#  Demonstration of high sensitivity of microwave-induced resistance
oscillations to circular polarization

M. L. Savchenko  Institute of Solid State Physics, Vienna University of
Technology, 1040 Vienna, Austria  Rzhanov Institute of Semiconductor Physics,
630090 Novosibirsk, Russia  A. Shuvaev  Institute of Solid State Physics,
Vienna University of Technology, 1040 Vienna, Austria  I. A. Dmitriev
Terahertz Center, University of Regensburg, 93040 Regensburg, Germany  S. D.
Ganichev  Terahertz Center, University of Regensburg, 93040 Regensburg,
Germany  Z. D. Kvon  Rzhanov Institute of Semiconductor Physics, 630090
Novosibirsk, Russia  Novosibirsk State University, 630090 Novosibirsk, Russia
A. Pimenov  Institute of Solid State Physics, Vienna University of Technology,
1040 Vienna, Austria

###### Abstract

We demonstrate that long-debated immunity of microwave-induced resistance
oscillations (MIRO) to the sense of circular polarization is not a generic
property of this phenomenon in solid-state two-dimensional electron systems.
Using a large-area GaAs-based heterostructure we detect up to 30 times larger
MIRO signal for the cyclotron resonance (CR) active helicity, fully consistent
with the concurrently measured transmission and the deduced CR shape of the
Drude absorption. We further elaborate conditions to avoid extrinsic factors
capable of producing an apparent immunity of the photoresponse.

In the last two decades, studies of high mobility 2D electron systems (2DES)
in a weakly quantizing magnetic field gave access to a family of fascinating
interrelated magnetooscillation phenomena reflecting various spatial and
spectral resonances that emerge in high Landau levels under application of
static and/or alternating (microwave or terahertz) electric fields Dmitriev
_et al._ (2012); Zudov  _et al._ (2001a); Mani  _et al._ (2002); Zudov  _et
al._ (2003); Yang  _et al._ (2003); Zudov  _et al._ (2001b); Yang  _et al._
(2002); Zhang  _et al._ (2008, 2007); Wiedmann  _et al._ (2010); Smet  _et
al._ (2005); Dorozhkin  _et al._ (2011); Bykov  _et al._ (2010); Levin  _et
al._ (2015); Dorozhkin  _et al._ (2016); Herrmann  _et al._ (2016); Shi  _et
al._ (2017). Experimental research in a growing number of high-mobility 2DES
Konstantinov  _et al._ (2013); Zudov  _et al._ (2014); Kärcher  _et al._
(2016); Yamashiro  _et al._ (2015); Zadorozhko  _et al._ (2018); Otteneder
_et al._ (2018); Friess  _et al._ (2020); Tabrea  _et al._ (2020); Mönch  _et
al._ (2020); Kumaravadivel  _et al._ (2019); Savchenko  _et al._ (2020) and
various conditions have been accompanied by theoretical developments which
provided new insights into the interplay of Landau quantization, disorder, and
interactions in electron kinetics in both weakly and strongly nonequilibrium
regimes of magnetotransport Dmitriev  _et al._ (2012); Ryzhii (1970); Durst
_et al._ (2003); Dmitriev  _et al._ (2003); Andreev  _et al._ (2003); Vavilov
and Aleiner (2004); Dmitriev  _et al._ (2005); Vavilov  _et al._ (2007);
Dmitriev  _et al._ (2009); Raichev (2008); Monarkha and Konstantinov (2019);
Dmitriev (2019); Greenaway  _et al._ (2019); Raichev and Zudov (2020);
Dmitriev  _et al._ (2004); Chepelianskii and Shepelyansky (2009); Mikhailov
(2011); Beltukov and Dyakonov (2016). These studies have been largely
motivated by the discovery of giant microwave-induced resistance oscillations
(MIRO) Zudov  _et al._ (2001a), magnetooscillations of photoresistance
controlled by the ratio of the microwave and cyclotron frequencies, as well as
the radiation-induced zero-resistance states (ZRS) Mani  _et al._ (2002);
Zudov  _et al._ (2003); Yang  _et al._ (2003) that emerge at deep minima of
MIRO and represent a rare example of electric domain instability associated
with negative absolute conductivity in strongly driven 2DES.

Figure 1:  a, Scheme of the experiment (the irradiated sample area is
highlighted). b, c, Magnetic field dependences of (b) the transmittance
$T(B)$, normalized to its maximum value $T_{\text{max}}$, and (c) MIRO in the
longitudinal photoresistance $\delta R$, normalized to the zero field dark
resistance $R(B=0)$, for the right-hand ($\sigma^{+}$, $\eta=1$, red) and
left-hand ($\sigma^{-}$, $\eta=-1$, blue) circularly polarized radiation. d,
The ratios $\delta R(\eta B)/\delta R(-\eta B)$ at extrema of the MIRO signals
(circles in panel c) illustrating the asymmetry of MIRO between the CR-active
and CR-passive polarities of $B$ for $\eta=1$ (red circles) and $\eta=-1$
(blue circles). The solid curve shows the ratio
$A^{\text{D}}(B)/A^{\text{D}}(-B)$ of the Drude absorption calculated for
$\eta=1$ using parameters extracted from the dark transport measurements and
transmission $T(B)$ shown in panel (b).

Despite much progress in unified understanding of the above phenomena, the
developed theory of MIRO is considered inadequate in view of reported puzzling
insensitivity of MIRO to helicity of the incoming radiation Smet  _et al._
(2005); Herrmann  _et al._ (2016). The microscopic theory Dmitriev  _et al._
(2012) predicts a strong asymmetry of MIRO with respect to the polarity of the
magnetic field $B$, applied perpendicular to the 2DES plane, in the case of
circular polarization of incident radiation. According to this theory, at low
radiation intensity $I$ the photoresistance, $\delta
R(B)=IA^{\text{D}}(B)f(|B|)$, can be represented as a product of the
quasiclassical Drude absorptance, $A^{\text{D}}(B)$, which should be strongly
enhanced near the cyclotron resonance (CR) either at positive or negative
$B=\eta B_{\text{CR}}$ depending on the helicity $\eta=\pm 1$ of the incoming
wave, and a mechanism-dependent function $f(|B|)$ which describes the
magnetooscillations and is insensitive to the sign of $B$ or $\eta$. In sharp
contrast to the expected pronounced $B$-asymmetry,

$\delta R(B)/\delta R(-B)=A^{\text{D}}(B)/A^{\text{D}}(-B),$ (1)

the experiments revealed completely symmetric Smet  _et al._ (2005) or weakly
asymmetric Herrmann  _et al._ (2016) magnetooscillations in the
photoresistance. At the same time, these experiments demonstrated a strongly
asymmetric transmittance $T(B)$ through the 2DES, with a single dip at $B=\eta
B_{\text{CR}}$, thus apparently confirming the validity of the quasiclassical
theory behind interrelated $A(B)$ and $T(B)$, as well as the purity of
circular polarization of the incoming wave.

Here we provide a counterexample of GaAs-based 2DES that exhibits an
unmitigated helicity dependence in both transmittance and MIRO in full
agreement with Eq. (1). We thus prove that, in contrary to a widespread view,
the long debated polarization immunity is not a generic property of MIRO in
solid-state 2DES but rather reflects certain yet unknown peculiarities of
technological design and corresponding realization of disorder in particular
structures. We also establish the necessary conditions to avoid extrinsic
electrodynamic effects capable to produce an apparent polarization immunity of
MIRO.

Methods.– Our simultaneous transmittance and photoresistance measurements, see
Fig. 1 (a), were carried out on a heterostructure containing 2DES in a
selectively doped 16-nm GaAs quantum well with AlAs/GaAs superlattice barriers
grown by molecular beam epitaxy SM (1); Baba  _et al._ (1983); Friedland  _et
al._ (1996); Umansky  _et al._ (2009); Manfra (2014). The lateral size of the
van der Pauw sample was $10\times 10\,$mm2, with ohmic Ge/Au/Ni/Au contacts at
the corners. The electron density and mobility extracted from magnetotransport
measurements were $n=7.0\times 10^{11}\,$cm-2 and $\mu=1.0\times
10^{6}\,$cm2/Vs. The sample was irradiated from the substrate side through
circular metallic (Fig. 2) or absorber (Fig. 1) apertures of varying diameter.
Backward-wave oscillators (BWO) were used as stable sources of normally
incident continuous monochromatic radiation with frequency $f=\omega/2\pi$ in
the range between 50 and $500$ GHz. A split-coil superconducting magnet
provided a magnetic field oriented perpendicular to the sample surface. The
photoresistance $\delta R$ (the difference of the resistance signals in the
presence and absence of irradiation) was measured using the double-modulation
technique SM (1). In parallel with the photoresistance, the transmittance
through the sample was measured using a liquid He-cooled bolometer. All
presented results were obtained at temperature of $3.7$ K.

Helicity dependence of MIRO, transmittance, and absorptance.– Figure 1 shows
representative examples of simultaneously measured transmittance $T(B)$ and
photoresistance $\delta R(B)$, recorded for both helicities $\eta=\pm 1$ of
$f=\omega/2\pi=324$ GHz circularly polarized radiation. The transmittance
traces in panel (b) display strong dips at the CRs, $B=\eta B_{\text{CR}}$,
marked by arrows. The absence of any features at opposite $B=-\eta
B_{\text{CR}}$ confirms a high degree of the circular polarization in the
transmitted signal. The photoresistance $\delta R(B)$ in Fig. 1 (c) shows
pronounced MIRO governed by the ratio $\omega/\omega_{\text{c}}$ of the
radiation and cyclotron frequencies. In sharp contrast to previous reports
Smet  _et al._ (2005); Herrmann  _et al._ (2016), our results reveal a high
asymmetry of MIRO with respect to polarity of $B$ which inverts with the
change of radiation helicity $\eta$. This is one of our central observations
which unequivocally demonstrates that the long debated polarization immunity
is not a generic property of MIRO in solid-state 2DES.

