusion at the waist area, where the shirt and jeans may overlap. These
discrepancies can accumulate and become noticeable, causing the avatar to
appear disjointed or proportionally incorrect.

Motivated by the idea that garments not only exist individually but also
seamlessly blend into the avatar’s overall look, we propose a dual-SDS loss,
which optimizes the layer’s Gaussian points $G_{m}$ while considering both
local and global aspects. At the local level, we focus on optimizing the
individual garment by optimizing its images (rendered from $G_{m}$) to
precisely align with the layer’s textual description. At the same time, we
also consider the global perspective by optimizing the unified image that also
incorporates the inner $m-1$ avatar components, up to the $m$-th layer. By
utilizing the Gaussian points from the layers up to the $m$-th layer
($\\{\mathbf{G}_{j}\\}^{m}_{j=1}$), this global view enables us to optimize
$G_{m}$ to be aware of the overall appearance, resulting in a seamless and
natural visual coherence using SDS loss.

More precisely, to achieve this, we first combine $\mathbf{G}_{m}$ with the
inner $m-1$ layers ($\\{\mathbf{G}_{j}\\}^{m-1}_{j=1}$) to obtain the “global”
avatar for the $m$-th layer as:
$\mathbf{G}_{av}^{m}=\\{\mathbf{G}_{j}\\}^{m}_{j=1}$. Then we follow Eq. 2 to
render a local image $\mathbf{c}^{l}$ from $\mathbf{G}_{av}^{m}$ using the
following formulation:

$\begin{split}\mathbf{c}^{l}(r)=\sum_{i\in\mathcal{M}(\mathbf{G}_{m},r)}c_{i}\sigma_{i}\prod_{j=1}^{i-1}\left(1-\sigma_{j}\right),\sigma_{i}=\alpha_{i}G\left(p,\mu_{i},\Sigma_{i}\right)&.\end{split}$
(6)

where $\mathcal{M}(\mathbf{G}_{m},r)$ refers to the set of Gaussian points in
$\mathbf{G}_{m}$ that are along the ray $r$. Meanwhile, to render a global
image $\mathbf{c}^{g}$, we modify Eq. 6 by replacing $\mathbf{G}_{m}$ with
$\mathbf{G}_{av}^{m}$.

Next, to optimize the avatar components, we apply the SDS loss to the rendered
local images $\mathbf{c}^{l}$ and global images $\mathbf{c}^{g}$ to encourage
them to match the natural images learned by the 2D diffusion generator. For
our SDS loss, we follow previous works [15] to adopt a 2D human skeleton
conditioned diffusion model [46] to enhance multi-view consistency of our
human avatar. Formally, conditioned on the 2D human skeleton $\mathbf{s}$, our
dual-SDS loss (modified from Eq. 1) for the $m$-th layer is expressed as:

$\displaystyle\begin{aligned} \nabla_{\theta}\mathcal{L}_{\mathrm{Dual-
SDS}}&=\lambda_{l}\cdot\mathbb{E}_{\bm{\epsilon}_{\mathbf{x}^{l}},t}\left[w_{t}\left(\bm{\epsilon}_{\phi}\left(\mathbf{x}^{l}_{t};\mathbf{s},y^{l}\right)-\bm{\epsilon}_{\mathbf{x}^{l}}\right)\frac{\partial\mathbf{x}^{l}}{\partial\theta}\right]\\\
&+\lambda_{g}\cdot\mathbb{E}_{\bm{\epsilon}_{\mathbf{x}^{g}},t}\left[w_{t}\left(\bm{\epsilon}_{\phi}\left(\mathbf{x}^{g}_{t};\mathbf{s},y^{g}\right)-\bm{\epsilon}_{\mathbf{x}^{g}}\right)\frac{\partial\mathbf{x}^{g}}{\partial\theta}\right],\\\
\end{aligned}$ (7)

where $y^{l}$ is text prompt of the $m^{th}$ garment; $y^{g}$ denotes the text
prompt of the $m^{th}$ avatar, which is a combination of the human body
description and the layer’s text description; $\theta$ represents the
parameters of the Gaussian points in the $m$-th layer ($G_{m}$); and
$\lambda_{l},\lambda_{g}$ are two pre-defined hyperparameters. To ensure
coherent avatar component generation, we replace the SDS loss in the both
coarse and fine generation process with our dual-SDS loss (see Figure 2). Note
that, since the bare human body serves as the fundamental avatar component, we
solely employ the SDS loss during the human body generation in the first layer
(i.e., when $m=1$).

