# Angel’s Girl for Blind Painters: an Efficient Painting Navigation System
Validated by Multimodal Evaluation Approach

Hang Liu, Menghan Hu, Yuzhen Chen, Qingli Li, Guangtao Zhai, Simon X. Yang,
Xiao-Ping Zhang, Xiaokang Yang, This work is sponsored by the Shanghai Sailing
Program (No. 19YF1414100), the National Natural Science Foundation of China
(No. 61831015, No. 61901172), the STCSM (No. 18DZ2270700), the Science and
Technology Commission of Shanghai Municipality (No. 18511102500), and
“Chenguang Program” supported by Shanghai Education Development Foundation and
Shanghai Municipal Education Commission (No. 19CG27).H. Liu, M. Hu, Y. Chen
and Q. Li are with the Shanghai Key Laboratory of Multidimensional Information
Processing, East China Normal University.M. Hu, G. Zhai, and X. Yang are with
the Key Laboratory of Articial Intelligence, Ministry of Education.Simon X.
Yang is with the Advanced Robotics and Intelligent Systems Laboratory, School
of Engineering, University of Guelph.Xiao-Ping Zhang is with the Department of
Electrical, Computer and Biomedical Engineering, Ryerson
University.Corresponding author: Menghan Hu<EMAIL_ADDRESS>
###### Abstract

For people who ardently love painting but unfortunately have visual
impairments, holding a paintbrush to create a work is a very difficult task.
People in this special group are eager to pick up the paintbrush, like
Leonardo da Vinci, to create and make full use of their own talents.
Therefore, to maximally bridge this gap, we propose a painting navigation
system to assist blind people in painting and artistic creation. The proposed
system is composed of cognitive system and guidance system. The system adopts
drawing board positioning based on QR code, brush navigation based on target
detection and bush real-time positioning. Meanwhile, this paper uses human-
computer interaction on the basis of voice and a simple but efficient position
information coding rule. In addition, we design a criterion to efficiently
judge whether the brush reaches the target or not. According to the
experimental results, the thermal curves extracted from the faces of testers
show that it is relatively well accepted by blindfolded and even blind
testers. With the prompt frequency of 1s, the painting navigation system
performs best with the completion degree of $89\%\pm 8.37\%$ and overflow
degree of $347\%\pm 162.14\%$. Meanwhile, the excellent and good types of
brush tip trajectory account for $74\%$, and the relative movement distance is
$4.21\pm 2.51$. This work demonstrates that it is practicable for the blind
people to feel the world through the brush in their hands. In the future, we
plan to deploy “Angle’s Eyes” on the phone to make it more portable. The demo
video of the proposed painting navigation system is available at:
https://doi.org/10.6084/m9.figshare.9760004.v1.

###### Index Terms:

Painting navigation system, Visually impaired artists, Assistive device, QR
code positioning, Multimodal evaluation metrics.

##  I Introduction

According to the recent report of the world health organization, about 1.3
billion people worldwide suffer from various forms of visual impairment, and
about 36 million people are blind [1, z]. Visual organ is one of the most
important sensory organs of human beings. More than 90$\%$ of sensory
information transmitted to human beings is visual [2, 3]. For blind people,
the decline or lack of visual perception brings great inconvenience to their
daily life. They can hardly complete some routine tasks just like walking,
driving, writing and recognizing objects [4, 5]. Vision loss can also greatly
affect artistic creations such as painting. Though having dexterous hands,
many of them find their artistic dreams hard to realize because of visual
inconvenience. They are eager to pick up the paintbrush, like Leonardo da
Vinci, to create and make full use of their own talents. Obstacles that mainly
come from their visual impairments keep their dreams so far away from them!

Painting can not only mould a person’s temperament, but also improve
communication between people [6]. Drawing images can assist the process of
remembering information, which turns out to be a good memory strategy to
quickly grasp a new concept [7, 8] and help acquire knowledge of different
subjects [9, 10]. While painting, people can release their pent-up emotions as
a way to maintain an optimistic attitude [11, 12]. After having taken training
in art, blind people can also better express themselves and adjust their mood
during the process of painting. More benefits can be further obtained by blind
people through artistic creation, such as the development of their brain areas
related to visual memory [13, 14].

White cane, dog guides and wearable vision assistance [15, 16], etc., have
been used to help visually impaired and blind people finish daily tasks.
Recent years have seen a rapid technological development in the navigation
system based on spatial orientation for blind people. The existing navigation
systems to which technologies of route planning and human-computer interaction
are usually applied can provide navigational aids for blind users and protect
them from a fall or a tumble [17, 18]. Zhang et al. designed an indoor
navigation system for blind people by using technologies of ARCore-based
visual positioning and touch-based human-computer interaction [2]. Murata et
al. designed a navigation assistance system for blind people using mobile
phone positioning technology, which offers guidance when blind people walk
around in a large-scale indoor public place [19]. Li et al. designed a new
navigation system based on overall vision, which can help blind people
themselves move about while being indoors [20]. Cordeiro et al. developed a
high level information fusion technology in their navigation system and a
system can automatically calculate the possibility of collision in the moving
process of blind users [21].

Most of the current researches focus on how to use robot sense technologies
(computer vision, ultrasonic sensing, etc.) to help blind people safely and
successfully perform basic daily tasks such as positioning [19, 2, 22] and
obstacle avoidance [21, 23, 24]. As far as we know, there are few studies that
employ sensing technologies such as computer vision to assist blind people in
accomplishing higher-level tasks, including painting.

Traditional drawing auxiliaries for blind people use their tactile perception
and low-tech analog tools to draw images [25, 26]. Vinter et al. designed a
drawing board made out of thin plastic, which is based on tactile perception
[27]. With a pen, the board enables blind people to draw images, though it can
only help create simple geometric patterns due to the low tactile perception
dimension (it is one-dimensional to our knowledge). Thus it is difficult to
help create more vivid images. Kamel and Landay designed a simple static grid
to help blind users, while painting, determine the paper’s locating points
from the start point to the end point [28]. The positioning scheme turns the
paper into the uneven surface paper, which may eventually have a negative
impact on the painting. On the other hand, it is relatively complicated for
blind people to operate owing to the absence of feedback. Concomitant with the
development of science and technology, researchers developed drawing equipment
for blind people based on tactile display. Recently, Bornschein et al. have
designed an array display for blind people to make tactile drawings by means
of two-dimensional tactile input and output matrices [29]. Tactile display
devices can interactively guide blind people in drawing, but they are
expensive and difficult to operate. With protruding points on the drawing
paper affecting user experience, the navigation system for blind people, which
takes tactile sense as the core solution, can only assist blind users to draw
simple and low-dimensional images. In view of the defects of tactile
navigation system for painting, we intend to design a navigation system for
painting using visual assistance, which may enhance blind people’s dimension
of perception with regard to painting space, so as to help add more artistic
appeal to the painting and bring more pleasures of creation.

Therefore, the main contribution of the current work is that we develop an
efficient painting navigation system based on visual aid and auditory feedback
for blind people to help them with painting training and artistic creation.
This painting navigation system is able to serve as an “Angle’s Eyes” of blind
painters, and provide the possibility for them to feel the world through the
brush in their hands.

Aiming at overcoming the difficulties of the painting navigation system for
blind people, we have carried out the following work: (1) to realize the real-
time monitoring and correction of the painting position, we adopt the QR code
positioning technology; (2) to accurately and efficiently identify brush tip
position, we utilize the dynamic brush tip recognition algorithm; (3) to
locate the tip position in an efficient, accurate, and real-time manner, we
divide the painting area using virtual grids. These virtual grids are simply
coded, allowing blind users to easily access the tip location; (4) to achieve
the human-machine information exchange when fulfilling drawing tasks, we
develop a digestible two-way voice interaction method. Blind people can tell
the navigation system where to paint via the pre-designed voice, and then
follow the voice cue to find the targeted region; and (5) to efficiently test
the performance of the painting navigation system, we use the multimodal
evaluation metrics including recognition accuracy and user experience
evaluation. In addition, to explore the navigation effect with different
frequencies of voice prompt, three prompt frequencies namely fast, medium and
slow are set during the comparative experiments.

##  II Design of painting navigation system

The photograph of painting navigation system is illustrated in Fig. 1. The
system mainly consists of drawing board, voice input/output component, main
camera, macro camera, extended display, QR code, data processing terminal,
adjustable camera mount, virtual grid and brush. The above components further
constitute the other modules in the system, thereby realizing the functions of
the painting navigation system. The demo video of the proposed painting
navigation system is available at:
https://doi.org/10.6084/m9.figshare.9760004.v1. In this demo video, the brush
color recognition module is demonstrated. Considering the length of the paper
and the high accuracy rate of the brush color recognition, this module is not
described in this paper.

Figure 1: Setup of the painting navigation system for blind painters.