Moreover, we find an excellent quantitative agreement between the shape of CR
in measured $T(B)$ and the $B$-asymmetry of the MIRO signal, in full
accordance with Eq. (1). This agreement is illustrated in Fig. 1 (d) where we
plot ratios $\delta R(\eta B)/\delta R(-\eta B)$ of MIRO signal between CR-
active and CR-passive polarities of $B$, for both helicities. Here we use
values of $\delta R$ at the opposite-lying MIRO extrema marked by circles in
panel (c). It is seen that the asymmetry is strongly enhanced in the region of
CR reaching values of $\sim 30$ for the main MIRO extrema around
$\omega=\omega_{\text{c}}$. Solid and dashed lines show the corresponding
ratio $A^{\text{D}}(B)/A^{\text{D}}(-B)$ of the Drude absorption calculated
using parameters extracted from the shape of $T(B)$ in panel (b), for 100%
right circular polarization and for 98% to 2% mixture of right and left
polarizations, respectively. An almost perfect agreement with Eq. (1)
demonstrates an ultimate sensitivity of MIRO to circular polarization. It is
important to emphasize that this comparison, detailed below, does not assume
any specific microscopic mechanism of MIRO. It rather establishes that
polarization dependences of MIRO and of Drude absorption are the same.

Modelling of transmittance and absorptance.– As detailed in Supplemental
Material SM (1), the shape of $T(B)$ can be well reproduced using the standard
expression, $T(B)=4/|s_{1}(1+Z_{0}\sigma_{\eta})+s_{2}|^{2}$, with the complex
dynamic conductivity $\sigma_{\eta}=\sigma_{xx}+i\eta\sigma_{yx}$ of 2DES
taken in the classical Drude form,
$\sigma^{\text{D}}_{\eta}=e^{2}n/(\mu^{-1}-iB_{\text{CR}}+i\eta B)$, and with
two complex parameters $s_{1,2}=\cos\phi-in_{r}^{\mp 1}\sin\phi$ describing
the Fabry-Pérot interference due to multiple reflections in the GaAs
substrate. Here, the interference phase $2\phi=4\pi w/\lambda_{r}$ is given by
the ratio of the sample thickness $w$ and the wavelength
$\lambda_{r}=c/fn_{r}$, $n_{r}$ is the refractive index of the substrate, and
$Z_{0}\approx 377$ $\Omega$ is the impedance of free space. The resulting
Drude transmittance $T^{\text{D}}$ and Drude absorptance,
$A^{\text{D}}=Z_{0}T^{\text{D}}\mathrm{Re}\,\sigma^{\text{D}}_{\eta}$, are
given by

$T^{\text{D}}(B)=|\alpha|^{2}\left|1-\dfrac{\beta}{\mu^{-1}+\beta-
iB_{\text{CR}}+i\eta B}\right|^{2},$ (2)
$A^{\text{D}}(B)=\dfrac{Z_{0}|\alpha|^{2}e^{2}n/\mu}{|\mu^{-1}+\beta-
iB_{\text{CR}}+i\eta B|^{2}},$ (3)

where $\alpha=2/(s_{1}+s_{2})$ and $\beta=enZ_{0}/(1+s_{1}/s_{2})$. The shape
of measured $T(B)$ in Fig. 1 is well reproduced by Eq. (2) using
$\mu^{-1}=0.01$ T extracted from magnetotransport measurements,
$B_{\text{CR}}=m_{\text{CR}}\omega/e=0.83$ T corresponding to the cyclotron
mass $m_{\text{CR}}=0.071m_{0}$, and $\beta=(0.183+i\,0.127)$ T SM (1). On top
of smooth Drude transmittance, our high resolution measurements are able to
resolve weak quantum $\omega/\omega_{\text{c}}$-oscillations studied in Ref.
[Savchenko  _et al._ , 2021]. The extracted parameters are used in calculated
ratios $A^{\text{D}}(B)/A^{\text{D}}(-B)$ in Fig. 1(d), which establish the
validity of Eq. (1).

Aperture dependence of the polarization-sensitive measurements. –

Figure 2:  a, MIRO signal measured at $\nu=329$ GHz ($\lambda\approx 0.9$ mm)
using metallic apertures with different diameter as indicated. b, Normalized
transmission through the sample measured in situ.

While the strong helicity dependence is unambiguously demonstrated in Fig. 1,
our further measurements have shown that this result can be strongly affected
by metallic aperture that is typically used to avoid illumination of the
contacts and sample edges in this type of experiments. To explore this issue
we performed a detailed study of the effect of aperture diameter on the
helicity dependence. Figure 2 shows the $B$-dependencies of the
photoresistance (top panel) and transmittance (bottom panel) measured at 329
GHz ($\lambda\approx 0.9$ mm) with varying diameter of the aperture. Top panel
demonstrates that the MIRO asymmetry strongly depends on the diameter of
aperture when other experimental parameters are kept unchanged. We clearly see
that the MIRO ratio $\delta R(B)/\delta R(-B)$ is the largest for 8 mm
aperture and tends towards unity for the diaphragms smaller than the estimated
size of the focal spot of about 4 mm. On the contrary, the transmittance
signal in the bottom panel does not considerably change for different
apertures.

We explain such behavior as follows: The MIRO signal is sensitive to the
polarization of the local electromagnetic field. If the aperture size is too
small such that the radiation interacts with the metallic edges, then the
local polarization in the nearby 2DES will be linear regardless of the
incident degree of the circular polarization. This follows from the boundary
conditions requiring that the $E$–field can only have a normal component at
the metal surface Landau and Lifshitz (Pergamon, Oxford, 1984). Therefore, the
radiation that reaches the metal aperture results in a distortion of the local
polarization and, consequently, of the detected photoresistance signal
reflecting the local absorption.

The appearance of local linearly-polarized electric field can be understood
considering a circularly polarized wave irradiating a circular metallic
waveguide, see Supplemental Material SM (1) for details. The distribution of
local circularly-rotating electric fields that fulfil the boundary conditions
is given by:

$E_{+}=-iEJ_{0}(k_{r}r),\qquad E_{-}=-ie^{2i\varphi}EJ_{2}(k_{r}r).$ (4)

Here $J_{n}$ are the Bessel functions of $n$-th order, $k_{r}$ is the radial
wavevector of the lowest propagating mode in a circular waveguide, $E_{\pm}$
are right- and left-rotating circular fields, $E$ is the amplitude of the
incident electric field.

Figure 3:  a, b, Amplitudes of the circular polarization decomposition of the
local field: the incident $E_{+}$ (a) and distorted $E_{-}$ (b) polarizations.
c, MIRO ratio in experiments with varying diameter of the diaphragm. Symbols
represent the experiment, lines are calculated using Eq. (5) and assuming that
the local ratio of circular and linear polarizations is equal to the relative
power transmitted through the aperture (see text for details). Arrow indicates
a characteristic size of the focal spot.

The distributions of the circular components $E_{+}$ and $E_{-}$ are shown in
Fig. 3 (a) and (b), respectively. The amplitude of $E_{+}\sim J_{0}(k_{r}r)$
polarization is rotationally symmetric across the waveguide with a flat
maximum in the middle. Obviously, this is the same polarization as that of the
incident circularly-polarized beam. On the contrary, the $E_{-}\sim
J_{2}(k_{r}r)$ is zero in the middle of the waveguide and changes sign four
times along the wall of the waveguide.

According to the Huygens-Fresnel principle the amplitude of the transmitted
wave is proportional to the sum of secondary sources from all points on the
wavefront. After integration of the $E_{-}$ fields, negative and positive
regions cancel each other. Thereby, the distorted polarization is absent in
the far field and produces no signal at the bolometer. That is the reason why
all curves in Fig. 2 (b) show only one well-defined CR. In contrast to the
transmittance, the absorbed power and MIRO are proportional to the square of
the local near field. Therefore, the response to the distorted polarization
does not vanish in resistivity signal.

In Fig. 3 (c) we show the ratio of MIRO amplitudes for active and passive
circular polarizations as function of $d/\lambda$, where $d$ is the diameter
of the metallic aperture and $\lambda$ is the radiation wavelength. In order
to estimate the ratio of intensities for active ($I_{\text{A}}$) and passive
($I_{\text{P}}$) circular polarizations we calculate the power ratio that is
cut off by the aperture in the focus of the lens. The radial distribution of
the field in the focus Born and Wolf (2000) is given by

$I=I_{0}\mathrm{J}_{1}(x)/x\ ,$ (5)

where $x=\pi d/2N\lambda$ is the normalized aperture diameter, and
$N=F/D\approx 3.6$ is the $f$-number of the focusing lens with diameter
$D\approx 4.5$ cm and focal length $F\approx 16$ cm. Model curves in Fig. 3
(c) are calculated using Eq. (5) and taking $I_{\text{A}}/I_{\text{P}}=50$
(solid line, $\lambda=0.92$ mm) and $I_{\text{A}}/I_{\text{P}}=32$ (dashed
line, $\lambda=1.42$ mm). The difference in the amplitudes originates from the
frequency dependence of the MIRO ratio from Eq. (3),
$I_{\text{A}}/I_{\text{P}}\sim f^{2}$. This yields a reasonable fit to the
experimental points in spite of qualitative character of the arguments.
Indeed, the MIRO ratio tends to unity for apertures below the diffraction spot
$d=1.22N\lambda$ indicated by the arrow.

Discussion. – Our results demonstrate that the long-debated polarization
immunity is not universal intrinsic property of MIRO in solid-state 2DES: (i)
we detect strong intrinsic helicity dependence of MIRO that accurately follows
the regular CR in the Drude absorption and (ii) we show that extrinsic factors
deteriorating the polarization state of radiation can be avoided using
sufficiently large samples and apertures. On the other hand, very recent
experiments Mönch  _et al._ (2022), where several samples of similar size were
studied at terahertz frequencies, revealed a helicity immunity of the resonant
photoresponse which directly measures the CR absorption via heating of 2DES.
This clearly indicates that the helicity immunity problem remains and,
moreover, has a more fundamental character, i.e. is not limited to MIRO. A
possible reason Mönch  _et al._ (2022) is that in particular 2DES the internal
high-frequency response of electrons to a uniform external field can be
essentially nonuniform, producing an intrinsic helicity distortion of the near
field in the vicinity of individual strong scattering centers or
inhomogeneities. Altogether, these results indicate an interesting research
direction deserving further experimental and theoretical efforts.