Overall, by dividing the avatar component generation process into coarse and
fine stages, we can optimize sparse Gaussian points to approximate the basic
shapes of diverse garments and then densify these Gaussians for high-quality
garment generation. Additionally, by applying the dual-SDS loss to optimize
Gaussians from both local and global perspectives, we ensure coherence between
the generated garment and other avatar components.

###  3.3 Garment Transfer

With the layered structure described in the previous subsections, our avatar
can be conveniently divided into multiple components, allowing users the
freedom to decorate it as they wish, such as replacing an old garment with a
new one, as shown in Fig. 1. This flexibility sparks an intriguing
possibility: could we replace our avatar’s garments by transferring garments
from other avatars rather than generating entirely new ones? Note that,
although previous methods have attempted this [5, 40], they are constrained to
transferring clothes between avatars with similar body shapes. Leveraging the
explicit representation of 3D GS and the control it offers, we aim to overcome
this limitation by enabling the transfer of garments between avatars with
differing body shapes.

However, the dense and unstructured nature of GS poses a unique obstacle in
adapting garments to avatars with varying body shapes. Unlike meshes, which
offer well-defined geometric properties conducive to deformation, controlling
thousands of Gaussian points for garment transfer demands a nuanced approach
(Challenge 3). Here, to transfer the garment to avatars with a different body
shape, we freeze all parameters of Gaussian points except the position and
scale, and introduce three regularization losses to guide the movement of
Gaussian points for adaptation.

Firstly, since well-fitting garments (either loose or tight) need to be
tailored to follow the body’s natural curves and proportions [8], we introduce
a Human Fitting Loss $\mathcal{L}_{HF}$ to regularize the shape of the garment
$\mathbf{G}_{m}$. This loss function projects the garment and the human body
separately onto 2D images, and optimizes the depth map of the garment to match
the depth map of the human body in the overlapping areas, encouraging the
garment to closely fit to the human contour. Formally, it can written as:

$\displaystyle\mathcal{L}_{HF}=||\mathbf{d}_{av}-\mathbf{d}_{m}||^{2}_{2}*M_{oc},~{}\text{where}~{}M_{oc}=M_{av}\cap
M_{m}$ (8)

where $\mathbf{d}_{av}$ and $\mathbf{d}_{m}$ represent the depth map rendered
by the target and $\mathbf{G}_{m}$ respectively, and $M_{oc}$ in a mask that
reflects the overlapping area between the garment mask $M_{m}$ and the target
avatar mask $M_{av}$, generated by the segmentor (SAM [21]).

On the other hand, preserving the overall shape of the garment is crucial for
successful transfer. To achieve this, we introduce a Similarity Loss
$\mathcal{L}_{ssim}$ that regularizes the transferred garment to resemble its
pre-transfer form as:

$\displaystyle\mathcal{L}_{ssim}=-SSIM(\mathbf{d}_{m},\bar{\mathbf{d}}_{m}),$
(9)

where $SSIM$ measures the structural similarity [41] and
$\bar{\mathbf{d}}_{m}$ is the depth map of the garment before deformation.

Finally, to prevent the garment from being obscured by other avatar
components, we introduce a Visibility Loss $\mathcal{L}_{vis}$ which refines
the positions of Gaussian points to ensure that all parts of the garment
remain visible when it is combined with other inner layers of the avatar.
Intuitively, a garment should be closer to the camera than the covered human
parts to remain visible. To achieve this, we optimize the depth value of the
garment points $G_{m}$ to be lower than that of the corresponding avatar
points in each camera view:

$\displaystyle\begin{aligned}
\mathcal{L}_{vis}=max(0,-(\mathbf{d}_{av}-\mathbf{d}_{o})*M_{m}+\delta_{occ})\end{aligned}$
(10)

where $\delta_{occ}$ is a margin gap set at 0.03.