###  II-A Information Stream in Painting Navigation System

To complete the painting task, the painting navigation system needs to process
multimodal and multilevel information. Consequently, in the process of system
design, it is necessary to understand the information flow. Fig. 2 shows the
path of the main information flow in the proposed painting navigation system.
The main part of painting navigation system is cognitive system and guidance
system. The cognitive system aims to help blind people understand the world
near the drawing board (macro control of drawing area, dynamic recognition of
brush position, access to the targeted drawing region, etc.), and it is
composed of QR code based drawing board positioning module and brush real-time
positioning module. The guidance system aims to build an informational bridge
between the real world and users or services, and its main part is human-
computer interaction module. As shown in Fig. 2, we design the main working
logic among the painting navigation system: locate the stable top view for the
painting navigation system $\rightarrow$ recognise the user’s voice command
information $\rightarrow$ identify the coordinate information via semantic
analysis $\rightarrow$ detect the brush position in real time $\rightarrow$
transmit location information of brush to users in real time. More detailed
working logic diagram is shown in Fig. 3.

Figure 2: Main information flow in painting navigation system. The subjective
assessment methods are used for evaluating the system performance on the
user’s feeling, and the objective assessment methods are used for evaluating
the performance of each technique. Figure 3: Detailed working logic among the
painting navigation system.

###  II-B QR Code based Drawing Board Positioning Module

To help the blind complete the painting task, the drawing board needs to be
positioned. We combine the QR code positioning and the perspective
transformation to achieve the positioning of the drawing board. Four ARUCO
squares with different encoded information are printed on the four sides of
the drawing board. ARUCO markers are synthetic square markers. ARUCO library
was originally developed by Rafael Muñoz and Sergio Garrido [30]. ARUCO
markers comprise a wide black border with an inner binary matrix, so that they
can be recognized quickly [31]. The ARUCO squares are marked as
[$ARUCO_{j}X_{1}$, $ARUCO_{j}Y_{1}$], [$ARUCO_{j}X_{2}$, $ARUCO_{j}Y_{2}$],
[$ARUCO_{j}X_{3}$, $ARUCO_{j}Y_{3}$], and [$ARUCO_{j}X_{4}$,
$ARUCO_{j}Y_{4}$], respectively, where $j$ $\in$ $\\{$1,2,3,4$\\}$. This is
the encoding information of the ARUCO squares. After the system detects an
ARUCO square with corresponding coded information, it will automatically
recognize the four vertex coordinates of the ARUCO square. The designed
drawing board is then imaged by the main camera. Assisted by QR code and
perspective transformation algorithm, the drawing board can be located with
any camera angles. The whole procedure for identifying four QR codes and
calculating their coordinates is presented in Fig. 4. According to the layout
of the ARUCO squares, the corner of ARUCO square closest to the center is one
of the final four location points, and therefore, the final coordinates of
drawing board can be calculated using:

$[X_{i},Y_{i}]=[ARUCO_{j}X_{k},ARUCO_{j}Y_{k}]$ (1)

when $i$ value is 1, 2, 3, and 4, the corresponding $k$ value is 4, 3, 2, and
1, which respectively correspond to the upper left corner, upper right corner,
left bottom corner, and right bottom corner of drawing board.

Figure 4: Procedure for identifying four QR codes and calculating their
coordinates.

Subsequently, the painting region is registered using the perspective
transformation. After this operation, we can realize the transformation of
painting area from squint angle to overhead angle. Let assume that the
coordinates of detected ARUCO squares in the original image and in the
transformed image are respectively $O$=($x_{i}$,$y_{i}$) and
$T$=($x_{i}^{{}^{\prime}}$,$y_{i}^{{}^{\prime}}$), where $i$ $\in$
$\\{$1,2,3,4$\\}$. The correlation between these two coordinates is
$T$=$O$$\times$$M$, where $M$ is the transfer matrix.

The conversion formula of perspective transformation is:

$[x^{{}^{\prime}}\ y^{{}^{\prime}}\ w^{{}^{\prime}}]=[u\ v\ w]M=[u\ v\
w]\begin{bmatrix}a_{11}&a_{12}&a_{13}\\\ a_{21}&a_{22}&a_{23}\\\
a_{31}&a_{32}&a_{33}\end{bmatrix}$ (2)

where ($u$,$v$) is the coordinates from original image, ($x$, $y$) is the
coordinates after conversion. According to formula 2, ($x$, $y$) can be
expressed as:

$(x,y)=(\frac{x^{{}^{\prime}}}{w^{{}^{\prime}}},\frac{y^{{}^{\prime}}}{w^{{}^{\prime}}})=(\frac{a_{11}u+a_{21}v+a_{31}}{a_{13}u+a_{23}v+a_{33}},\frac{a_{12}u+a_{22}v+a_{32}}{a_{13}u+a_{23}v+a_{33}})$
(3)

Let $w=1$, $a_{31}=1$,$a_{32}=1$, $a_{33}=1$, $M$ can be expressed as:

$M=\begin{bmatrix}a_{11}&a_{12}&a_{13}\\\ a_{21}&a_{22}&a_{23}\\\
a_{31}&a_{32}&a_{33}\end{bmatrix}$ (4)

Therefore, we can calculate $M_{1}$ in transformation ($x_{0}$,
$y_{0}$)$\rightarrow$(0, 0), ($x_{1}$, $y_{1}$)$\rightarrow$(1, 0), ($x_{2}$,
$y_{2}$)$\rightarrow$(1, 1), ($x_{3}$, $y_{3}$)$\rightarrow$(0, 1), and can
calculate $M_{2}$ in transformation (0, 0)$\rightarrow$($x_{0}^{’}$,
$y_{0}^{’}$), (1, 0)$\rightarrow$($x_{1}^{’}$, $y_{1}^{’}$), (1,
1)$\rightarrow$($x_{2}^{’}$, $y_{2}^{’}$), (0, 1)$\rightarrow$($x_{3}^{’}$,
$y_{3}^{’}$). The transformation ($x_{0}$, $y_{0}$)$\rightarrow$($x_{0}^{’}$,
$y_{0}^{’}$), ($x_{1}$, $y_{1}$)$\rightarrow$($x_{1}^{’}$, $y_{1}^{’}$),
($x_{2}$, $y_{2}$)$\rightarrow$($x_{2}^{’}$, $y_{2}^{’}$), ($x_{3}$,
$y_{3}$)$\rightarrow$($x_{3}^{’}$, $y_{3}^{’}$) can be seen as: ($x_{0}$,
$y_{0}$)$\rightarrow$(0, 0)$\rightarrow$($x_{0}^{’}$, $y_{0}^{’}$), ($x_{1}$,
$y_{1}$) $\rightarrow$(1, 0)$\rightarrow$($x_{1}^{’}$, $y_{1}^{’}$), ($x_{2}$,
$y_{2}$)$\rightarrow$(1, 1)$\rightarrow$($x_{2}^{’}$, $y_{2}^{’}$), ($x_{3}$,
$y_{3}$)$\rightarrow$(0, 1)$\rightarrow$($x_{3}^{’}$, $y_{3}^{’}$). So that we
can calculate $M$: $M$ = $M_{1}$$M_{2}$.

The coordinates of corner points determined by the image processing method are
discrete observations, and they inevitably will change over time by the user
intervention (move the camera or the panel). To reduce this error, when the
camera detects the ARUCO squares simultaneously, the position of drawing board
is updated.

###  II-C Brush Real-time Positioning Module

To navigate the painting process, it is necessary to identify and locate the
position of brush tip. The process is divided into four steps (Fig. 5): 1)
brush identification: the dynamic target recognition algorithm [32] is adopted
to identify the dynamic objects in the drawing area. In the process of
painting, the drawing area is still, while the brush is dynamic. Therefore,
the brush can be identified through the dynamic target recognition algorithm;
2) brush tip detection: YOLOv3 [33] is used to accurately position the brush
tip; 3) tip’s edge detection: Canny edge operator is applied to detect the
nip’s edge; and 4) tip’s center determination: the points on the edge are
numbered in order. Each edge is a line made up of many points. We assume the
total number of points that make up the line is $M$, and the serial number of
the points is $i$. The curvature of $i$th point is presented as $Cur_{i}$, and
it can be calculated using:

$Cur_{i}=\sqrt{(\sum_{k=-j}^{k=j}(x_{i+k}-x_{i}))^{2}+(\sum_{k=-j}^{k=j}(y_{i+k}-y_{i}))^{2}}$
(5)

where $j$ denotes the curvature calculation range, and $k=1,2,...,j$ is the
serial number within the range determined by $j$. The value of $j$ can be
assigned based on the scale of application scenario. That is, it mainly
depends on the performance of the used camera and the distance between the
used camera and panel. In this case, we set the $j$ as 5.