Conclusions. – In the sub-terahertz frequency range we observe MIRO in
GaAs/AlGaAs 2DES that are ultimately sensitive to the helicity of circularly
polarized radiation. The helicity dependence accurately follows that of the
Drude absorption, in full agreement with natural expectations. Moreover, we
demonstrate that observation of intrinsic polarization dependence requires
large sample sizes and large apertures. Otherwise, the near field reaching
2DES has a significant component of opposite helicity, which does not affect
the transmittance measured in the far field, but essentially changes the
asymmetry of the MIRO signal leading to apparent polarization immunity. Our
results provide the opportunity to reliably test other systems potentially
featuring an intriguing intrinsic polarization immunity of the photoresponse.

Acknowledgements. – The authors thank E. Mönch, D. A. Kozlov, D. G. Polyakov,
and J. H. Smet for valuable discussions. We are grateful to A. K. Bakarov and
A. A. Bykov for providing high-quality GaAs/AlGaAs samples. We acknowledge the
financial support of the Austrian Science Funds (I 3456-N27, I 5539-N), and of
the German Research Foundation (Deutsche Forschungsgemeinschaft) via grant DM
1/5-1 (I.A.D.) and via sub-project A04 of the Project-ID 314695032 – SFB 1277
(S.D.G).

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SUPPLEMENTAL MATERIAL

##  S1 Helicity dependence of transmittance, Drude absorptance, and MIRO

The main experimental finding of our work is strong helicity dependence of
MIRO signal in the studied 2DES. It sharply contrasts all previous studies of
solid-state 2DES which reported polarization immunity of MIRO in the case of
circularly polarized radiation. Thus, our findings prove that the polarization
immunity is not a universal intrinsic property of MIRO but rather a sample-
dependent property possibly reflecting different disorder realization in
particular structures.

Moreover, for our sample we are able to demonstrate that, in agreement with
theoretical predictions Dmitriev  _et al._ (2012), the ratio of measured MIRO
signal for opposite magnetic field polarities accurately follows that of the
Drude absorptance $A^{\text{D}}(B)$, as long as extrinsic electrodynamic
effects related to too small aperture or sample size in comparison to the
laser beam and wavelength are suppressed, see Sec. S4. As detailed below, this
conclusion is based on analysis of simultaneously measured transmittance which
readily provides the parameters of the corresponding $A^{\text{D}}(B)$ taking
into account both strong reflection of radiation from 2DES in the region of CR
and Fabry-Pérot interference in the dielectric substrate. For completeness, an
explicit derivation of the corresponding standard expressions for
transmittance and absorptance for uniform 2DES from Maxwell equations is
provided in Sec. S3.

In Fig. S1 we show the transmittance data presented in Fig. 1 of main text
together with the Drude fit obtained using Eq. (2) of the main text (shown
below and derived in Sec. S3):

$T^{\text{D}}(B)=|\alpha|^{2}\left|1-\dfrac{\beta}{\mu^{-1}+\beta-
iB_{\text{CR}}+i\eta B}\right|^{2}.$ (S1)

In the classical Drude approximation (S1), the shape of transmittance is fixed
by the position of the CR, $B_{\text{CR}}=2\pi fm_{\text{CR}}/e=0.83$ T, which
can be accurately determined from the position of the deep minimum in measured
$T(B)$; by the mobility $\mu=10^{6}$ cm2/m s, which was extracted from dark
resistance measurements, see Sec. S8, and by complex fitting parameter
$\beta=enZ_{0}/(1+s_{1}/s_{2})$, see the main text and Sec. S3, which provides
a combined description of strong reflection of radiation from 2DES in the
region of CR and Fabry-Pérot interference due to multiple reflections in the
dielectric substrate. Fit of the measured transmittance using
$\beta\approx(0.183+i\,0.127)$ T is shown by red solid line. It is seen that
the shape of measured $T(B)$ (black line) is well captured by Eq. (S1), apart
from weak quantum oscillations coupled to harmonics of CR which were studied
in our previous work Savchenko  _et al._ (2021) and are not directly relevant
to the present discussion of helicity dependence of MIRO. A dashed line in
Fig. S1 shows $T^{\text{D}}(B)$ obtained using Eq. (S1) where all parameters
are kept the same apart from $\mu^{-1}$, that is set to zero. The dashed and
solid red lines are very close to each other, which reflects the fact that in
our high-mobility and high-density 2DES, the CR broadening is mainly due to
strong reflection of radiation from 2DES and not due to impurity scattering,
$\mathrm{Re}\,\beta\gg\mu^{-1}=0.01$ T.

The analysis of $T(B)$ readily gives the corresponding shape of the Drude
absorptance,

$A^{\text{D}}(B)=\dfrac{Z_{0}|\alpha|^{2}e^{2}n/\mu}{|\mu^{-1}+\beta-
iB_{\text{CR}}+i\eta B|^{2}},$ (S2)

illustrated by blue line in Fig. S1. Similar to transmittance, the shape of
$A^{\text{D}}(B)$ (normalized to its maximal value $A_{\text{max}}$ in Fig.
S1) is almost insensitive to scattering. This is illustrated by dashed blue
line showing $A^{\text{D}}(B)/A_{\text{max}}$ in the clean limit
$\mu\to\infty$. The value $A_{\text{max}}\propto\mu^{-1}$ is, of course,
sensitive to scattering, but this does not affect the helicity dependence of
absorptance and MIRO and thus is irrelevant for our discussion. It is also
worth mentioning that the Fabry-Pérot interference in the substrate, producing
an asymmetric shape of $T(B)$ in the case of $\mathrm{Im}\,\beta\neq 0$, also
leads to a significant shift of the CR maximum in absorption from
$B_{\text{CR}}$ to $B_{\text{CR}}-\mathrm{Im}\,\beta$, see arrows in Fig. S1.

Figure S1:  Magnetic field dependence of transmittance measured at frequency
$f=324$ GHz (black), its Drude fit using Eq. (S1) (red), and the corresponding
Drude absorption (S2), normalized to its maximal value, $A_{\text{max}}$
(blue). The dotted lines show transmission and normalized absorption in a
clean limit, i.e for transport mobility $\mu\rightarrow\infty$.

According to theoretical predictions Dmitriev  _et al._ (2012), MIRO in high-
mobility 2DES in the case of circular polarization can be represented as a
product

$\delta R(B)=I_{\eta}A_{\eta}^{\text{D}}(B)f(|B|),$ (S3)

where $I_{\eta}$ and $\eta=\pm 1$ are intensity and helicity of the incident
wave, $A_{\eta}^{\text{D}}(B)$ is the corresponding Drude absorption (S2), and
$f(|B|)$ is a mechanism-specific function which describes magnetooscillations
and depends only on the magnitude but not polarity of the magnetic field
applied at normal to the 2DES plane. From the theoretical viewpoint, the
relation (S3) in high-mobility 2DES remains valid as long as the intensity is
low enough, such that the photoresponce remains linear, $\delta R(B)\propto
I_{\eta}$. This linearity in our study is confirmed by measurements of MIRO at
different power levels of the source, see Sec. S5. The form of MIRO in Eq.
(S3) implies that the $B$-asymmetry (and, thus, the helicity dependence) of
the Drude absorption and MIRO should be the same:

$\delta R(B)/\delta R(-B)=A^{\text{D}}(B)/A^{\text{D}}(-B),$ (S4)

see Eq. (1) of the main text. This relation does not involve the mechanism-
specific function $f(|B|)$ and thus can be verified independently, without
full analysis of the detected MIRO within specific mechanisms which will be
presented elsewhere.

Comparison of the MIRO and Drude absorption ratios in Fig. 1(d) demonstrates
that the relation (S4) holds for our data. We attribute somewhat lower MIRO
ratios in comparison to the Drude absorption ratios calculated for 100 %
$\eta=1$ circular polarization to the presence of a small component with an
opposite helicity in the incoming radiation. To estimate the amount of such
admixture, we also calculate the absorption ratio for an imperfect
polarization,

$A^{\text{D}}(B)/A^{\text{D}}(-B)=\sum_{\eta}c_{\eta}A_{\eta}^{\text{D}}(B)/\sum_{\eta}c_{\eta}A_{\eta}^{\text{D}}(-B),$
(S5)

and find that admixture of 2 % of $\eta=-1$ circular polarization, i.e.
$c_{-1}=0.02$ and $c_{1}=0.98$, is sufficient to perfectly fit the data for
$\delta R(B)/\delta R(-B)$, see dashed line in Fig. 1(d).

The data in Fig. 1 were obtained using the absorbing aperture of $\approx 10$
mm diameter at $f=324$ Ghz. Figure S2 shows several further examples of the
analysis presented above, but now for data obtained with metallic aperture of
$8$ mm diameter at three different frequencies of $\eta=1$ radiation. Also
here we observe an excellent agreement between helicity dependence
($B$-asymmetry) of MIRO and absorption. The best fit in the region of CR is
obtained for using an admixture of 3% (for two lower $f$) or 5% (for the
highest $f$) of $\eta=-1$ component in the intensity of incident wave. Apart
from confirmation of the results in Fig. 1, it shows that using $8$ mm
metallic aperture at $f$ above $300$ GHz is sufficient to suppress the
extrinsic effects capable to mask strong intrinsic helicity dependence of
MIRO. These effects, see Sec. S4, become strong at lower frequencies, see Sec.
S6, or for smaller aperture size, see Fig. 2 of the main text. Thus, our
results, establishing the conditions necessary to avoid deterioration of the
polarization state of radiation reaching 2DES, provide the opportunity to
reliably test other systems potentially featuring an intriguing intrinsic
polarization immunity of the photoresponse.