##  4 Experiments

Figure 3: Qualitative results. We compare our method with SOTA 3D human
generators on six different prompts, each showing three camera views.  Figure
4: Individual components for each avatar.

###  4.1 Implementation Details

We begin by sampling $5k$ points from SMPL to initialize sparse Gaussian
points in each layer, subsequently densifying the Gaussian points four times
to ensure high-quality avatar component generation. In each layer, we optimize
the Gaussian points over $5k$ iterations with a batch size of 2, taking
approximately 20 minutes on a single NVIDIA RTX 4090 GPU workstation. The
samples generated by our models are rendered as images with a resolution of
$1024\times 1024$ for optimization purposes. Given a text prompt in the
format: ”a {human description} has {hair description}, wearing {garment
description}, {garment description}, …”, our method can automatically
decompose the text description into multiple layer-specific text prompts and
generate layers corresponding to each layer’s text prompt for avatar modeling.

###  4.2 Main Results

#### Qualitative comparisons.

To evaluate the quality of the generated clothed human models, we compare our
LAGA method with two state-of-the-art avatar generation models: DreamWaltz
[15] and HumanGaussian [26]. The qualitative results are presented in Figure
3. As shown across the first row of Figure 3, the skirts generated by our
approach exhibit more natural geometry as compared to existing methods. In the
second and third rows of Figure 3, we also observe that the avatars generated
by our method consistently align well with the given text prompts and capture
more detailed features for each garment. Additionally, our avatars tend to
look more photorealistic than those produced by HumanGaussian and contain more
details and finer textures than those produced by DreamWaltz. Overall, this
qualitatively demonstrates our method’s superior performance at rendering more
realistic human appearances that are aligned with the text prompts, modeling
more natural structures for both tight and loose garments, and capturing finer
details for each avatar component.

Table 1:  User study: Ours vs HumanGaussian  Comparison | Preference (%)
---|---
Texture quality |  81.73 vs 18.27
Geometry quality |  82.85 vs 17.15
Text Alignment |  63.38 vs 36.62
Reality |  93.85 vs 6.15

#### Quantitative comparison.

We randomly selected 20 text prompts for avatar generation and compared our
method with the state-of-the-art (SOTA) method, HumanGaussian [26].
Specifically, we adapted the CLIP Score [47] to measure the alignment between
the generated avatars and the given text, and used the Fréchet Inception
Distance (FID) [10] to evaluate the distribution gap between images rendered
by avatars and a real 2D human dataset [7]. We find that our method
consistently surpasses HumanGaussian on both metrics (e.g., 33.55 vs. 31.08 on
CLIP Score ($\uparrow$) and 283 vs. 322 on FID ($\downarrow$)).

Moreover, we conducted a user study and followed [26] to evaluate the quality
of generated avatars from three aspects: (1) Texture Quality, (2) Geometry
Quality, and (3) Text Alignment. Additionally, we added a question on the
realism aspect to assess the photorealistic quality of avatars. As shown in
Table 1, our method consistently outperforms the SOTA across all the evaluated
aspects.

#### Decomposition Ability.

As shown in Fig. 4, our avatars can be conveniently decomposed to a human body
with a set of garments, where each avatar component contains detailed
appearance/textures and high-quality geometry. We note that this
decomposability further supports users to customize avatars easily.

###  4.3 Ablation Study

Figure 5: Ablation for C2F. (a) Avatar w/ C2F. (B) Avatar w/o C2F.

#### Impact of Coarse-to-Fine (C2F) strategy.

As shown in Fig. 5, directly optimizing Gaussian points sampled from SMPL
without using our Coarse-to-Fine strategy may result in the generation of
garments with geometric errors and large blurry areas.

Figure 6: Ablation for dual-SDS loss. (a) Avatar w/ dual-SDS. (B) Avatar w/o
dual-SDS.

#### Impact of dual-SDS loss.

As shown in Fig. 6, when replacing dual-SDS loss with a normal SDS loss, the
generated garments tend to struggle to fit well with the human body.