In the process of drawing, there is a movement speed of the brush tip.
Therefore, the time delay inevitably exists between the past position of brush
tip announced by the painting navigation system via voice and the current
position of brush tip detected by the system. This means that by the time the
user hears the voice announcement, the pen has already moved out of the
targeted area. To fill this time gap as much as possible, we design a new rule
for brush tip positioning. Fig. 6 shows the rule of judging whether the brush
tip reaches target area. We choose a central area from the target area as ‘the
reference area’. The length and width of ‘the reference area’ are labeled as
$a$ and $b$, respectively. The coordinates of central point and brush tip are
set as $(x_{0},y_{0})$ and $(x_{t},y_{t})$, respectively. Assume ${\Delta
x}_{t}=x_{t}-x_{0}$ and ${\Delta y}_{t}=y_{t}-y_{0}$. If ${\Delta x}_{t}$ and
${\Delta y}_{t}$ meet the criterion ${2\Delta x}_{t}\leq\,a$ and ${2\Delta
y}_{t}\leq\,b$, the brush tip reaches the target successfully at the moment
$t$, or the painting navigation continues. This rule reduces the time delay
and is being optimized in our subsequent work.

Figure 5: Process of brush tip detection: a) brush region identification using
dynamic target detection; b) brush tip detection; c) tip’s edge detection via
Canny edge operator; and d) determination of tip’s center based on maximum
curvature. Figure 6: A micro-scenario of the brush tip’s arriving at target
monitoring. The legend indicates the positive direction. The yellow area
denotes the target area while the red area represents central area. ${\Delta
x}_{t}$ represents ($x_{t}-x_{0}$) and ${\Delta y}_{t}$ equals
($y_{t}-y_{0}$). If ${2\Delta x}_{t}\leq\,a$ and ${2\Delta y}_{t}\leq\,b$, the
brush tip reaches the target successfully at the moment $t$.

###  II-D Human-computer Interaction Module

To allow the blind people to better grasp the location information of the
painting area, we use the grid division method to divide the painting area
into 64 small independent areas. It should be noted that these sub-regions are
programmed by virtual grids, which are invisible for people. The schematic
diagram of panel region segmentation and coding is shown in Fig. 7. Each small
area is coded with two letters. The first and second letters of sub-region
represent the row and column where it locates, respectively. For example, the
sub-region in the first column and the fourth row is encoded as “bd”, and the
sub-region in the fourth column and the fifth row is encoded as “de”.

Based on these virtual sub-regions, the process of human-computer interaction
consists of three steps: 1) the user activates the system by the pre-set
voice, and presses a button and enters the desired navigation location by
voice. The speech recognition unit recognizes the user’s voice commands and
parses the data to obtain the targeted location information that needs to be
navigated; 2) the navigation system gains the coordinate of brush tip using
brush positioning module, and then calculates the difference between the
coordinates of the target location and the brush tip. Subsequently, four voice
prompts namely down, up, left and right are used to guide the user to move the
brush to the target location. To avoid confusion, the system only gives
guidance information in one direction at a time. For each navigation, the
system first navigates in vertical dimension, and then guides the user in
horizontal dimension when the vertical and horizontal coordinates of the brush
tip are the same. The guidance in one dimension ends, while the guidance in
another dimension begins. The above operations alternate back and forth until
the targeted region is reached; and 3) when the tip reaches the target
position, the system prompts the user to reach the desired painting area by
voice.

Figure 7: Schematic diagram of panel region segmentation and coding.

###  II-E Multimodal evaluation approach

To verify the practicability of the navigation system, we invite twenty-five
blindfolded people, one blind person, and four blindfolded painters who have
received professional training in painting to use our painting navigation
system. With respect to the testers receiving professional training in
painting, we invite them to use the developed system for personalized
painting. For the testers without receiving professional training in painting,
the target block filling task is designed to evaluate the system performance.
The steps of this filling task are shown in Algorithm 1. This procedure is
also the workflow of the developed navigation system. The main workflow is: 1)
the tester enters coordinate information by voice; 2) the tester looks for the
target location by following the voice prompt; 3) the tester fills in with the
brush; and 4) the system analyzes the filling condition of the target square
to judge whether the color block has been filled. During the experiment, we
record the following test information: 1) the thermal video of tester’s face;
2) probability distribution of brush tip’s occurrence frequency; and 3) the
path of brush tip. After the experiment, we conduct the questionnaire survey
on the testers. The questionnaire is carefully designed based on empathy map.

The introductions for six evaluation approaches are elaborated as follows:

1) Analysis of facial temperature changes: the thermal camera is used to
record the temperature changes of tester in the process of the painting
experiment. By analyzing the local temperature changes in the facial area of
the testers, we can analyze their emotional fluctuations when using the
navigation system. The fluctuation degrees of the temperature of subjects’
faces can reflect the user’s acceptance of the painting system[34].

Figure 8: The illustration of ‘relative movement distance’. The ideal distance
is the length of the straightline between the start point and the end point.
Additionally, the relative movement distance can be obtained by (6). Figure 9:
Thermal diagrams of 9 blindfolded testers and 1 blind tester (these thermal
curves may reflect their emotional fluctuations when using the navigation
system). These thermal curves are derived from 10 testers during two-target
destinations experiments using the navigation system. (A total of 13 testers
were invited, but in three sets of experiments, the thermal imaging camera
malfunctioned or was forgotten to be switched on, so there were three sets of
missing thermal imaging data.)

2) Analysis of probability distribution of brush tip: during navigation, the
system will record the coordinates of the tip every certain time interval
(about 0.3s in this work). After the navigation, the system will automatically
generate the probability distribution map of brush tip. This map reflects the
occurrence frequency of brush tip: in the painting area, the positions with a
high probability are rendered with darker color, while those with a low
probability are rendered with lighter color. On the other hand, the brush
tip’s probability distribution directly indicates the working area involved by
the brush during the task: if the task areas are filled with darker color and
the other areas are filled with lighter color, the navigation performance is
considered to be satisfactory.

3) Analysis of trajectory of brush tip: when the task is completed, the
trajectory of brush tip is generated by connecting the positions of brush tip
in sequence. Through this trajectory, we can analyze the movement velocity,
the movement distance, and movement direction of brush. Intuitively, the
distance between two adjacent points is greater, which indicates the movement
of brush is faster. Simultaneously, the navigation efficiency can be presented
by this trajectory: the shorter the trajectory path is, the higher efficiency
the navigation has. Furthermore, to make movement distance easier to
understand, we introduce ‘relative movement distance’, as elaborated in Fig.
8. We set the straight-line distance between the start point and the end point
as ‘ideal distance’. Subsequently, the ‘relative movement distance’ is
calculated by:

$R=\frac{L_{I}}{L_{M}}$ (6)

where $L_{I}$ denotes the length of the straightline between the start point
and the end point. $L_{M}$ stands for the total length of the brush
trajectory. $R$ means the relative movement distance.

Meanwhile, the navigation system is more efficient when the ‘relative movement
distance’ is smaller.

4) Analysis of task completion: when the filling area in the target block and
the overflowing area account for more than 80$\%$ and less than 375$\%$
respectively, the system considers that the task is completed. The completion
degree and the overflow degree are used to evaluate how well the task is done.
Particularly, we calculate the overflow degree in the following equation:

$O_{D}=\frac{S_{C}-S_{T}}{S_{T}}$ (7)

where $S_{C}$ denotes the area of completed block and $S_{T}$ represents the
area of target block. $O_{D}$ means overflow degree.

The completion degree can be calculated using:

$O_{C}=\frac{S_{R}}{S_{T}}$ (8)

where $O_{D}$ means completion degree. $S_{R}$ and $S_{T}$ represent the area
of completed block in the target area and the area of target block,
respectively.

The smaller the value of overflow degree is, the more accurately it is
painted. The larger the value of completion degree is, the better the task is
completed.

5) Analysis of task completion time: we set three different prompt frequencies
(high frequency: 1s; middle frequency: 2s; low frequency: 3s), and record the
task completion time of each frequency. The task completion time is long,
which indicates the navigation performance is poor; the completion time is
short, which indicates the navigation performance is good. In addition, the
influence of prompt frequencies on the performance of painting navigation
system is analyzed via the tasks with the different prompt frequencies.

6) Analysis of system satisfaction: based on empathy map, we thoughtfully
design the questionnaire to the satisfaction of each tester with the system.
You can get the the blank questionnaire at:
https://doi.org/10.6084/m9.figshare.12611621.v1. The questionnaire contents
include but are not limited to: basic information about the tester;
satisfaction; whether the guiding voice conveyed information clearly enough;
whether the system provided an accurate painting navigation; how difficult for
you to use this system; how much do you think it will help visually impaired
painters.

##  III Results of validation experiments

The developed navigation system is fairly thoroughly validated with the
blindfolded people, the blind person, and blindfolded painters using the
multimodel evaluation approaches. The original results of evaluation
experiments can be found at: https://doi.org/10.6084/m9.figshare.12611621.v1.
The results of validation are elaborated below.