##  S2 Transmittance, MIRO, and MIRO ratios at different frequencies

Figure S2:  Experimental transmittance and MIRO measured at $f=314$ GHz
(left), $329$ GHz (middle) and $416$ GHz (right), and their analysis. a, b and
c, Magnetic field dependences of transmittance, their Drude fits and
corresponding calculated normalized Drude absorption. d, e and f, Magnetic
field dependences of MIRO in the longitudinal photoresistance $\delta R$,
normalized to the zero field dark resistance $R(B=0)$. Dots mark MIRO extrema;
the corresponding ratios $\delta R(B)/\delta R(-B)$ vs. $1/B$ are plotted in
g, h and i illustrating the asymmetry of MIRO between the CR-active and CR-
passive polarities of $B$. The wine curves show the ratio
$A^{\text{D}}(B)/A^{\text{D}}(-B)$ of the Drude absorption calculated for 100%
$\eta=1$ polarization using parameters extracted from the dark transport
measurements and transmission $T(B)$ shown in top panels. The experimental
points are best fitted if the absorption is calculated using an admixture of
3% (g and h) or 5% (i) of $\eta=-1$ CR-passive component in the intensity of
incident wave.

##  S3 Derivation of expression for transmission of a plane electromagnetic
wave though a sample containing a uniform isotropic 2DES

Here we apply a standard theory of transmission though a stratified media to
our case of a circularly polarised wave normally incident on a sample
containing a uniform isotropic 2DES, and obtain expressions for transmittance
and absorptance used in the main text and Sec. S1.

Consider an incident plane electromagnetic wave with electric field given by
the real part of ${\bf E}_{i}=E_{0}{\mathbf{e}}_{\eta}\exp(-i\omega t+ikz)$
where the polarization vector ${\bf e}_{\eta}={\bf e}_{x}+i\eta{\bf e}_{y}$
corresponds to a circular polarization with helicity $\eta=\pm 1$. The wave is
normally incident on the back (substrate) side of the sample at $z=0$. The
sample is modelled as a dielectric slab with refractive index $n_{r}$ and
thickness $w$ that contains a 2DES at a negligibly small distance $w-z_{1}\ll
1/k$ from the opposite front interface at $z=w$. The wave is partially
transmitted and partially reflected at both back and front interfaces. By
continuity of the tangential electric field at all interfaces (note that
normal components of the high-frequency field do not appear in this problem in
the case of a uniform 2DES), the electric field acting on electrons in this
setup is given by ${\bf E}|_{z=w}=t{\bf E}_{i}|_{z=0}$, and the same
transmission amplitude $t$ determines the transmittance $T(B)=|t|^{2}$. For a
uniform isotropic 2DES, characterised by a local dynamic conductivity tensor
$\hat{\sigma}$ with components $\sigma_{xx}=\sigma_{yy}$ and
$\sigma_{xy}=-\sigma_{yx}$, the sense of rotation of fields in all reflected
and transmitted partial waves is the same, and coincides with that of the
induced electrical current in 2DES, ${\bf j}=\hat{\sigma}{\bf
E}=\sigma_{\eta}{\bf E}$. Indeed, the conductivity tensor $\hat{\sigma}$ is
diagonal in the helicity basis, $\hat{\sigma}{\bf e}_{\eta}=\sigma_{\eta}{\bf
e}_{\eta}$ with $\sigma_{\eta}=\sigma_{xx}+i\eta\sigma_{xy}$. Therefore,
propagation of both circularly polarized modes can be considered
independently. The problem is reduced to determination of the scalar
coefficients $c_{\pm}(z)$ in electric and magnetic field distributions in the
whole space,

$\displaystyle{\bf E}(z)$ $\displaystyle=$ $\displaystyle
E_{0}{\mathbf{e}}_{\eta}e^{-i\omega t}[c_{+}(z)e^{ikz}+c_{-}(z)e^{-ikz}],$
$\displaystyle Z_{0}{\bf H}(z)$ $\displaystyle=$
$\displaystyle(kc/\omega)E_{0}({\mathbf{e}}_{z}\times{\mathbf{e}}_{\eta})e^{-i\omega
t}[c_{+}(z)e^{ikz}-c_{-}(z)e^{-ikz}],$ (S6)

where $Z_{0}$ is the vacuum impedance, and the wave vector $k=n_{r}\omega/c$
inside and $k=\omega/c$ outside the sample. According to the Maxwell
equations, both ${\bf E}$ and ${\bf H}$ are continuous at the dielectric
interfaces. Across the 2DES plane, the magnetic field experience a jump given
by ${\bf H}(w+0)-{\bf H}(w-0)=-{\mathbf{e}}_{z}\times{\bf j}$. Implementing
these boundary conditions, one arrives at a matrix equation $A(w+0)={\cal
M}_{\text{2DES}}{\cal M}_{\text{diel}}A(0)$ for a vector $A(z)=(E,Z_{0}H)^{T}$
constructed from the electric and magnetic field amplitudes. This equation,
explicitly given by

$\binom{t}{t}=\begin{pmatrix}1&0\\\
-Z_{0}\sigma_{\eta}&1\end{pmatrix}\begin{pmatrix}\cos\phi&in_{r}^{-1}\sin\phi\\\
in_{r}\sin\phi&\cos\phi\end{pmatrix}\binom{1+r}{1-r}\,,\qquad\phi=wn_{r}\omega/c,$
(S7)

relates the value of $A(w+0)=(t,t)^{T}$ for the wave transmitted through the
front interface to $A(0)=(1+r,1-r)^{T}$ combining the incident and reflected
waves at the back interface. Two transfer matrices ${\cal M}_{\text{diel}}$
and ${\cal M}_{\text{2DES}}$ describe propagation through the dielectric
substrate and 2DES, correspondingly. Solution of Eq. (S7) yields the standard
expression for transmittance,

$T(B)=|t|^{2}=\dfrac{4}{|s_{1}(1+Z_{0}\sigma_{\eta})+s_{2}|^{2}},\qquad
s_{1,2}=\cos\phi-in_{r}^{\mp 1}\sin\phi,$ (S8)

as well as related expressions for reflectance $|r|^{2}$ and absorptance
$A(B)=1-|r|^{2}-|t|^{2}=Z_{0}|t|^{2}\text{Re}\sigma_{\eta}$.

With the complex dynamic conductivity $\sigma_{\eta}$ of 2DES taken in the
classical Drude form,
$\sigma^{\text{D}}_{\eta}=e^{2}n/(\mu^{-1}-iB_{\text{CR}}+i\eta B)$, from Eq.
(S8) one obtains Eqs. (2) and (3) of the main text for the Drude transmittance
$T^{\text{D}}(B)$ and absorptance $A^{\text{D}}(B)$. In Sec. S1, these
expressions are used to demonstrate that the $B$-asymmetry of the Drude
absorptance and MIRO in our sample are the same, as long as extrinsic
electrodynamic effects are excluded, see Sec. S4. In Sec. S1, it is also
demonstrated that the shape of both $T^{\text{D}}(B)$ and $A^{\text{D}}(B)$ in
our sample are almost insensitive to the impurity scattering, and can well
reproduced using conductivity
$\sigma^{\text{C}}_{\eta}=ie^{2}n/(B_{\text{CR}}-\eta B)$ of a clean 2DES, see
dashed lines in Fig. S1.

##  S4 Influence of extrinsic factors which explains differences in
polarization dependence of transmission and photoresistance

Mathematically, the appearance of local linearly-polarized electric field can
be understood considering a circularly polarized wave falling on a circular
metallic waveguide. Although in the general case several eigenmodes of the
waveguide will be excited, the mode closest to a circular plane wave is the
TE1,1 mode. Electric fields of this mode in cylindrical coordinates are given
by (common factor is $\exp(\imath(n\varphi+k_{z}z-\omega t))$):

$\displaystyle E_{r}$ $\displaystyle=$ $\displaystyle-
iE_{0}\frac{J_{n}(k_{r}r)}{k_{r}r}\,,$ $\displaystyle E_{\varphi}$
$\displaystyle=$ $\displaystyle E_{0}\frac{dJ_{n}(k_{r}r)}{d(k_{r}r)}\,,$ (S9)
$\displaystyle E_{z}$ $\displaystyle=$ $\displaystyle 0\,.$

Here $J_{n}$ are the Bessel functions of the $n$-th order, $n=1$ for TE1,1
mode, the radial and axial wavevectors are connected by the dispersion
relation $\omega^{2}/c^{2}=k_{r}^{2}+k_{z}^{2}$ and the radial wavevector is
given by $k_{r}=u/R$ with the first root of the derivative of the first Bessel
function $u\approx 1.8412$.

The calculated field lines of electric (orange lines) and magnetic (green
lines) fields of TE1,1 mode are shown in the left panel of Fig. S3. The
electric field lines start and end at the metallic surfaces and are
perpendicular to the cylinder axis. This field distribution rotates clockwise
as a function of time. In the center of the waveguide the TE1,1 mode
reproduces exactly the circularly polarized wave and fulfils the boundary
conditions of a normal electric field at the edges. Locally, electric fields
can be decomposed into a sum of left-rotation and right-rotating circular
fields via $E_{\pm}=E_{x}\pm iE_{y}$. Here $E_{x}$ and $E_{y}$ are the fields
in Eq. (S9) expressed in the cartesian coordinates. Finally, the momentarily
distribution of local circularly-rotating fields are given by:

$E_{+}=-\imath e^{2\imath\varphi}EJ_{2}(k_{r}r),\qquad E_{-}=-\imath
EJ_{0}(k_{r}r).$ (S10)

Figure S3:  Left panel: momentarily distribution of electric (orange) and
magnetic (green) fields for a TE1,1 mode of a circular waveguide. Middle and
right panels: decomposition of the eigenmode into local right- (middle) and
left-rotating electric fields.