Figure 7: Ablation for regularization loss. (a) Source Avatar. (B) Target
avatar w/ regularization. (c) Target avatar w/o regularization.

#### Impact of adaptation regularization loss.

Directly transferring the garment from the source to the target avatar without
regularization results in incoherence between the transferred garment and the
target avatar (see Fig. 7).

##  5 Conclusion

In this paper, we propose a LAGA, layered 3D human generation framework based
on 3D GS, which generates decomposable clothed avatars with diverse garments
and supports garment transfer across avatars with various shapes. Our key
insight lies in recognizing the high flexibility and controllability of GS,
which unlocks significant potential for more flexible, layered avatar
generation. Specifically, we introduce a coarse-to-fine generation strategy to
facilitate diverse garment creation and a dual-SDS loss to ensure coherence
between each avatar component. We also introduce three regularization losses
to guide the movement of Gaussian points for garment adaptation. Extensive
experiments demonstrate that our approach surpasses existing methods in
generating 3D clothed humans.

## References

  * Cao et al. [2024] Yukang Cao, Yan-Pei Cao, Kai Han, Ying Shan, and Kwan-Yee K Wong.  Dreamavatar: Text-and-shape guided 3d human avatar generation via diffusion models.  2024\.
  * Corona et al. [2021] Enric Corona, Albert Pumarola, Guillem Alenya, Gerard Pons-Moll, and Francesc Moreno-Noguer.  Smplicit: Topology-aware generative model for clothed people.  In _Proceedings of the IEEE/CVF conference on computer vision and pattern recognition_ , pages 11875–11885, 2021.
  * Favalli et al. [2012] Massimiliano Favalli, Alessandro Fornaciai, Ilaria Isola, Simone Tarquini, and Luca Nannipieri.  Multiview 3d reconstruction in geosciences.  _Computers & Geosciences_, 44:168–176, 2012.
  * Feng et al. [2017] Andrew Feng, Evan Suma, and Ari Shapiro.  Just-in-time, viable, 3d avatars from scans.  In _ACM SIGGRAPH 2017 Talks_ , pages 1–2. 2017.
  * Feng et al. [2022] Yao Feng, Jinlong Yang, Marc Pollefeys, Michael J Black, and Timo Bolkart.  Capturing and animation of body and clothing from monocular video.  In _SIGGRAPH Asia 2022 Conference Papers_ , pages 1–9, 2022.
  * Foo et al. [2023] Lin Geng Foo, Hossein Rahmani, and Jun Liu.  Ai-generated content (aigc) for various data modalities: A survey.  _arXiv preprint arXiv:2308.14177_ , 2, 2023.
  * Fu et al. [2022] Jianglin Fu, Shikai Li, Yuming Jiang, Kwan-Yee Lin, Chen Qian, Chen Change Loy, Wayne Wu, and Ziwei Liu.  Stylegan-human: A data-centric odyssey of human generation.  In _European Conference on Computer Vision_ , pages 1–19. Springer, 2022.
  * Gill [2015] Simeon Gill.  A review of research and innovation in garment sizing, prototyping and fitting.  _Textile Progress_ , 47(1):1–85, 2015.
  * He et al. [2024] Kai He, Kaixin Yao, Qixuan Zhang, Jingyi Yu, Lingjie Liu, and Lan Xu.  Dresscode: Autoregressively sewing and generating garments from text guidance.  _arXiv preprint arXiv:2401.16465_ , 2024.
  * Heusel et al. [2017] Martin Heusel, Hubert Ramsauer, Thomas Unterthiner, Bernhard Nessler, and Sepp Hochreiter.  Gans trained by a two time-scale update rule converge to a local nash equilibrium.  In _Advances in Neural Information Processing Systems_. Curran Associates, Inc., 2017.