###  III-A Experience of blindfolded and blind users

Six multimodal evaluation metrics are used to assess the experience of the
developed navigation system for both blindfolded and blind users.

1) Analysis of facial temperature changes: the facial temperature changes of
the thirteen users recorded by thermal camera are extracted by image
processing algorithm, and the obtained thermal diagrams of ten users are shown
in Fig. 9. To some extent, these thermal curves can reflect the user’s
emotional fluctuations during the experiment. The fluctuation degrees of all
testers are relatively small except the tester 7’s, suggesting the navigation
system is relatively well accepted by testers. Furthermore, we compare the
thermal curves between the blindfolded and blind users. Intuitively, the
emotional fluctuation degree of the blind user is much smaller (Fig. 9), which
indicates that the blind user can better navigate this painting navigation
system. Due to the loss of vision, the blind people generally do things more
slowly than the people with normal vision. Accumulated over time, the blind
people will be more patient than most people with normal vision. As a result,
the blind people will also appear to be “calmer” when using painting
navigation system. This phenomenon is quantitatively and objectively revealed
in Fig. 9.

Figure 10: Two typical real drawings and their corresponding brush tip
probability distributions for blindfolded and blind users: a) and b) are the
real drawing and the corresponding brush tip probability distribution for
blindfolded user; and c) and d) are the real drawing and the corresponding
brush tip probability distribution for blind user. In the brush tip
probability distribution, the length and width of drawing board are divided
into 25 blocks and 15 blocks, respectively. Meanwhile, the legend explains the
correspondence between color and frequency. The darker the color of block is,
the more often the tip appears.

2) Analysis of probability distribution of brush tip: the two typical real
drawings of blindfolded and blind users and their corresponding brush tip
probability distributions are shown in Fig. 10. We compare these two sets of
data and find it obvious that the probability distribution is in line with the
real image. The task areas are rendered with darker color while the others
have lighter color, which indicates the performance of the navigation system
is satisfactory. Because the traces of the brush tip leave during navigation.
It can be observed that a few areas with color are unrelated to the working
area. These light color area are reasonable and can be omitted when analyzed.
By analyzing all the experimental data, we find that the number of light color
regions is related to the distance between the point where the brush enters
the drawing board and the target area.

TABLE I: Average and standard deviation values of three indicators namely Completion Degree, Overflow Degree, and Relative Movement Distance for two-target experiments. Target |  Completion Degree |  Overflow Degree |  Relative Movement Distance
---|---|---|---
Target BC and Target EG |  89$\%$$\pm$8.37$\%$ |  347$\%$$\pm$162.14% |  4.21$\pm$2.51
Target BC |  85$\%$$\pm$7.83$\%$ |  367$\%$$\pm$198.62$\%$ |  2.93$\pm$1.44
Target EG |  93$\%$$\pm 6.99$$\%$ |  325$\%$$\pm$115.41$\%$ |  6.70$\pm$4.47
Figure 11: Trajectories of brush tip and their corresponding distance
diagrams. Trajectories of brush tip are divided into three categories namely
excellent, good and bad according to its trajectory quality: I, II, and III
represent the excellent, good and bad categories, respectively; a) and b)
represent the trajectory of brush tip and the corresponding distance diagram.
The x coordinate represents the serial number of the sampling points (The
longer the completion time is, the more the sampling points are.) and the y
coordinate denotes the relative distance (The unit of it is pixel.).

3) Analysis of trajectory of brush tip: all brush tip trajectories are divided
into three categories according to its trajectory quality: excellent, good and
bad. Subsequently, we obtain the corresponding distance diagram composed of
the distance from the sample point in the trajectory to the destination. Fig.
11 shows the trajectories and distance diagrams of these three typical
categories. We can easily get the movement direction of brush and distance
change. Obviously, the less messy trajectory is, the more efficient navigation
is. In other words, the curve of excellent category in distance diagram is
smoother with less fluctuation from the upper left to the lower right. The
final results show that the excellent and good types account for 74% (among 23
valid processed results, the number of type excellent and type good results is
17), indicating the efficiency of the navigation system.

Furthermore, when calculating the relative movement distance, we especially
divide the two targets into two parts and then calculate them in three
conditions: Target BC and Target EG, Target BC, and Target EG, as shown in
TABLE I. It can be noted that the relative distance of target BC is much
shorter than target EG’ s. To some extent, hoping to finish the experiment as
soon as possible, the users move the brush too much, so that the final
distance becomes longer. In our experiment, we regard 3.5 as excellent and 4.5
as good. Therefore, the average relative movement distance 4.21 is satisfying.
The results will be even better if users experience it with calmer mood. In
other words, the navigation system may perform better in realistic operation.

Figure 12: The original drawing and the labeled one. The target area is
labeled in every drawing, then the completion ratio and overflow ratio are
computed.

4) Analysis of task completion: completion degree and overflow degree of the
task are shown in TABLE I while the original and the labeled drawings are
shown in Fig. 12. Because of the drawing ways of users, almost every target
block is overflowed, so we introduce the indicator: overflow degree. The
equation is shown in (7).

Notice the completion degrees in all conditions, 89$\%$, 85$\%$ and 93$\%$,
are all a lot more than 80$\%$, which suggests the work is well done. The
overflow degree meets the completion criterion, 375%, while the overflow
degree of target BC is larger than target EG’ s. Considering users have the
experience of completing the first target BC, they are more proficient in
finishing target EG. Accordingly, the overflow degree is better. The
completion degree is excellent and the overflow degree is good while the
standard deviation of both indicators is relatively small. Therefore, the
navigation system is considered efficient according to the two indicators.

Figure 13: Mathematical statistics of the task completion time: maximal time,
minimal time, average time and standard deviation of completion time. Each red
point is generated after 13 testers have finished the experiments.

5) Analysis of task completion time: in Fig. 13, we show completion time of
all testers’ finishing drawing two target destinations. All results are in the
range of 110s to 256s, with the average time 169s and standard deviation 44s,
showing the painting navigation system works well for testers. The blind
user’s time is at a normal level but a little longer than most blindfolded
users, which indicates that the painting navigation system may be fit for the
blind. One possible reason is that blind people are more patient.
Particularly, two testers finished the task within 120s.

6) Analysis of system satisfaction: after sorting questionnaires of the
testers, we find the evaluation on satisfaction is positive. It is true of the
two following respects namely whether the guiding voice conveyed information
clearly enough and whether the system provided an accurate painting
navigation. Thus, the results indicate high efficiency of the navigation
system. In terms of satisfaction, all testers are satisfied while one third
are very pleased. Most users feel easy even very easy to use the navigation
system while 13.33% regard the navigation system a little difficult.
Meanwhile, all testers think the system is helpful for blind painters;
specifically, the testers thinking it helpful and very helpful account for
28.57% and 64.29%, respectively. All feel they can improve proficiency in
operating the system through training. In addition, users also raise hope of
improvement in the sensitivity of the system perception, the frequency and way
of voice guidance, and the robustness of the system, etc.

###  III-B Influence of different prompt frequencies

Figure 14: The completion time in three different prompt frequencies. Testers
complete drawing two target destinations in prompt frequency of 1s, 2s, and
3s.

To validate our system reliability, we carry on experiments with three
different prompt frequencies. The results are shown in Fig. 14. Among three
prompt frequencies, the completion time is the shortest at the high frequency
of 1s, followed by the middle, 2s, and the longest at low, indicating the
system works best at the frequency of 1s. On the other hand, it can be noted
that the task completion time of a few users decreases as prompt frequency
increases and the completion time is proximate under three conditions. The
ability to accept new things and reaction time varies from person to person,
so it is reasonable and acceptable that a few special results appear. Overall,
the task completion times for three different prompt frequencies are
relatively short.

###  III-C Comparison between different target destinations

To verify the system adaption, we further invite another 13 blindfolded users
to carry out comparison experiments under the condition of three target
destinations and the prompt frequency of 1s.

TABLE II: Comparison of task completion time in different target destination experiments. Targets Number |  Maximum time (s) |  Minimum time (s) |  Average time (s) |  Standard deviation (s)
---|---|---|---|---
Two |  256 |  110 |  169 |  44
Three |  385 |  123 |  261 |  85

All the testers succeed in drawing three targets successfully. We show the
statistical results in TABLE II. The extra time of average time is about 90s
in three-target-destination experiment. Given the greater difficulty, the
performance is reasonable and good, which suggests the painting navigation
system works well in multi-destination experiment. Meanwhile, the other items
namely the maximum and minimum time and standard deviation, show the high
efficiency of the painting navigation system.

###  III-D Experience of four blindfolded professional painters

Figure 15: Completed works of professionals with the guidance of the painting
navigation system.