The distributions of the circular components $E_{-}$ and $E_{+}$ are shown in
Fig. S3 in the middle and right panels, respectively. The amplitude of $E_{-}$
polarization is rotation-symmetric across the waveguide with a flat maximum in
the middle. Obviously, this is the same polarization as that of incident
circularly-polarized beam. On the contrary, the $E_{+}$ polarization is zero
in the middle of the waveguide and changes sign four times along the wall of
the waveguide (see red and blue regions in the right panel). This is the
distorted polarization due to the boundary condition at the metal surface.

Importantly, the distorted polarization is absent in the far field and
produces zero signal at the bolometer. According to the Huygens-Fresnel
principle the amplitude of the transmitted wave is proportional to the sum of
secondary sources from all of the points on the wavefront. After integration
of the $E_{+}$ fields, negative and positive regions cancel each other.
Contrary to a linear response in transmittance, the MIRO signal reflects local
near field containing both circular components. Therefore, the response to the
distorted polarization does not vanish in MIRO signal.

Figure S4: Dependence of the MIRO ratio on the sample aperture. MIRO ratio in
experiments with varying diameter of the diaphragm. Symbols - experiment,
lines are calculated using Eq. (S11) and assuming that the the local ratio of
circular and linear polarizations is equal to the relative power transmitted
through the diaphragm (see text for details). Arrow indicates a characteristic
size of the focal spot.

Solid symbols in Fig. S4 show the ratio of MIRO amplitudes for active and
passive circular polarizations as function of the size of the aperture. To
compare the results in different experiments we plot MIRO as a function of
ratio $d/\lambda$, where $d$ is the diameter of the metallic diaphragm and
$\lambda$ is the wavelength. The data have been obtained for $\nu=325$ GHz
(spheres) and $\nu=211$ GHz (triangles). Although an estimate of the local
field distributions based on the TE1,1 mode provides a qualitative explanation
of the observed effect, it does explain the relation between MIRO ratio and
the diameter of the aperture. In order to get an estimate of this relation we
suggest to attribute it to a power ratio that is cut off by the diaphragm in
the focus of the lens. The radial distribution of the field in the focus Born
and Wolf (2000) is given by

$I=I_{0}\mathrm{J}_{1}(x)/x\ ,$ (S11)

where $x=\pi d/2N\lambda$ is the renormalized ratio of the diaphragm diameter
$d$ and the wavelength $\lambda$. Here $N=F/D\approx 3.6$ is the $f$-number of
the focusing lens with diameter $D\approx 4.5$ cm and focal length $F\approx
16$ cm. We assume that the ratio of the circularly- and linearly-polarized
light in the sample plane is equal to the fraction of the power transmitted
through the diaphragm. Model curves in Fig. S4 are calculated using Eq. (S11)
and taking $I_{A}/I_{\text{P}}=50$ (solid line) and
$I_{\text{A}}/I_{\text{P}}=32$ (dashed line) for $\nu=325$ GHz and $\nu=211$
GHz, respectively. The difference in the amplitudes originates from the
frequency dependence of the MIRO ratio Herrmann  _et al._ (2016)
$I_{A}/I_{\text{P}}\sim\nu^{2}$. We conclude a reasonable fit to the
experimental points in spite of qualitative character of the given arguments.

##  S5 Power dependence of MIRO

Figure S5:  (a) Magnetic field dependences of photoresistance $\delta R(B)$
measured at frequency $f=202.4\,$GHz and for the right-hand circular
polarization for different levels of the radiation power $P$ (in units of full
power $P_{\text{max}}$, see legend). (b) The amplitude of MIRO $\delta
R^{\text{amp}}$ for $f=202.4$ and 325 GHz versus radiation power $P$
(symbols). The straight line demonstrates that the MIRO amplitude is
proportional to $P$ in the whole studied range.

##  S6 Transmittance and MIRO at different frequencies

The sample insert consists of a fixed part with the beam aperture and the
movable part with the sample. The sample is fixed on a thin (6 to 13 $\mu$m)
Mylar foil which is clipped to the movable rod of the insert (Fig. S6 (a)).

In Fig. S6 (b) we show the frequency dependence of transmittance $T(f)$ at
$B=0$ which clearly demonstrates the Fabry-Pérot interference due to internal
reflections between back and front interfaces of the sample.Black spheres
represent the experimental data, while the red line is calculated according to
Eq. (2) of the main text (or Eq. (S8) in SM). Big color spheres correspond to
6 frequencies at which transmittance and MIRO are measured on panels (c) and
(d).

In Fig. S6 (c) and (d) we show the dependences of normalized transmittance and
photoresistance on normalized $B/B_{CR}$ measured using 8 mm aperture and
circularly polarized radiation. Panel (d) demonstrates that the MIRO asymmetry
strongly depends on the frequency – it increases as frequency goes up. This
observation can be explained by the influence of the metallic aperture at low
ratios of the aperture size vs. the radiation wavelength. This finding is in
line with observation and explanation of the influence of the aperture size on
MIRO asymmetry, see Fig. 2 and discussion in the main text and in Sec. S4.

Figure S6:  (a) Mounting of the sample. (b) Transmittance $T(f)$ at $B=0$ as a
function of radiation frequency $f$. Symbols represent the experimental data
points, while the red line shows a fit according to Eq. (2) of the main text
[Eq. (S8) in SM]. Big color spheres correspond to frequencies at which
measured transmittance and MIRO are presented on bottom panels. (c) and (d)
Dependences of normalized to its maximum value transmittance
$T/T_{\text{max}}$ and photoresistance $\delta R/|\delta R|^{\text{max}}$ vs
$B/B_{CR}$ measured at indicating frequencies and for the left-hand circular
polarization.

##  S7 MIRO measurements using double modulation technique

Usually the microwave-induced resistance oscillations (MIRO) are measured
under continuous microwave illumination. The photoresponce is thereby obtained
by comparing the magnetic field dependencies $R^{\text{on}}$ and
$R^{\text{off}}$ of the longitudinal resistance in the presence and absence of
radiation. But at low radiation power the amplitude of MIRO becomes small, and
this approach is not optimal. Moreover, in our setup the transmittance of
radiation is measured using a mechanical chopper such that the incoming
radiation is modulated at frequency $f_{\text{chopper}}$. Therefore, we
measure photoresistance $\delta R=R^{\text{on}}-R^{\text{off}}$ using a double
modulation technique specified below.

In our measurements, see Fig. S7 (a), the chopper frequency
$f_{\text{chopper}}=23\,$Hz and a small bias current
$I_{\text{dc}}=1-50\,\mu$A is applied to the sample at much higher frequency
$f_{\text{current}}=433\,$Hz. The photoresistance is collected as a part of
the signal that is modulated at both frequencies: the first lock-in collects
the total signal at higher frequency $f_{\text{current}}$, while its output is
fed to the input of the second lock-in tuned to the lower frequency
$f_{\text{chopper}}$. The output signal of the second lock-in gives the value
of $\delta R$.

The comparison of the direct measurements of $\delta
R=R^{\text{on}}-R^{\text{off}}$ and using of the double modulation technique
is shown in Fig. S7 (b) and (c). It is seen that both methods coincide rather
well.

Figure S7:  (a) Illustration of the double-modulation technique used in the
measurements of photoresistance $\delta R$. Here the chopper frequency
$f_{\text{chopper}}=23\,$Hz and the bias current is applied at higher
frequency $f_{\text{current}}=433\,$Hz. The difference photoresistance signal
$\delta R$ is obtained by using two lock-ins connected in series, where the
first one collects the signal which oscillates in phase with the applied bias
at frequency $f_{\text{current}}=433\,$Hz, while the second collects the part
$\delta R=R^{\text{on}}-R^{\text{off}}$ of the resulting dc resistance which
oscillates in phase with the microwave power modulated at frequency
$f_{\text{chopper}}=23\,$Hz. (b) Direct measurement of the resistance with
(red) and without (black) radiation. (c) Comparison of $\delta R$ direct
measurements (black) and double modulation technique (blue).

##  S8 Transmittance, longitudinal resistance, and MIRO before and after room
light illumination of the sample

Figure S8:  Magnetic field dependences of normalized transmittance
$T/T_{\text{max}}(B)$ (a), longitudinal resistance $R(B)$ (b), and
photoresistance $\delta R(B)$ (c) measured simultaneously at frequency
$f=325\,$GHz and for the right-hand circular polarization. Black and red
colors correspond to the sample state before and after room light illumination
of the sample, respectively. It is seen that in studied sample the room light
illumination does not affect much the electron density (which would otherwise
modify the shape of transmittance), the mobility, as well as the MIRO strength
and high $B$-asymmetry reflecting high sensitivity of MIRO to radiation
helicity.

##  S9 Technological design of the studied 2DES

Figure S9:  Heterostructure cross-section above quantum well with 2DES (left)
and bellow it (right).


# Memory Maps for Video Object Detection and Tracking on UAVs

Benjamin Kiefer1, Yitong Quan1 and Andreas Zell1 1All authors are with the
Faculty of Computer Science, University of Tuebingen, Germany.
<EMAIL_ADDRESS>
###### Abstract

This paper introduces a novel approach to video object detection detection and
tracking on Unmanned Aerial Vehicles (UAVs). By incorporating metadata, the
proposed approach creates a memory map of object locations in actual world
coordinates, providing a more robust and interpretable representation of
object locations in both, image space and the real world. We use this
representation to boost confidences, resulting in improved performance for
several temporal computer vision tasks, such as video object detection, short
and long-term single and multi-object tracking, and video anomaly detection.
These findings confirm the benefits of metadata in enhancing the capabilities
of UAVs in the field of temporal computer vision and pave the way for further
advancements in this area.

##  I Introduction

When we make predictions about the presence and location of objects, we have
an internal understanding of our surrounding world: implicitly, we know where
we are in relation to the object and we know about the topology of a given
scene. This internal understanding of the surrounding geometry allows us to
reason robustly about the existence and location of objects. Furthermore,
while we make detection errors when shown ambiguous static scenes, over time,
we are able to strengthen our belief about our predictions. This is due to
slight changes in appearance caused by different view points, slight movement
of objects or just by integrating our predictions over a certain period of
time.