  * Hong et al. [2022] Fangzhou Hong, Mingyuan Zhang, Liang Pan, Zhongang Cai, Lei Yang, and Ziwei Liu.  Avatarclip: zero-shot text-driven generation and animation of 3d avatars.  _ACM Transactions on Graphics (TOG)_ , 41(4):1–19, 2022.
  * Hong et al. [2023] Yicong Hong, Kai Zhang, Jiuxiang Gu, Sai Bi, Yang Zhou, Difan Liu, Feng Liu, Kalyan Sunkavalli, Trung Bui, and Hao Tan.  Lrm: Large reconstruction model for single image to 3d.  _arXiv preprint arXiv:2311.04400_ , 2023.
  * Hu et al. [2023] Shoukang Hu, Fangzhou Hong, Tao Hu, Liang Pan, Haiyi Mei, Weiye Xiao, Lei Yang, and Ziwei Liu.  Humanliff: Layer-wise 3d human generation with diffusion model.  _arXiv preprint arXiv:2308.09712_ , 2023.
  * Huang et al. [2023] Xin Huang, Ruizhi Shao, Qi Zhang, Hongwen Zhang, Ying Feng, Yebin Liu, and Qing Wang.  Humannorm: Learning normal diffusion model for high-quality and realistic 3d human generation.  _arXiv preprint arXiv:2310.01406_ , 2023.
  * Huang et al. [2024] Yukun Huang, Jianan Wang, Ailing Zeng, He Cao, Xianbiao Qi, Yukai Shi, Zheng-Jun Zha, and Lei Zhang.  Dreamwaltz: Make a scene with complex 3d animatable avatars.  _Advances in Neural Information Processing Systems_ , 36, 2024.
  * Jain et al. [2022] Ajay Jain, Ben Mildenhall, Jonathan T Barron, Pieter Abbeel, and Ben Poole.  Zero-shot text-guided object generation with dream fields.  In _Proceedings of the IEEE/CVF conference on computer vision and pattern recognition_ , pages 867–876, 2022.
  * Jiang et al. [2020] Boyi Jiang, Juyong Zhang, Yang Hong, Jinhao Luo, Ligang Liu, and Hujun Bao.  Bcnet: Learning body and cloth shape from a single image.  In _Computer Vision–ECCV 2020: 16th European Conference, Glasgow, UK, August 23–28, 2020, Proceedings, Part XX 16_ , pages 18–35. Springer, 2020.
  * Jiang et al. [2023] Ruixiang Jiang, Can Wang, Jingbo Zhang, Menglei Chai, Mingming He, Dongdong Chen, and Jing Liao.  Avatarcraft: Transforming text into neural human avatars with parameterized shape and pose control.  In _Proceedings of the IEEE/CVF International Conference on Computer Vision_ , pages 14371–14382, 2023.
  * Jun and Nichol [2023] Heewoo Jun and Alex Nichol.  Shap-e: Generating conditional 3d implicit functions.  _arXiv preprint arXiv:2305.02463_ , 2023.
  * Kerbl et al. [2023] Bernhard Kerbl, Georgios Kopanas, Thomas Leimkühler, and George Drettakis.  3d gaussian splatting for real-time radiance field rendering.  _ACM Transactions on Graphics_ , 42(4), 2023.
  * Kirillov et al. [2023] Alexander Kirillov, Eric Mintun, Nikhila Ravi, Hanzi Mao, Chloe Rolland, Laura Gustafson, Tete Xiao, Spencer Whitehead, Alexander C Berg, Wan-Yen Lo, et al.  Segment anything.  In _Proceedings of the IEEE/CVF International Conference on Computer Vision_ , pages 4015–4026, 2023.
  * Kolotouros et al. [2024] Nikos Kolotouros, Thiemo Alldieck, Andrei Zanfir, Eduard Bazavan, Mihai Fieraru, and Cristian Sminchisescu.  Dreamhuman: Animatable 3d avatars from text.  _Advances in Neural Information Processing Systems_ , 36, 2024.
  * Li et al. [2023] Jiahao Li, Hao Tan, Kai Zhang, Zexiang Xu, Fujun Luan, Yinghao Xu, Yicong Hong, Kalyan Sunkavalli, Greg Shakhnarovich, and Sai Bi.  Instant3d: Fast text-to-3d with sparse-view generation and large reconstruction model.  _arXiv preprint arXiv:2311.06214_ , 2023.