To validate the actual drawing function of the painting navigation system, we
invite four professional painters from the Fine Arts Department to draw under
the guidance of the painting navigation system, and the four completed works
are shown in Fig. 15. The professional painters can finish drawing
successfully and create fascinating works, showing the practicability of the
painting navigation system. Moreover, the professionals consider the
experience of painting satisfactory, which further shows the potential of the
navigation system to be actually applied to the blind.

###  III-E Influence of background sound noise on speech recognition accuracy

To test the noise resistance of the system, we conduct the experiments to
analyze the influence of background sound noise on speech recognition
accuracy. Speaker devices are used to create different noise conditions. We
use a noise detector to measure the noise level at the microphone position. In
the range of 19dB $\sim$ 95.3dB, 10 noise levels are selected for this test.
“CD”, “AB”, “EF”, “HG”, and “FD” are the target commands in this test. We
invite testers to test each instruction four times under each noise condition.

The test results are shown in Fig. 16. Speech recognition will be affected by
environmental noise to a certain extent. When the noise is 43.7dB or less, the
recognition accuracy of speech recognition is 100 $\%$. When the noise is
above 90dB, the speech recognition accuracy will decrease significantly. The
standard of 45 dB indoors in residential areas is identified as the maximum
levels below which no effects on public health and welfare occur [35].
According to the test results, the speech recognition accuracy of the system
meets the needs when the ambient noise is less than 45dB.

Figure 16: Speech recognition accuracy of the system under different
background noise conditions.

###  III-F Influence of lighting condition on recognition accuracy of brush
tip

We choose five different brightness values between 2LUX and 183LUX in this
test. To suppress other factors, the test background is blank. Since the
moving speed of brush tip will also affect the test results, the two moving
speeds namely the high speed ($>$10cm/s) and the low speed ($<$2cm/s) are set
in the test process. The test number of each group is 100.

The test results are shown in Fig. 17. When the brush moves at a low speed,
the recognition accuracy of brush tip is above 95$\%$. Under the dark light
condition, the recognition accuracy of brush tip for high-speed moving brush
tip is between 60$\%$ and 65$\%$. With the increase of brightness, the
recognition accuracy of brush tip also increases. When the brightness is
183LUX, the recognition accuracy of brush tip at a high moving speed is
96$\%$. In most applications such as offices and classes, the common light
level is around 250LUX [36]. Therefore, the above results indicate that the
system can operate under the normal ambient lighting conditions.

Figure 17: The recognition accuracy of brush tip with the high moving speed or
the low moving speed in different lighting conditions.

###  III-G Influence of complexity of drawing board background on recognition
accuracy of brush tip

We test the influence of the complexity of content in drawing board on
recognition accuracy of brush tip. The moving speed of brush tip is set low
during the test. Experiments are carried out under five different lighting
conditions. We use four paintings (Fig. 15) drawn by blindfolded volunteers
using the painting navigation system as the backgrounds in this test. The test
number of each group is 100.

The test results are shown in Fig. 18. In the case of very low illumination,
the recognition accuracy of brush tip is low in complex background. When the
brightness of the drawing board is normal (>20LUX), the average recognition
accuracy is more than 90$\%$. According to the above tests, the painting
navigation system can work in the drawing board of complex content.

Figure 18: The recognition accuracy of brush tip in the drawing board of
complex content and different lighting conditions.

##  IV Conclusions and future work

In this work, we propose an efficient painting navigation system to assist
blind painters in painting training and artistic creation. It consists of
cognitive system and guidance system. Specifically, the cognitive system is
mainly composed of QR code based on drawing board positioning module and brush
real-time positioning module. Additionally, we use QR code positioning
technology, the dynamic image recognition algorithm, virtual grids to locate
the position of the tip, and a digestible two-way voice interaction technology
to make the navigation system serve as an “Angel’s Eyes” of blind painters. In
mulimodal evaluation, we find the painting navigation system is relatively
well accepted by testers especially the blind tester through their thermal
curves. With the prompt frequency of 1s, testers can finish the experiment
most successfully with the completion degree of 89$\%$ and overflow degree of
347$\%$, showing the efficiency of our system. Analyzing trajectory of brush
tip, the type excellent and good account for 74$\%$, and the relative movement
distance is 4.12. It is foreseeable that the adaptation will improve after
adopting the system and training. Furthermore, the painting navigation system
performs well in multi-destination work with the average completion time 261s
in three-destination experiment. Most testers believe that they can improve
proficiency in operating the navigation system through training.

In the future research, we will aim at improving sensitivity of the system
perception, navigation and feedback accuracy. We also plan to deploy the
system on the phone to make it more portable.

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#  VLBI Detection of a Potential Active Radio Source Driving 100-kpc Scale
Emission in the Ultraluminous Infrared Galaxy IRAS 01004$-$2237

Takayuki J. Hayashi National Astronomical Observatory of Japan
2-21-1 Osawa, Mitaka
Tokyo 181-8588, Japan  Azabu Junior and Senior High School
2-3-29 Motoazabu, Minato
Tokyo 106-0046, Japan  Yoshiaki Hagiwara Toyo University
5-28-20 Hakusan, Bunkyo
Tokyo 112-8606, Japan  Masatoshi Imanishi National Astronomical Observatory of
Japan
2-21-1 Osawa, Mitaka
Tokyo 181-8588, Japan  Toyo University
5-28-20 Hakusan, Bunkyo
Tokyo 112-8606, Japan  Department of Astronomy, School of Science, Graduate
University for Advanced Studies (SOKENDAI)
2-21-1 Osawa, Mitaka
Tokyo 181-8588, Japan

###### Abstract

Galaxy mergers induce the accretion of gas and dust toward the central region
of the galaxy, leading to subsequent activities of star formation and active
galactic nuclei (AGNs). These processes serve as energy sources for the
infrared emission in ultraluminous infrared galaxies (ULIRGs). Recently, a
selected number of ULIRGs were reported to display extended radio continuum
emission on a scale of $\sim 100$ kpc related to AGNs, whose properties and
role in merging systems still need to be better understood. This paper
presents the results of multifrequency observations of the nearby ULIRG IRAS
01004$-$2237, exhibiting 100-kpc scale continuum emission at radio
wavelengths, conducted by the Very Long Baseline Array at 2.3 and 8.4 GHz. The
absence of extended X-ray emission in IRAS 0100$-$2237 suggested an AGN origin
for the radio emission, but further evidence was needed. At 8.4 GHz, we detect
compact radio continuum emission with a brightness temperature exceeding
$10^{7.2}$ K in the nuclear region of the object. Conversely, no significant
emission is observed at 2.3 GHz, indicating its flat or inverted spectrum.
Both synchrotron self-absorption and free-free absorption can explain the
spectral feature of the source. Given the suggestion of AGN presence at other
wavelengths, this emission is a plausible candidate for the AGN core powering
the extended radio emission.

Ultraluminous infrared galaxies (1735) — Radio continuum emission (1340) —
Active galactic nuclei (16) — Very long baseline interferometry (1769)

††journal: Astrophysical Journal††facilities:  VLBA (NRAO) ††software:  AIPS
(Greisen, 2003), astropy (Astropy Collaboration et al., 2013, 2018) CASA
(McMullin et al., 2007), difmap (Shepherd, 1997).

##  1 Introduction

Galaxies with large infrared luminosity greater than $10^{12}L_{\odot}$ are
known as ultraluminous infrared galaxies (ULIRGs; Sanders & Mirabel, 1996).
ULIRGs are systems of a major merger and harbor substantial quantities of
infrared-emitting dust centrally concentrated within their nuclei (Sanders et
al., 1988; Borne et al., 2000; Veilleux et al., 2002). Their powerful energy
sources are energetic radiation from active galactic nuclei (AGNs) and
starbursts (Genzel et al., 1998; Veilleux et al., 2009). Both phenomena are
activated by the inflow of gas resulting from merger events, with the former
possessing the capacity to terminate the latter by expelling the gas (Hopkins
et al., 2006, 2008). The role of AGNs during mergers remains a subject of
contention, closely linked to understanding the history of star formation and
the growth of supermassive black holes within the obscured galactic population
during the early Universe (Lonsdale et al., 2006b; Pérez-Torres et al., 2021).