We argue that this awareness of our surrounding is particularly important in
aerial scenarios, where we need to reason about our environment in the
presence of many uncertainties, caused by the smallness of objects. Motivated
and inspired by this human-based analogy, in this work, we aim to improve
several computer vision tasks for object detection and tracking on UAVs.

Figure 1: Illustration of predictions and the corresponding 3D
geometry/topology. We aggregate information over time, taking the correct 3D
geometry into account.

Conventional techniques for object detection and tracking from UAV
perspectives ignore the intrinsic geometry and topology present in UAV-
generated imagery, frequently relying on off-the-shelf methods designed for
COCO-like scenarios or with slight modifications, see e.g. [1]. This makes it
difficult for these methods to aggregate uncertain predictions over time,
since movements in image space cannot correctly be tracked and, hence,
features are hard to be associated temporally.

We argue that this shortcoming can easily be mitigated by leveraging freely
available sensors onboard the UAV. GPS alongside compass and IMU measurements
allow us to reason about our and the objects’ locations in 3D coordinates. In
turn, this allows us to create a _temporal memory map_ of previous
predictions, so that we can aggregate information over time in a geometrically
sensible way, resulting in more robust predictions.

In this work, we show how correctly considering the 3D geometry allows us to
propose a temporal memory map that results in more robust predictions. In
particular, our contributions are as follows:

  * •

We derive mathematical formulas detailing the 3D geometry around a UAV.

  * •

Leverage metadata, we propose a memory map to robustify several temporal
computer vision tasks, such as video object detection, tracking and anomaly
detection.

  * •

We capture PeopleOnGrass-Video, a benchmark featuring 4K 30 FPS manually
annotated video, featuring precise metadata labels and make it publicly
available. Furthermore, we capture and annotate more data for multiple further
experiments and release it publicly.

  * •

We show in multiple experiments on diverse benchmarks the utility of our
method.

##  II Related Work

Figure 2: Illustration of variables and formulas to estimate the vertical
distance $y$ (red lines) and the horizontal distance $x$ (yellow lines,
illustrated on bottom left) from the UAV to the swimmer (orange cross).

Although video object detection (VOD) on UAVs has become more relevant, with
many applications emerging and many network architectures becoming fast enough
to deploy on embedded devices, there is still no consensus on which VOD
approach seems to be the most promising. Broadly speaking, there are optical
flow-based networks, memory networks and tracking-based networks [2]. While
memory networks, such as STDnet-ST [3], achieve high accuracies, their heavy
architectures prohibit their deployment on embedded devices. Optical flow-
based networks are faster, but their benefit over single-frame object
detectors is limited [4]. Most tracking-based networks first do single-frame
object detection and use the association for the detection reciprocally [5].
In fact, the best two VOD models of the last VisDrone-VID challenge were
single-frame methods, entirely ignoring the temporal domain [6].

Furthermore, all common video object detectors on UAVs ignore the underlying
3D geometry of the scene and only operate in image space [2]. While there is
much research focusing on geolocation, it is only focused on obtaining world
coordinates of objects for downstream tasks, such as following a target [7].
Similarly, occupancy networks and other mapping approaches aim at obtaining a
map for mapping or scene understanding [8].

As opposed to these works, we aim to leverage metadata to build a memory map
in GPS space that _improves the video object detection performance_. Since we
only rely on freely available metadata onboard the UAV, this approach is
viable for small UAVs with a standard RGB camera in low-cost settings (compare
to active geolocation via laser [9]).

##  III Deriving Formulas for 3D Geometry

Figure 3: Corresponding image example for the computation in Figure 2. Here,
we have that $h=20m$ and $\beta=15^{\circ}$ resulting in $y=110m$ and $x=25m$.
This means, that the swimmer is $110m$ in front and $25m$ to the right of the
UAV as measured on the ground. Note that we also estimate the horizon line as
indicated by the blue line.

Figure 2 illustrates that we would like to know the GPS position of the
swimmer as indicated by the orange cross. How do we obtain that? First, we
discuss how to obtain relative coordinates to the UAV, then how to use these
to obtain actual world coordinates via passive geolocation.

###  III-A Relative Coordinates

We consider a mathematical perspective projection camera model since this
resembles the common use-case for cameras on UAVs. We consider our camera to
have a focal length $f$ given in pixels. For simplicity, we assume our image
to be of 4K (3840x2160) resolution. Other resolutions follow an analogous
derivation. Our camera is looking down at an angle of $\beta$, which is the
variable gimbal angle. The gimbal also balances a potential UAV roll angle, so
that we assume there to be a zero camera roll angle.

First, we estimate the on-ground distance from the UAV to the red line, which
we denote as $y$ (see Figure 2). We assume the ground to be flat, i.e. we
ignore elevation change and the curvature of the earth. The latter is a
reasonable assumption for heights that are typical for UAV missions [10],
while the first may make a difference in very dynamic terrains.

Using the focal length $f$ and the y-axis pixel position offset $v$ from the
horizontal center pixel line of the image, we compute $y$ by computing the
angle $\alpha$ via

$\alpha=\arctan\left(\frac{v}{f}\right).$ (1)

This allows us to compute $y$ via

$y=\tan(90^{\circ}-(\beta-\alpha))h.$ (2)

Having the vertical ground-distance to the object of interest, we compute the
horizontal ground-distance $x$ by looking from the top as indicated on the
bottom left of Figure 2. For that, we need the variables $d$ and $w$, which
both are easily computed via Pythagoras’ theorem, which then yield $x$:

$\displaystyle d=\sqrt{h^{2}+y^{2}},\text{ }w=\sqrt{f^{2}+v^{2}},\text{
}x=\frac{u}{w}d.$ (3)

For simplicity, we ignored the sign of $x$, which indicated whether we are on
the left or on the right of the vertical center line. Naturally, in the actual
implementation, we incorporate that. Likewise for the special cases when an
object of interest is behind the UAV, which happens for gimbal angles close to
$90^{\circ}$.

Furthermore, we compute the horizon line in image space following a similar
derivation as [11]. Ignoring the effect of atmospheric refraction, we estimate
the distance to the horizon line $l$ as a function of the height of the UAV as

$l=3.57h^{1/2}.$ (4)

This approximation is fairly accurate for heights that are typical for our
scenarios (far below 1000m) [10]. We compute the angle $\gamma$ to the horizon
via

$\gamma=\arcsin(h/l).$ (5)

Using the focal length $f$ and the camera gimbal pitch $\beta$, we compute the
camera perspective projection of the horizon on the image plane, which yields
the height offset $o$ in pixels to the horizontal center line of the image
plane as

$o=\tan(|\gamma-\beta|)\cdot f\cdot\operatorname{sgn}(\gamma-\beta).$ (6)

Finally, we need to truncate $o$ to be within the range of the number of
allowable horizontal pixels. We refer to [11] for a discussion on accuracy.
Lastly, note if there is a lens distortion, then we undistort the image before
running the above algorithm.

###  III-B Absolute Coordinates

Using the relative coordinates of an object ($x$\- and $y$\- ground-distances
to UAV), we compute its GPS coordinates based on the UAV’s GPS coordinates as
follows. Given the camera heading angle $\theta$, we compute the rotation
matrix and rotate the relative coordinates of an object to obtain

$\begin{bmatrix}x_{r}\\\ y_{r}\\\
1\end{bmatrix}=\begin{bmatrix}\cos(\theta)&\sin(\theta)&0\\\
\sin(\theta)&\cos(\theta)&0\\\ 0&0&1\end{bmatrix}\begin{bmatrix}x\\\ y\\\
1\end{bmatrix}.$ (7)

Finally, we map the relative coordinates to GPS coordinates via

$\displaystyle la^{object}$ $\displaystyle=la+\frac{y_{r}}{r}\frac{180}{\pi},$
(8) $\displaystyle lo^{object}$
$\displaystyle=lo+\frac{x_{r}}{r}\frac{180}{\pi}\frac{1}{\cos(lat\ \pi/180)}.$
(9)

We note that we compute the earth radius based on the latitude to account for
the slight ellipsoid nature of the earth. Lastly, note that we can reverse the
computation to map from 3D to 2D, i.e. the image space (see code that we’ll
make publicly available).

##  IV Method: Temporal Memory

Classical grid maps in robotics, such as occupancy grid maps, divide the
environment into single grid cells and estimate the occupancy probability for
each cell [12]. We also aim to build temporary memory maps but in the context
of modeling dynamic objects of interest. While there are several works
extending occupancy grid maps to account for dynamic objects, e.g. [13], our
focus is on leveraging maps to improve the downstream performance of computer
vision detection and tracking algorithms over time. Hence, we propose a simple
class of what we denote _temporal memory maps_.

###  IV-A Map Representation

We consider a UAV-centric map with a fixed size context window, i.e., given
the latitude $la_{t}$ and longitude $lo_{t}$ of the UAV at discrete time step
$t$, the memory map is defined to be

$\displaystyle M_{t}=\left\\{\begin{pmatrix}x\\\
y\end{pmatrix}\bigg{|}\begin{matrix}x\in\\{la_{t}-\frac{c}{2}+\frac{j}{n}|j\in
0,...,n(la_{t}+\frac{c}{2})\\}\\\ y\in\\{lo_{t}-\frac{c}{2}+\frac{j}{n}|j\in
0,...,n(lo_{t}+\frac{c}{2})\\}\end{matrix}\right\\},$ (10)

which denotes a quadratic, north-oriented map around $la_{t}$ and $lo_{t}$ of
edge size $c$ with $n^{2}$ equidistantly spaced elements. Note that $c$ and
$n$ should be problem-dependent reasonable quantities. This treatment makes
sure that the surrounding environment of the UAV can be considered at all
times. Note that $c$ should be large enough to account for the relevant field
of view of the UAV and $n$ should be large enough to have sufficient
resolution. Furthermore, the map will forget information that is outside of
the context window, which needs to be considered in downstream applications.