  * Liao et al. [2023] Tingting Liao, Hongwei Yi, Yuliang Xiu, Jiaxiang Tang, Yangyi Huang, Justus Thies, and Michael J Black.  Tada! text to animatable digital avatars.  _ArXiv_ , 2023.
  * Lin et al. [2023] Chen-Hsuan Lin, Jun Gao, Luming Tang, Towaki Takikawa, Xiaohui Zeng, Xun Huang, Karsten Kreis, Sanja Fidler, Ming-Yu Liu, and Tsung-Yi Lin.  Magic3d: High-resolution text-to-3d content creation.  In _Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition_ , pages 300–309, 2023.
  * Liu et al. [2023] Xian Liu, Xiaohang Zhan, Jiaxiang Tang, Ying Shan, Gang Zeng, Dahua Lin, Xihui Liu, and Ziwei Liu.  Humangaussian: Text-driven 3d human generation with gaussian splatting.  _arXiv preprint arXiv:2311.17061_ , 2023.
  * Loper et al. [2023] Matthew Loper, Naureen Mahmood, Javier Romero, Gerard Pons-Moll, and Michael J Black.  Smpl: A skinned multi-person linear model.  In _Seminal Graphics Papers: Pushing the Boundaries, Volume 2_ , pages 851–866. 2023.
  * Mildenhall et al. [2021] Ben Mildenhall, Pratul P Srinivasan, Matthew Tancik, Jonathan T Barron, Ravi Ramamoorthi, and Ren Ng.  Nerf: Representing scenes as neural radiance fields for view synthesis.  _Communications of the ACM_ , 65(1):99–106, 2021.
  * Mohammad Khalid et al. [2022] Nasir Mohammad Khalid, Tianhao Xie, Eugene Belilovsky, and Tiberiu Popa.  Clip-mesh: Generating textured meshes from text using pretrained image-text models.  In _SIGGRAPH Asia 2022 conference papers_ , pages 1–8, 2022.
  * Nichol et al. [2022] Alex Nichol, Heewoo Jun, Prafulla Dhariwal, Pamela Mishkin, and Mark Chen.  Point-e: A system for generating 3d point clouds from complex prompts.  _arXiv preprint arXiv:2212.08751_ , 2022.
  * Poole et al. [2022] Ben Poole, Ajay Jain, Jonathan T Barron, and Ben Mildenhall.  Dreamfusion: Text-to-3d using 2d diffusion.  In _The Eleventh International Conference on Learning Representations_ , 2022.
  * Radford et al. [2021] Alec Radford, Jong Wook Kim, Chris Hallacy, Aditya Ramesh, Gabriel Goh, Sandhini Agarwal, Girish Sastry, Amanda Askell, Pamela Mishkin, Jack Clark, et al.  Learning transferable visual models from natural language supervision.  In _International conference on machine learning_ , pages 8748–8763. PMLR, 2021.
  * Rombach et al. [2022] Robin Rombach, Andreas Blattmann, Dominik Lorenz, Patrick Esser, and Björn Ommer.  High-resolution image synthesis with latent diffusion models.  In _Proceedings of the IEEE/CVF conference on computer vision and pattern recognition_ , pages 10684–10695, 2022.
  * Saharia et al. [2022] Chitwan Saharia, William Chan, Saurabh Saxena, Lala Li, Jay Whang, Emily L Denton, Kamyar Ghasemipour, Raphael Gontijo Lopes, Burcu Karagol Ayan, Tim Salimans, et al.  Photorealistic text-to-image diffusion models with deep language understanding.  _Advances in neural information processing systems_ , 35:36479–36494, 2022.
  * Song et al. [2020] Yang Song, Jascha Sohl-Dickstein, Diederik P Kingma, Abhishek Kumar, Stefano Ermon, and Ben Poole.  Score-based generative modeling through stochastic differential equations.  _arXiv preprint arXiv:2011.13456_ , 2020.
  * Tang et al. [2023] Jiaxiang Tang, Jiawei Ren, Hang Zhou, Ziwei Liu, and Gang Zeng.  Dreamgaussian: Generative gaussian splatting for efficient 3d content creation.  _arXiv preprint arXiv:2309.16653_ , 2023.