When the preceding star formation is halted by AGN activities, outflows
emanating from the central engine are inferred to play a crucial role (e.g.,
Silk & Rees, 1998; Cano-Díaz et al., 2012; Cresci et al., 2015; Carniani et
al., 2016; Hekatelyne et al., 2024), where radio emitting non-thermal jets are
also supposeed to contribute to this phenomenon (e.g., Dugan et al., 2017;
Nesvadba et al., 2017; Singha et al., 2023; Su et al., 2023). Despite its
importance, many questions about radio emission from AGNs in ULIRGs still need
to be answered. A well-established correlation, spanning up to five orders of
magnitude, exists between far-infrared and radio emissions from galaxies
(e.g., Helou et al., 1985; Condon et al., 1991a, b; Appleton et al., 2004; Gim
et al., 2019). The intense radio emission, deviating significantly from this
correlation, is attributed to the influence of AGN activities (e.g., Yun et
al., 2001; Calistro Rivera et al., 2017; Wang et al., 2024). However, recent
studies have shown that radio excess can only be used to collect the most
radio-loud AGNs (e.g., Morić et al., 2010; Solarz et al., 2019). Investigating
the individual radio activity of AGNs remains crucial, even for objects whose
radio excess has not been detected (cf. U et al., 2012).

This work will focus on a nearby ULIRG, IRAS 01004$-$2237, located at
$z=0.118$. Infrared luminosity of the object is $10^{12.2}L_{\odot}$, and its
optical class is type-2 Seyfert (Yuan et al., 2010; Rodríguez Zaurín et al.,
2013). While this object does not exhibit a pronounced radio excess, aligning
with the far-infrared/radio correlation, Hayashi et al. (2021) have reported
100-kpc scale extended emission at radio, whose morphology is reminiscent of
FR-2 radio galaxies (Fanaroff & Riley, 1974). Recently, large-scale ($\sim
100$ kpc) radio continuum emission has been detected in a select number of
ULIRGs (e.g., Nandi et al., 2021; Kukreti et al., 2022), and the properties of
such emission in merging systems are still less known. Observational studies
of IRAS 01004$-$2237 will yield valuable insights into the driving mechanism
of AGN jets and their role in ULIRGs. At this moment, Hayashi et al. (2021)
have suggested that no detection of extended X-ray emission (Voges et al.,
1999; Teng et al., 2005) supports an AGN origin of the extended radio
emission, not a radio mini-halo or a radio relic associated with galaxy
clusters (Feretti et al., 2012; van Weeren et al., 2019). However, because
this argument is only circumstantial and eliminative, it is necessary to
detect a high-brightness radio emission from an AGN through high-resolution
observations at the milliarcsecond (mas) scale.

In this paper, we present the results of multi-frequency radio observations
conducted using the Very Long Baseline Array (VLBA). The high-resolution
achieved by very long baseline interferometry (VLBI) offers valuable insights
into the presence of an AGN core responsible for the extended radio emission
in IRAS 01004$-$2237\. While VLBI imaging observations of ULIRGs have been
widely conducted, they have been confined to a limited number of objects. For
instance, in Mrk 231, a lobe structure and a recently emanating jet due to AGN
activities have been identified (Carilli et al., 1998; Taylor et al., 1999;
Ulvestad et al., 1999a, b; Lonsdale et al., 2003; Reynolds et al., 2009, 2013,
2017, 2020; Wang et al., 2021). A young radio source, indicative of the
possible emergence of a new quasar in the context of merging galaxies, has
been reported for IRAS 00182$-$7112 (Norris et al., 2012). In contrast, VLBI
observations have also revealed radio supernovae (RSNe) and supernova remnants
(SNRs), providing evidence of starburst activities in objects like Arp 220
(Lonsdale et al., 1998; Smith et al., 1998; Rovilos et al., 2005; Lonsdale et
al., 2006a; Parra et al., 2007; Batejat et al., 2011, 2012; Varenius et al.,
2019) and IRAS 17208$-$0014 (Momjian et al., 2003, 2006). Furthermore,
composites of both AGNs and starbursts have been identified in several
objects, such as IRAS 23365+3604 (Romero-Cañizales et al., 2012) and Mrk 273
(Carilli & Taylor, 2000; Bondi et al., 2005). The new VLBA observations for
IRAS 01004$-$2237 presented in this paper are expected to provide new insights
into the origin of radio emission in the nuclear region of ULIRGs.

In this research, we employed the standard cosmological model with cold dark
matter and a cosmological constant, adopting $H_{0}=70$ km s-1 Mpc-1,
$\Omega_{\rm M}=0.3$, and $\Omega_{\Lambda}=0.7$, supported by observational
studies from the past decades (e.g., Planck Collaboration et al., 2020). Under
this model, at a redshift of the source ($z=0.118$), 1 milliarcsecond
corresponds to a scale of 2.132 pc, and the luminosity distance,
$D_{\mathrm{L}}$, is 549.7 Mpc. The paper defines a spectral index, $\alpha$,
as $S_{\nu}\propto\nu^{\alpha}$, where $S_{\nu}$ represents flux density at
frequency, $\nu$.

##  2 Observations and Data Reduction

The VLBA observation targeting IRAS 01004$-$2237 was executed on 2022 May 6,
operating under the project code BH237C. The observation comprised a 6-hour
session involving all ten VLBA stations. Throughout the observation, four
128-MHz frequency channels were employed for both right and left circular
polarizations. Simultaneous observations were conducted at the $S$ and $X$
bands. The $S$-band observation operated at a center frequency of 2.268 GHz
(hereafter 2.3 GHz) with a bandwidth of 128 MHz. The $X$-band observation
spanned center frequencies of 8.304, 8.432, and 8.560 GHz for each channel,
with the central frequency being 8.432 GHz (hereafter 8.4 GHz), and a total
bandwidth of 384 MHz. Data were sampled at the Nyquist rate with two bits per
sample, resulting in a total data rate of 4 Gbit s-1. Only the parallel
polarization hands were processed on the DiFX correlator (Deller et al.,
2011). Each 128 MHz frequency band was further subdivided into 256 spectral
channels to maintain wide-field imaging capabilities and to deal with radio
frequency interference.

The observations were conducted in phase-referencing mode. Scans lasting 3–4
minutes on IRAS 01004$-$2237 were interspersed with 2-minute scans on a
calibrator, J0108$-$2157, positioned 1.3 degrees from IRAS 01004$-$2237\.
During the scans for the target, both the antennas and the correlator were
aligned with the optical position of IRAS 01004$-$2237\. The total integration
time for the target amounted to 145 minutes. Table 1 provides a summary of the
observations for IRAS 01004$-$2237.

Table 1: VLBA Observations Summary for IRAS 01004$-$2237\.

|  |  |  |  |  | Beam Size |
---|---|---|---|---|---|---|---
Date | Integration Time | Phase Calibrator | Band | Frequency | Band Width | FWHM | PA |
| (min) |  |  | (GHz) | (MHz) | (mas2) | (deg) |
2022 May 6 | 145 | J0108$-$2157 | $S$ | 2.268 | 128 | $7.01\times 2.27$ | $-1.6$ |
|  |  | $X$ | 8.432 | 384 | $1.75\times 0.59$ |  +$0.1$ |

Note. — Simultaneous observations were conducted at both the $S$\- and
$X$-bands. Beam sizes are determined in the uniformly weighted images.

The data reduction followed a standard procedure employing the Astronomical
Image Processing System (AIPS; Greisen, 2003) software developed at the
National Radio Astronomy Observatory (NRAO). All analysis processes were
conducted independently in the 2.3-GHz and 8.4-GHz bands. Initially, we
executed amplitude calibration using system noise temperature measurements
throughout the observation and gains provided by each station. Subsequently,
fringe fitting took place following corrections for Earth orientation
parameters and ionospheric dispersive delay. Finally, we carried out bandpass
calibration for both amplitude and phase using a fringe finder, S5 0016$+$73\.
We confirmed that all calibrators were detected on all baselines at all
frequencies, except for baselines involving the Fort Davis station at the
8.4-GHz band. At each stage for the 2.3-GHz data, we identified and flagged
radio frequency interference in the time and frequency domains using the AIPS
task RFLAG and SPLAG.

Imaging processes were conducted using the difmap software (Shepherd, 1997).
To derive antenna-based gain corrections, we applied self-calibration for the
calibrator, J0108$-$2157, and determined both amplitude and phase time
variations. The solutions obtained were subsequently transferred to the target
along with the delay and rate solutions obtained through the fringe fitting.
To identify the target, whose location within the telescope’s field of view
was unknown, we initially utilized the task tclean in the Common Astronomy
Software Applications (CASA; McMullin et al., 2007) package, equipped with
widefield imaging mode and multiterm multifrequency synthesis capabilities.
This approach led to the successful detection of the target at the 8.4-GHz
band, positioned $\sim 1$ arcsecond from the phase center, but not at the
2.3-GHz band. After adjusting the phase center of the visibility data to the
location of the detected radio source using the AIPS task UVFIX, we conducted
the subsequent imaging process for the 8.4-GHz data, which included phase-only
self-calibration, using the difmap software. Throughout the observations at
the 8.4-GHz band, gain fluctuations consistently aligned with the absolute
flux density uncertainties of 5% for VLBA at 15 GHz (Homan et al., 2002),
which was also applied to 8.4-GHz data in Reynolds et al. (2020).