From here, the exact procedure of how to update and leverage the map differs
between the computer vision tasks. Broadly speaking, all methods define a
memory map on $M_{t}$, indicating likelihoods of object locations.

###  IV-B Video Object Detection

Figure 4: Distance (x-axis) to size (y-axis) relation for all swimmers in
SeaDronesSee object detection train set (orange dots). The blue area denotes
the accepted area of sizes.

After analyzing single-image object detectors, we found that most trained
object detectors can detect almost all objects before the non-maximum
suppression (NMS) stage, which in our case is doing both, removing duplicate
boxes and low-confidence ones. Perhaps unsurprisingly, this is due to object
detectors distributing many anchors across the image, from which potential
objects are regressed. However, detections tend to cluster around actual
objects, thereby achieving theoretical recall values of close to one.

An immediate observation yields that we can filter out predictions based on
their sizes. Common object detectors employ multiple stages, responsible for
multiple scales. Often, the detectors output predictions, whose sizes are far
off from any reasonable quantities. By looking at the distance $d$ and the
class indicator of any predicted object, we establish a distance-to-size (size
measured by diameter of the box) relation and analyze it on the SeaDronesSee
object detection train set (see Figure 5). For each class separately, we
perform a Gaussian process regression on these data points. This yields a mean
function $m(x)$ and a covariance function $cov(x)$. We scale the covariance
function by a factor dependent on the distance from the maximal to the minimal
bounding box size in a small interval around $x$. Finally, we check whether a
new prediction is inside the resulting accepted area, and if not, we discard
that prediction (see Figure 4). Applying this procedure on the three best
models of the SeaDronesSee Object Detection v2 challenge, Table I shows that
we can already remove a small amount of FPs.

Figure 5: Blue boxes are true positive detections, the red box is a false positive swimmer detection that was successfully filtered out by analyzing the distance-size relation. Model name | #B | Rem.FP | Rem.TP | %
---|---|---|---|---
Maritime-VSA [14] | 674K | 8,087 | 24 | 1.2
DetectoRS [14] | 838K | 6,705 | 67 | 0.8
YOLOv7-Sea [14] | 378K | 4,926 | 54 | 1.3
TABLE I: Numbers of removed (Rem.) boxes (B) for best three models trained and
tested on SeaDronesSee Object Detection v2.

Nevertheless, there needs to be a suppression stage because the high recall
still comes at the cost of many false positive bounding boxes. We argue that
robust detection can be achieved by temporally and geometrically sensible
aggregation of many of the low-confidence detections that cluster around
actual objects. Since we do this aggregation in actual GPS space, we can
cumulate likelihoods from different viewpoints, hence this treatment is
theoretically invariant to camera movements, which often cause traditional
methods, tracking features across frames, to fail (e.g. see Figure 7).

Figure 6: Before NMS, there are many low-confidence detections, but they
cluster around actual objects. Ignoring the confidence, these detections would
yield a recall value of one. For visualization, only one-colored boxes. Figure
7: A heading change of the camera results in three swimmers (detected in left
frame) being lost in subsequent frames (right frame) (DeepSORT [14]).

To provide evidence for the initial claim about the high recall before NMS, we
train a Faster R-CNN ResNet-18 and a YOLOv7 (configs from [14]) on
SeaDronesSee v2 [14]. For evaluation, we remove the NMS stage and obtain
recall values of 97.4 % and 98.8%, resp. Compare that to the recall after NMS
stage: 86.4% resp. 87.6%. See also Figure 6 for a sample image showing pre-NMS
detections.

This leads us to hypothesize that a large part of missing detections can be
obtained (and also false detections can be suppressed) if the confidence
scores are modified such that low-confidence detections in _GPS areas_ , where
there have been detections for several consecutive time steps, are boosted,
and, simultaneously, (semi-)confident false positive detections are suppressed
if they only appear in certain frames (randomly).

Memory Map Construction:

Therefore, we propose to map all detections before NMS to GPS space as
follows. For every box detection
$b_{i}=[x^{i}_{1},x^{i}_{2},y^{i}_{1},y^{i}_{2}]$, $i=1,\dots,m$, we take its
bounding box center $[(x^{i}_{2}+x^{i}_{1})/2,(y^{i}_{2}+y^{i}_{1})/2]$ and
compute its GPS coordinates $g^{b_{i}}=[la^{b_{i}},lo^{b_{i}}]$ via the
formulas in Section III. We compute the closest grid window to $g^{b_{i}}$ via

$w^{b_{i}}=\operatorname*{arg\,min}_{m\in M_{t}}||g^{b_{i}}-m||.$ (11)

Ideally, this is the actual GPS position of that prediction. However, to
account for imprecision in the sensor data and deviations from taking the
center of the bounding box (which may not be the GPS center of the object), we
assign weight to the neighbouring space as well, albeit less, since
$w^{b_{i}}$ is our best single-point prediction111Naively applying this method
on all boxes before filtering of incorrectly sized boxes leads to too large or
small bounding boxes becoming boosted.. Hence, we construct a memory map
likelihood over $M_{t}$ as follows: We add a truncated Gaussian density with
radius $r$ at $w^{b_{i}}$, i.e.,

$\tilde{p}_{t}(x)\leftarrow\tilde{p}_{t}(x)+se^{-x^{2}}\text{ for
}x\in{[w^{b_{i}}-r,w^{b_{i}}+r]\subset M_{t}},$ (12)

where we slightly abuse the notation by mixing scalars and vectors
(computation to be understood component-wise). Note that we hid the other
parameters (constants and variance) in the scaling factor $s$, which we will
_additionally_ make dependent on the confidences $c_{i}$ belonging to $b_{i}$.

After every time step, we truncate $\tilde{p}$, such that the memory map
values are $\leq 1$ at all times:

$p_{t}(x)=\min(\tilde{p}_{t}(x),1).$ (13)

Furthermore, we introduce a forgetting factor $\phi$, by which the memory map
$p_{t}$ is rescaled after each update step so that the memory map will not be
overloaded over time.:

$p_{t}(x)\leftarrow\phi p_{t}(x).$ (14)

Note that we explicitely did not model $p_{t}$ as a probability distribution
over $M_{t}$ as this would introduce a competition of weights among the
objects leading to deteriorated results when the number of objects and their
prediction certainty vary (similar to a discrete Bayes filter [15], although
here, we do not have a control update).

Adjusting the Detector Confidences According to $p_{t}$:

At time $t$, each bounding box $b_{i}$ has a confidence $c_{i}\in[0,1]$, which
we will update based on $p_{t-1}$ via

$\hat{c}_{i}=c_{i}+p_{t-1}(w^{b_{i}}).$ (15)

Note that we do not update the map based on the updated confidence
$\hat{c}_{i}$ but on the original $c_{i}$. Lastly, note that we perform this
procedure _class-wise_ , so we keep a map for each class separately. After the
procedure, we proceed with standard NMS.

###  IV-C Extension to Object Tracking and Reidentification

Similarly as for VOD, a _temporal memory map_ helps in tracking scenarios. We
apply the memory map to object tracking via a simple extension.

For frame $t$, we use the GPS location of each tracked object in frame $t-1$.
We take the boosted predictions of frame $t$ closest to the old GPS location
with a confidence above a threshold as the new location (in image and GPS
space) of the object to be tracked. We will see that this simple formulation
of a tracker helps to track objects over time in presence of camera movements,
such as in Figure 7. Even if a fast camera movement yielding blurry frames
results in the object detector missing the object temporally - if an object
will be redetected in subsequent frames - the object can be assigned the
correct ID again.

While there is benefit in using memory maps for _short-term_ tracking tasks,
they are especially beneficial in _long-term_ tracking, where ground truth
objects may leave the frame entirely. The task of reidentification in
classical scenarios is solved by feature-based comparison of objects across
time. In UAV-based domains, this often fails for small objects as features
look similar across different objects. However, the treatment in GPS space
allows us to remember where an object was, allowing us to reidentify it in
subsequent frames over a pre-defined time horizon.

###  IV-D Extension to Video Anomaly Detection

The goal of video anomaly detection is to output regions of the frames that
are considered anomalous, either spatially (from appearance) or temporally
(unseen movements). Since anomalies are not well-defined, methods achieve only
limited success in completely detecting all anomalies, and the aerial nature
leads to highly ambiguous scenes leading to many false positive detections as
well [11]. Hence, this task is far from solved.

However, we may assume anomalies to be temporally stable, i.e. they exist over
a considerable period of time. This makes it ideal to aggregate information at
certain GPS positions over a sequence of frames. Since it is hard to
explicitly define regions that are anomalous, most methods output an anomaly
heatmap, indicating areas of likely anomalies. Therefore, we propose to map
the entire image plane to GPS space and aggregate anomalous regions over time
in a geometrically reasonable way. We note that this requires an efficient
vectorized implementation to still achieve real-time inference. Section V-C
discusses this shortly.

For the correct mapping of pixels to GPS coordinates, we need to make sure
that the projection is well-defined. Therefore, we apply the previously
introduced horizon cutter, which first computes the horizon and only maps the
pixels below it to GPS space. We ignore pixels too far in the horizon as this
results in too much noise.

We replace the 2D difference heat map from [11] with our memory map, which
will be added to the previous memory map. After each step, we also apply a
forgetting factor $\phi$. Afterwards, we apply the same post-processing steps
as indicated there.

##  V results and analysis

Figure 8: Example frame from our captured benchmark POG-V taken at $31$m
altitude and a gimbal pitch angle of $41^{\circ}$.