  * Wang et al. [2023a] Jionghao Wang, Yuan Liu, Zhiyang Dou, Zhengming Yu, Yongqing Liang, Xin Li, Wenping Wang, Rong Xie, and Li Song.  Disentangled clothed avatar generation from text descriptions.  _arXiv preprint arXiv:2312.05295_ , 2023a.
  * Wang et al. [2021] Peng Wang, Lingjie Liu, Yuan Liu, Christian Theobalt, Taku Komura, and Wenping Wang.  Neus: Learning neural implicit surfaces by volume rendering for multi-view reconstruction.  _arXiv preprint arXiv:2106.10689_ , 2021.
  * Wang et al. [2023b] Tengfei Wang, Bo Zhang, Ting Zhang, Shuyang Gu, Jianmin Bao, Tadas Baltrusaitis, Jingjing Shen, Dong Chen, Fang Wen, Qifeng Chen, et al.  Rodin: A generative model for sculpting 3d digital avatars using diffusion.  In _Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition_ , pages 4563–4573, 2023b.
  * Wang et al. [2023c] Yi Wang, Jian Ma, Ruizhi Shao, Qiao Feng, Yu-Kun Lai, Yebin Liu, and Kun Li.  Humancoser: Layered 3d human generation via semantic-aware diffusion model.  _arXiv preprint arXiv:2312.05804_ , 2023c.
  * Wang et al. [2004] Zhou Wang, Alan C Bovik, Hamid R Sheikh, and Eero P Simoncelli.  Image quality assessment: from error visibility to structural similarity.  _IEEE transactions on image processing_ , 13(4):600–612, 2004.
  * Wu et al. [2016] Jiajun Wu, Chengkai Zhang, Tianfan Xue, Bill Freeman, and Josh Tenenbaum.  Learning a probabilistic latent space of object shapes via 3d generative-adversarial modeling.  _Advances in neural information processing systems_ , 29, 2016.
  * Xiang et al. [2021] Donglai Xiang, Fabian Prada, Timur Bagautdinov, Weipeng Xu, Yuan Dong, He Wen, Jessica Hodgins, and Chenglei Wu.  Modeling clothing as a separate layer for an animatable human avatar.  _ACM Transactions on Graphics (TOG)_ , 40(6):1–15, 2021.
  * Zhang et al. [2024a] Frank Zhang, Yibo Zhang, Quan Zheng, Rui Ma, Wei Hua, Hujun Bao, Weiwei Xu, and Changqing Zou.  3d-scenedreamer: Text-driven 3d-consistent scene generation.  _arXiv preprint arXiv:2403.09439_ , 2024a.
  * Zhang et al. [2024b] Huichao Zhang, Bowen Chen, Hao Yang, Liao Qu, Xu Wang, Li Chen, Chao Long, Feida Zhu, Daniel Du, and Min Zheng.  Avatarverse: High-quality & stable 3d avatar creation from text and pose.  In _Proceedings of the AAAI Conference on Artificial Intelligence_ , pages 7124–7132, 2024b.
  * Zhang et al. [2023] Lvmin Zhang, Anyi Rao, and Maneesh Agrawala.  Adding conditional control to text-to-image diffusion models.  In _Proceedings of the IEEE/CVF International Conference on Computer Vision_ , pages 3836–3847, 2023.
  * Zhengwentai [2023] SUN Zhengwentai.  clip-score: CLIP Score for PyTorch.  https://github.com/taited/clip-score, 2023.  Version 0.1.1.
  * Zhu et al. [2020] Heming Zhu, Yu Cao, Hang Jin, Weikai Chen, Dong Du, Zhangye Wang, Shuguang Cui, and Xiaoguang Han.  Deep fashion3d: A dataset and benchmark for 3d garment reconstruction from single images.  In _Computer Vision–ECCV 2020: 16th European Conference, Glasgow, UK, August 23–28, 2020, Proceedings, Part I 16_ , pages 512–530. Springer, 2020.
  * Zhu et al. [2023] Junzhe Zhu, Peiye Zhuang, and Sanmi Koyejo.  Hifa: High-fidelity text-to-3d generation with advanced diffusion guidance.  In _The Twelfth International Conference on Learning Representations_ , 2023.