##  3 Results

We detected a point source at R.A. = 01h 02m 49s.991, and DEC. = $-$22∘ 21′
57.271′′. The peak flux density in the naturally weighted image at the 8.4-GHz
band, which is optimized for sensitivity, exceeds the 10$\sigma$ level of the
thermal noise. The position coincides with a continuum source detected at
239.4 GHz (Imanishi et al., 2019) and X-ray point source observed by the
Chandra X-ray Observatory (Teng et al., 2005). Therefore, this signal must be
real.

Figure 1 shows a uniformly weighted image of the target at the 8.4-GHz band
after phase-only self-calibration. The thermal noise and maximum flux density
measured in the image are 73 and 603 $\mu$Jy beam-1, respectively. The
Gaussian fit for the image yields a full width half maximum (FWHM) of the
source as $1.72\pm 0.26\times 0.61\pm 0.03$ mas2 at a position angle (PA) of
$176.9\pm 1.8$ degrees, which is similar to the beam size of the image. Thus,
the source is unresolved at the 8.4-GHz band, and we set the beam size as the
upper limit of the deconvolved source size. We estimated the flux density of
the source by summing the CLEAN components within the beam, yielding a value
of 556 $\mu$Jy444 The difmap software computes the peak flux density by
converting the flux density per pixel in the image into flux density per beam
size. Consequently, the flux density value of an unresolved source, smaller
than the beam size, can be less than its peak flux density value. . Based on
these constraints, the brightness temperature of the source, $T_{\mathrm{b}}$,
can be calculated using the equation:

$\displaystyle\left(\frac{T_{\mathrm{b}}}{\mathrm{K}}\right)=$ $\displaystyle
1.8\times
10^{9}(1+z)\left(\frac{S_{\nu}}{\mathrm{mJy}}\right)\left(\frac{\nu}{\mathrm{GHz}}\right)^{-2}\left(\frac{\phi}{\mathrm{mas}}\right)^{-2},$
(1)

where $\phi$ represents the source size (cf. Ulvestad et al., 2005).
Consequently, we obtained $T_{\mathrm{b}}>10^{7.2}$ K for the detected source.

At the 2.3-GHz band, we obtained a thermal noise level of 159 $\mu$Jy beam-1
for a uniformly weighted image with a beam size of $7.01\times 2.27$ mas2 at a
PA of $-1.6$ degrees. We adopted 3$\sigma$ as an upper limit of the flux
density at the frequency. As a result, the spectral index between 2.3 and 8.4
GHz, $\alpha^{8.4}_{2.3}$, can be constrained as $\alpha^{8.4}_{2.3}>0.12$.
Figure 2 illustrates the radio spectrum of the source with measurements for
the extended structure obtained from previous studies. Table 2 summarizes our
measurements.

Table 2: Flux measurement of IRAS 01004$-$2237

|  | Source Size on the Image |  |
---|---|---|---|---
Band | RMS | FWHM | PA | Peak flux density | Integrated flux density
(GHz) | ($\mu$Jy beam-1) | (mas2) | (deg) | ($\mu$Jy beam-1) | ($\mu$Jy)
2.3 | 159 | … | … |  $<$473 |  $<$473
8.4 |  073 | $1.72\pm 0.26\times 0.61\pm 0.03$ | $176.9\pm 1.8$ | $603\pm 79$ | $556\pm 78$

Note. — All values are measured in the uniformly weighted images. The flux
density error is determined by taking the root mean square (RMS) of the
thermal noise and the systematic uncertainty of amplitude calibration, set at
5%.

Figure 1:  (a) A JVLA image at 9.0 GHz with a resolution of $13.0\times 4.7$
arcsecond2 at a PA of 143 degrees, presented in Hayashi et al. (2021). Contour
levels commence at 17 $\mu$Jy beam-1, corresponding to the 3$\sigma$ noise
level of the image, and are subsequently multiplied by a factor of 2. The peak
flux density in the image is 2.7 mJy beam-1. For more details on imaging
processes, please see the reference paper. (b) A uniformly weighted VLBA image
at 8.4 GHz with a resolution of $1.75\times 0.59$ mas2 at a PA of 0.1 degrees.
Contour levels commence at 219 $\mu$Jy beam-1, corresponding to the 3$\sigma$
noise level of the image, and are subsequently multiplied by a factor of
$\sqrt{2}$. The peak flux density in the image is 603 $\mu$Jy beam-1.  Figure
2:  Radio spectrum of IRAS 01004$-$2237\. Crosses denote the integrated flux
density of the source as provided by TGSS at 150 MHz (Intema et al., 2017),
GLEAM survey at 200 MHz (Hurley-Walker et al., 2017), WISH at 352 MHz (De
Breuck et al., 2002), RACS at 887.5 MHz (Hale et al., 2021), and VLA
observations by Hayashi et al. (2021). Open circles represent the core flux
density reported by Hayashi et al. (2021). A filled circle and an open
triangle depict the flux density at 8.4 GHz and its 3$\sigma$ upper limit at
2.3 GHz, respectively, obtained through VLBA observations in this study. A red
solid line illustrates the model for the VLA core as reported in Hayashi et
al. (2021), assuming a non-thermal component (dotted line) absorbed by ambient
thermal plasma with free-free emission (dashed line).

##  4 Discussion

###  4.1 Physical constraints of the compact radio source

The radio emission from the compact source exhibits a high brightness
temperature of $T_{\mathrm{b}}>10^{7.2}$ K, as detected by the VLBA
observations at the 8.4-GHz band, which indicates the presence of non-thermal
phenomena. This source exhibits a spectral index of $\alpha^{8.4}_{2.3}>0.12$,
suggesting the potential influence of Synchrotron self-absorption (SSA) and/or
free-free absorption (FFA).

The magnetic field strength responsible for SSA, $B_{\mathrm{SSA}}$, is
determined by

$\displaystyle\left(\frac{B_{\mathrm{SSA}}}{\mathrm{mG}}\right)=$
$\displaystyle 3.1\times
10^{4}\left(\frac{\nu_{\mathrm{p}}}{\mathrm{GHz}}\right)^{5}\left(\frac{S_{\mathrm{p}}}{\mathrm{mJy}}\right)^{-2}\left(\frac{\phi}{\mathrm{mas}}\right)^{4}(1+z)^{-1},$
(2)

where $S_{\mathrm{p}}$ is the peak flux density observed at frequency,
$\nu_{\mathrm{p}}$ (Kellermann & Pauliny-Toth, 1981). On a different aspect,
employing minimum energy conditions, where the energy densities of electrons
and magnetic fields are roughly equal, we can compute the equipartition
magnetic field strength, $B_{\mathrm{e}q}$, as

$\displaystyle\left(\frac{B_{\mathrm{e}q}}{\mathrm{mG}}\right)=2.9\times
10^{-11}\left(\frac{R}{\mathrm{pc}}\right)^{-\frac{6}{7}}\left(\frac{L}{\mathrm{erg/s}}\right)^{\frac{2}{7}}(1+k)^{\frac{2}{7}},$
(3)

where $R$, $L$, and $k$ represent the radius of the component, bolometric
luminosity, and energy ratio between heavy particles and electrons
(Pacholczyk, 1970). We assume $k=1$, but it is worth noting that
$B_{\mathrm{e}q}$ remains relatively insensitive to the specific values of
$k$. We approximate $L\simeq 4\pi
D_{\mathrm{L}}^{2}S_{\mathrm{p}}\nu_{\mathrm{p}}$ for the bolometric
luminosity (e.g., Feng et al., 2006) and assume spectral indices of optically
thin and thick parts as $\alpha=-0.7$ and $2.5$, respectively. Figure 3
represents the physical conditions constrained by Equations (2) and (3).

Figure 3:  Physical conditions of the non-thermal plasma under the assumptions
of SSA and equipartition. The plot demonstrates the relationship between
plasma radius, $R$, and magnetic field strength, $B$. The blue lines represent
constraints imposed by SSA (Equation 2), while the orange lines indicate
constraints under the equipartition condition (Equation 3). The solid, dashed,
dash-dotted, and dotted lines of each color correspond to peak frequencies at
rest, $\nu_{\mathrm{p}}$, of 3, 5, 8, and 15 GHz, respectively. The
equipartition condition given in Equation 3 is insensitive to luminosity,
resulting in the overlapping of the orange solid line with the dashed and dot-
dashed lines.

Assuming that SSA is a consequence of an equipartition magnetic field, i.e.,
$B_{\mathrm{SSA}}=B_{\mathrm{e}q}$, and the spectral peak is present at a few
GHz, we derive a magnetic field strength on an order of $100$ mG and a source
size of an order of 0.01 pc (see Figure 3). The latter corresponds to $\sim
10^{4}$ times the Schwarzschild radius of the source. These values align
reasonably with expectations for the base of the jet (e.g., Ro et al., 2023)
or SNRs (e.g., Chevalier, 1998), indicating that SSA is capable of explaining
the flat or inverted spectrum observed in the source.