Since there is only one publicly available dataset for VOD and Multi-Object
Tracking that employs precise metadata (SeaDronesSee-MOT [16]), we collect and
manually annotate another dataset, People-On-Grass-Video (POG-V), depicting
people walking on grass and similar terrain (see example in Figure 8). It
comes with the same type of metadata annotation as SeaDronesSee-MOT. In
particular, we used a Zenmuse X5 camera mounted on a DJI Matrice 100 for
collection. We collected 10,633 frames in 30 fps videos with 3840x2160
resolution. We annotated 48,802 instances of people using
DarkLabel222https://github.com/darkpgmr/DarkLabel. We made sure to have a
great variance w.r.t. to altitude ($h=10m$-$100m$) and gimbal pitch angle
($\beta=17^{\circ}$-$90^{\circ}$).

Note that we focus on the detection of people in both benchmarks only, since
this is the hardest class to detect [14]. For that, we fuse the classes
_swimmers_ , _swimmers with life jacket_ and _life jacket_ into a single
people class in SeaDronesSee-V (SeaDronesSee-MOT without instance IDs).

For short-term tracking, we also employ SeaDronesSee-MOT. It currently only
supports short-term tracking, i.e. objects that left the scene and reappear do
not have the same id. Therefore, we relabel a video clip of SeaDronesSee-MOT,
such that it also supports long-term tracking, which we need to assess the
performance of long-term tracking (reidentification).

For Video Anomaly Detection, we fall back to the OpenWater data set of the
Maritime Anomaly Detection Benchmark [17] since it is the only one featuring
metadata.

Finally, we perform additional experiments to evaluate an extension to
multiple UAVs in a collaborative scenario.

###  V-A Video Object Detection

| SeaDronesSee-V | POG-V |
---|---|---|---
Model name | AP50 | AR | AP50 | AR | FPS
DFF [18] | 53.7 | 34.2 | 30.3 | 18.8 | 3.4
FGFA [19] | 53.9 | 34.1 | 34.7 | 24.8 | 1.6
T.R.A. [20] | 60.6 | 42.9 | 29.9 | 19.3 | 2.4
YOLOv7Tiny | 68.2 | 41.1 | 81.3 | 36.2 | 25.1
+Mem. Map | 72.8 | 44.0 | 84.4 | 38.8 | 25.1
TABLE II: Video Object Detection accuracy for Swimmers and People on
SeaDronesSee-Video and POG-Video, respectively. The last column denotes
running times (wall-clock time in frames per second) benchmarked on an Nvidia
Xavier AGX.

We apply the proposed memory map on the output of a YOLOv7-Tiny [21] trained
and tested on SeaDronesSee-V and POG-V, respectively. We choose a grid with
$0.5$m resolution and a size of $300$m. We truncate the Gaussian updates with
a radius of $6$m.

As baselines, we take the well-known Video Object Detectors Deep Feature Flow
(DFF) [18], Flow-guided Feature Aggregation (FGFA) [19] and the recent
Temporal RoI Align (T.R.A.) [20] as implemented in [22] with their default
configuration.

Table II shows that incorporating our memory maps leads to increased AP50 and
AR (average recall with averaged IoU levels 0.5:0.05:0.95 and at most 100
detections) values by successfully boosting the confidence scores. In
particular, we achieve a +4.6 and +3.1 AP50 increase over the single-image
YOLOv7-Tiny object detector on SeaDronesSee-V and POG-V, respectively.
Interestingly, popular video object detectors lack behind in performance
because they are not targeted to aerial VOD. Moreover, the increased AR values
shows that our method detects more objects, which is the main challenge in
UAV-based detection.

Figure 9 visualizes the temporal memory map, projected to the image space. It
shows the heatmap values of likely object locations, which were aggregated
from the previous frames. The red areas cluster around actual objects. This
results in pre-NMS boxes becoming boosted, as Figure 10 shows. While the
baseline YOLOv7-Tiny originally did not detect a single swimmer, now we detect
eight.

Figure 9: Heatmap illustration of memory map on a SeaDronesSee-V test frame.
We project actual GPS latitude and longitude lines to image space. We also
project the memory map from GPS space to image space and visualize it as a
heatmap. The right image part shows that the memory map successfully puts
weight around actual swimmers’ locations. Compare also to the zoomed-in crop
and Figure 1 and 10. Figure 10: Before NMS, many swimmers are predicted (black
boxes), several of which are automatically removed due to incorrect sizes (red
boxes). Only the confidences of the green boxes are boosted. Applying a
confidence threshold of 0.5 yields that 8 swimmers are detected as opposed to
none for the baseline (experiment with YOLOv7-Tiny).

Furthermore, the standard video object detectors are not suitable for
deployment on embedded devices. Our method only adds a negligible time to a
standard YOLOv7-Tiny, which can run in real-time on an Nvidia Xavier AGX.

###  V-B Object Tracking

Applying our method on SeaDronesSee-MOT yields an increase in HOTA and MOTA
and a decrease of ID switches and fragmentations over the DeepSORT short-term
tracker (see Table III).

To test the reidentification capability, we run our method on top of a
DeepSORT with reidentification module on the relabeled video as described
earlier. We can successfully reassign the same id to all the objects in the
video whereas the baseline fails to do so (4 people are reassigned new IDs.)

###  V-C Video Anomaly Detection

Table IV shows that adding the module to the anomaly detector from [11] yields
an increase of +3 AR to 82.8 (average recall over multiple levels of
broadcasting rate; measured differently than average recall from object
detection, please refer to [11]). This performance increase is also reflected
in the recall at broadcasting rate of 5$\%$, i.e. there is a +3.8 Rp=5%
improvement over the Autoencoder.

Figure 11 shows the resulting difference anomaly map aggregated over the last
frames and the resulting regions of interest that are returned.

Figure 11: Difference anomaly map aggregated in 3D space over several frames
(top) and resulting regions of interested (bottom).

The speed does not increase considerably over the Autoencoder, still achieving
real-time inference benchmarked on an Nvidia Xavier AGX as Table IV shows.

Model name | HOTA$\uparrow$ | MOTA$\uparrow$ | IDs$\downarrow$ | Frag$\downarrow$
---|---|---|---|---
ByteTracker [14] | 65.0 | 76.9 | 68 | 841
DeepSORT [14] | 66.6 | 80.0 | 44 | 805
+Memory Map | 67.2 | 80.8 | 35 | 721
TABLE III: Multi-Object Tracking accuracy on SeaDronesSee-MOT. We used the output of DeepSORT and built on top a mem. map to become more robust towards id switches and fragmentations. Model name | AR$\uparrow$ | R${}^{p=5\%}\uparrow$ | FPS
---|---|---|---
Gaussian Mixture Model [14] | 45.9 | 2.6 | 17
Mean Filter [14] | 73.9 | 54.3 | 50
Frame Differencing [14] | 76.1 | 54.8 | 62
Autoencoder [14] | 79.8 | 71.0 | 27
+Memory Map | 82.8 | 74.8 | 27
TABLE IV: Video Anomaly Detection accuracy on SeaDronesSee-MOT. We built our
memory maps on top of the Autoencoder [11].

Figure 12: Two UAVs inspect the same scenery from different locations at the
same time. The red camera (left) has a good view on both objects and the goal
(G) while the blue camera (right) is underexposed (brightened for
visualization) and one person is partially occluded by a tree. We aggregate
both memory maps together to obtain more robust detections. Without
considering the underlying geometry, this is not possible with standard video
object detectors.

###  V-D Cooperative Detection via Multiple UAVs

The GPS memory map allows for a joint representation of objects’ locations. In
this section, we demonstrate that it can be leveraged in a collaborative
setting with multiple UAVs. This allows for cross-UAV knowledge transfer and
leads to more robust predictions. Furthermore, it allows for detections of
(partially) occluded objects. For example, Figure 12 shows the same scenery
captured from different locations at the same time with two people are walking
on the grass.

Having a joint location likelihood representation allows the UAVs to share
information. We apply the same memory map from before on both UAVs’ object
detectors’ output, but this time, we average their memory maps in the
overlapping region. For that, we take an EfficientDet-D$0$ trained on POG [17]
and test it on the following data. We capture four minutes of footage in a
similar environment as POG from the viewpoint of two UAVs, a DJI Matrice 210
and a DJI Mavic 2 Pro, denoted _2AVs_. We varied variables, such as altitude,
pitch and heading viewing angle and GPS location. We annotated the people
visible in both video streams and compare the performance of the single-frame
object detector with the memory map from before. We obtain an AP50 of 61.3 for
the single-frame object detector compared to an AP50 of 68.9 for the memory
map.

To shot the utility of a joint memory map for tracking, we compare a fast
single-object tracker, PrDiMP18 [23], to a simple tracker based on the memory
map. For that, we apply an EfficientDet-D$0$ on a consecutive subset of 2AVs
that contains partial occlusions of a person in one video stream (blue camera
in Fig. 12). While the baseline tracker cannot handle the occlusion and fails
to track the person behind the tree entirely (4.3 AP50) for the blue camera,
our method leverages the joint memory map that transfers knowledge from the
red UAV to the blue (86.3 AP50).

The joint memory map also allows for reidentification in long-term tracking
tasks _while the object is moving_. To test this, we take a standard DeepSORT
trained on POG with the default Reid model within mmtracking [22] as baseline.
We take a subset of 2AVs where one camera leaves the scenery entirely, while
the other is tracking the object throughout. When reappearing, it immediately
uses the track id information from the other camera, while DeepSORT failed to
reidentify the object, which we believe to be attributed to the object size.

##  VI Conclusion and Discussion

While not using meta-data remains the standard in computer vision on UAVs,
using metadata to boost the performance shows promising results without
inducing a large computational overhead. We showed that we can improve
standard methods by considering the underlying 3D geometry. Reasoning about
detections, tracklets and anomalies in an interpretable and robust way allows
for more trustworthy methods.

Although in our experiments on POD-Video we did not encounter any problems
with terrain elevation change, future work remains to show how strict the
assumption of even-level terrain is on other benchmarks. For that, it is
inevitable to collect larger and more diverse benchmarks.

In future works, it will be interesting to see how a symbiosis of metadata and
other computer vision tasks looks like. Lastly, it seems relevant to dive into
the topic of uncertainty quantification methods to account for the errors in
metadata values.

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