Although SSA is a plausible explanation, the substantial presence of ambient
plasma associated with the host galaxy can alternatively play a significant
role in enhancing the optical depth of FFA. This, in turn, contributes to the
observed flat or inverted spectrum of the source. We can calculate the optical
depth of FFA by the plasma, $\tau_{\nu}$, as

$\displaystyle\tau_{\nu}=0.46\left(\frac{r}{\mathrm{pc}}\right)\left(\frac{T_{\mathrm{e}}}{\mathrm{K}}\right)^{-\frac{3}{2}}\left(\frac{n_{\mathrm{e}}}{\mathrm{cm}^{-3}}\right)^{2}\left(\frac{\nu}{\mathrm{GHz}}\right)^{-2.1}\epsilon,$
(4)

where $r$, $T_{\mathrm{e}}$, $n_{\mathrm{e}}$, and $\epsilon$ represent the
radius, electron temperature, electron density, and volume filling factor of
the thermal plasma, respectively (eg., Kameno, 2001). The spectrum peaks at
the frequency where $\tau_{\nu}\sim 1$ is satisfied. Figure 4 depicts the
physical condition of the plasma constrained by Equation (4) assuming
$T_{\mathrm{e}}=10^{4}$ K. At the same time, the thermal plasma, which gives
rise to FFA, radiates free-free emission (FFE). In an optically thin regime,
we can derive the electron density of the thermal plasma producing FFE as

$\displaystyle\left(\frac{n_{\mathrm{e}}}{\mathrm{cm}^{-3}}\right)=$
$\displaystyle 3.6\times
10^{3}\left(\frac{r}{\mathrm{pc}}\right)^{-\frac{3}{2}}\left(\frac{T_{\mathrm{e}}}{\mathrm{K}}\right)^{\frac{1}{4}}\left(\frac{S_{\mathrm{ff}}}{\mathrm{Jy}}\right)^{\frac{1}{2}}\left(\frac{D_{\mathrm{L}}}{\mathrm{Mpc}}\right)\epsilon^{-1/2},$
(5)

where $S_{\mathrm{ff}}$ is the flux density at an optically thin regime (e.g.,
Harper-Clark & Murray, 2009). FFE contributes an order of 0.1 mJy to IRAS
01004$-$2237 in an optically thin regime (Imanishi et al., 2019; Hayashi et
al., 2021, see Figure 2). Figure 4 also illustrates the physical parameters
constrained based on the conditions imposed by the FFE.

Assuming the spectral peak is present at a few GHz, we estimate $r$ and
$n_{\mathrm{e}}\epsilon^{1/2}$ to be an order of $100$ pc and $100$ cm-3,
respectively (see Figure 4). These estimates are consistent with the
conditions found in local ULIRGs, whose typical size of thermal plasma
exhibiting FFE is $\sim$ 1 kpc (Barcos-Muñoz et al., 2017), and typical
electron densities are $\sim$ 100 cm-3 determined through optical emission-
line ratios (Veilleux et al., 1999). Therefore, FFA resulting from thermal
plasma within the merging system can also explain the flat or inverted
spectrum observed in the compact radio source.

Figure 4:  Physical conditions of the ambient thermal plasma assuming an
electron temperature of $10^{4}$ K. The plot demonstrates the relationship
between the plasma radius, $r$, and electron density considering the filling
factor, $n_{\mathrm{e}}\epsilon^{1/2}$. The blue lines represent constraints
imposed by FFA (Equation 4), with the solid, dashed, dash-dotted, and dotted
lines corresponding to peak frequencies at rest, $\nu_{\mathrm{p}}$, of 1, 2,
5, and 10 GHz, respectively. The orange lines indicate the constraints imposed
by FFE (Equation 5), with the solid, dashed, dash-dotted, and dotted lines
corresponding to flux density at optically thin regime due to FFE of 0.1, 0.2,
0.5, and 1.0 mJy, respectively.

###  4.2 Origin of the radio emission

Whether SSA or FFA is at play, the compact radio source in IRAS 01004$-$2237
is indicative of non-thermal phenomena, suggesting an AGN, RSN, or SNR.
Compact starbursts without those non-thermal phenomena usually represent
$T_{\mathrm{b}}\lesssim 10^{5}$ K, and never achieve the measured high
brightness temperature of $T_{\mathrm{b}}>10^{7.2}$ K (Condon, 1992). At this
moment, discerning these non-thermal phenomena remains challenging solely
based on the radio data. It is advisable to consider them in conjunction with
multi-wavelength data.

There is an optical counterpart located as encompassing the compact radio
source, which is classified as a Seyfert-2 AGN (Yuan et al., 2010; Rodríguez
Zaurín et al., 2013) and hosts a supermassive black hole with a mass of
$2.5\times 10^{7}M_{\odot}$ (Dasyra et al., 2006). This AGN is currently
active, marked by an increase of luminosity and spectral change in optical and
infrared wavelengths attributed to tidal disruption events, whereby stars
undergo gravitational disruption as they closely approach the supermassive
black holes (Dou et al., 2017; Tadhunter et al., 2017, 2021). At X-ray, a
point source has been identified at the coordinates of R.A. = 01h 02m 49s.99,
DEC. = $-$22∘ 21′ 57.3′′ obtained through the Chandra X-ray Observatory (Teng
et al., 2005), aligning with the position of the compact radio source. Its
X-ray spectrum is very soft, and the absence of direct AGN emission below 10
keV suggests a Compton-thick circumnuclear environment (Nardini & Risaliti,
2011). This argument is consistent with infrared spectra of IRAS 01004$-$2237
that reveal indications of obscuration of an AGN (Imanishi et al., 2007, 2008;
Veilleux et al., 2009; Nardini et al., 2010). Considering these information,
it is conceivable that an AGN with substantial absorption due to FFA can be
identified at radio wavelengths. Thus, the compact object detected by VLBA is
a candidate for the AGN core powering the extended radio emission.

Despite the optical luminosity of the source not meeting the criteria, the
host galaxy of IRAS 01004$-$2237 possesses a nearly stellar radial profile
similar to that of quasars (Surace et al., 1998) and lacks tidal tails or
loops, indicating an old merger (Veilleux et al., 2002). As mentioned in
Hayashi et al. (2021), the absence of extended X-ray features (Voges et al.,
1999; Teng et al., 2005) hints at the potential AGN origin of the 100-kpc
scale radio emission. Moreover, this object exhibits an HCN-to-HCO+ ($J=3$–2)
flux-density ratio higher than unity in the northwest-southeast direction
within its central few 100 pc (Imanishi et al., 2019), where mechanical
heating attributed to an AGN jet is one considerable explanation (cf. Aalto et
al., 2012; Izumi et al., 2013; Hagiwara et al., 2023). Thus, we can infer that
this object is a ULIRG that was once shrouded by dust and actively forming
stars, but is presently undergoing a process of dust dispersion due to AGN
activities, including those of jets (cf. Su et al., 2023). This ULIRG might be
in a transition phase to a quasar, as reported in the case of IRAS
00182$-$7112 (Spoon et al., 2007, 2009; Norris et al., 2012). Further
validation of this picture will necessitate the identification of jet emission
at radio that connects the pc-scale compact source with the extended structure
on the 100-kpc scale (e.g., Pérez-Torres et al., 2010; Su et al., 2023).

##  5 Summary

Our VLBA imaging of the ULIRG IRAS 01004$-$2237 at the 2.3-GHz and 8.4-GHz
bands revealed a pc-scale compact radio source exhibiting a brightness
temperature of $T_{\mathrm{b}}>10^{7.2}$ K and a spectral index of
$\alpha^{8.4}_{2.3}>0.12$. An investigation into the physical conditions of
this compact radio source revealed that both SSA and FFA could elucidate the
observed data. Presently, uncertainty persists regarding whether this source
originates from an AGN or starbursts, such as RSNe and SNRs. Based on the
indication of AGN presence at other wavelengths, the identified radio source
is considered candidates for the AGN core. Further observations of this object
are eagerly anticipated to provide clarity on the origin of the radio
emission.

This research has made use of the VizieR catalogue access tool, CDS,
Strasbourg, France. Additionally, we utilized the NASA/IPAC Extragalactic
Database (NED), which is operated by the Jet Propulsion Laboratory, California
Institute of Technology, under contract with the National Aeronautics and
Space Administration. Cosmological calculations are conducted using a
calculator provided by Wright (2006). The NRAO operating VLBA is a facility of
the National Science Foundation operated under cooperative agreement by
Associated Universities, Inc. This work made use of the Swinburne University
of Technology software correlator (Deller et al., 2011), developed as part of
the Australian Major National Research Facilities Programme and operated under
licence.

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