# HaGRID — HAnd Gesture Recognition Image Dataset

Kapitanov Alexander Makhlyarchuk Andrew Kvanchiani Karina
SberDevices, Russia
{AAKapitanov, AAlMakhlyarchuk<EMAIL_ADDRESS>
###### Abstract

In this paper, we introduce an enormous dataset HaGRID (HAnd Gesture
Recognition Image Dataset) for hand gesture recognition (HGR) systems. This
dataset contains 552,992 samples divided into 18 classes of gestures. The
annotations consist of bounding boxes of hands with gesture labels and markups
of leading hands. The proposed dataset allows for building HGR systems, which
can be used in video conferencing services, home automation systems, the
automotive sector, services for people with speech and hearing impairments,
etc. We are especially focused on interaction with devices to manage them.
That is why all 18 chosen gestures are functional, familiar to the majority of
people, and may be an incentive to take some action. In addition, we used
crowdsourcing platforms to collect the dataset and took into account various
parameters to ensure data diversity. We describe the challenges of using
existing HGR datasets for our task and provide a detailed overview of them.
Furthermore, the baselines for the hand detection and gesture classification
tasks are proposed. The HaGRID and pre-trained models are publicly
available111https://github.com/hukenovs/hagrid222https://gitlab.aicloud.sbercloud.ru/rndcv/hagrid.

##  1 Introduction

The use of gestures in human communication plays an important role [1]:
gestures can reinforce statements emotionally or completely replace them. What
is more, hand gesture recognition (HGR) can be a part of human-computer
interaction. Such systems have a wide range of real-world applications in the
automotive sector [2], [3], home automation systems [4], a vast variety of
video/streaming platforms (Zoom, Skype, Discord, Jazz, etc.), and others [5],
[6]. Besides, the system can be a part of a virtual assistant or service for
active sign language users – hearing and speech-impaired people [7], [8].
These areas require the system to work online and be robust to background,
scenes, subjects, and lighting conditions.

Figure 1: The 18 gesture classes included in HaGRID (“inv.” is the
abbreviation of “inverted”).

Dataset | Samples | Classes | Subjects | Scenes | Resolution | Environment | Continuous
---|---|---|---|---|---|---|---
American Sign Language, 1998 [9] | 2,500 | 40 | 1 | 1 | 320 × 243 | - | w/o transition state
Cambridge Hand GD, 2007 [10] | 900 | 9 | 2 | 1 | 320 × 240 | static | w/ transition state
ChaLearn Multi-modal GD, 2013 [11] | 13,858 | 20 + 1 | 27 | 2 | 640 × 480 | static | not continuous
ChaLearn IsoGD, 2016 [12] | 47,933 | 249 | 21 | 15 | 240 × 320 | static | not continuous
nvGesture, 2016 [13] | 1,532 | 25 + 1 | 20 | 1 | 320 × 240 | static, dynamic | w/ transition state
EgoGesture, 2018 [14] | 24,161 | 83 + 1 | 50 | 6 | 640 × 480 | static, dynamic | w/ transition state
ArASL, 2018 [15] | 54,049 | 32 | 40 | - | 64 × 64 | static | not continuous
IPN Hand, 2020 [16] | 4,218 | 13 + 1 | 50 | 28 | 640 × 480 | static, dynamic | w/o transition state
HANDS, 2021 [17] | 12,000 | 29 | 5 | 5 | 960 × 540 | static | not continuous
HaGRID, 2022 | 552,992 | 18 + 1 | 34,730 |  $\geqslant$ 34,730 | 1920 × 1080 | static | not continuous

Table 1: The main parameters of the mentioned hand gesture datasets. + 1 in
the third column means that the dataset contains an extra class “no gesture”.
The number of scenes in the last row cannot be less than the number of
subjects. Note that, the HaGRID consists of at least 90% FullHD images.

In this paper we present the HaGRID dataset to design HGR systems. It contains
more than half a million images divided into 18 classes of gesture signs
(Figure 1), which are not language-oriented. Such gestures are chosen for the
design of a device control system and serve one semiotic functional role [18].
Semiotic gestures help communicate information between people and, in our
cases, they are used for human-computer interaction. Section 3 will describe
how to design dynamic gestures using selected static gestures, i.e. create
ergotic gestures (another functional role, which corresponds to the capacity
to manipulate objects) by semiotic gestures. A small lexicon of functional
gestures in the dataset is conceived to reduce HGR system complexity and avoid
unnecessary cognitive load on the device user [19]. It is necessary to have
comfortably designed actions while using gesture control systems. All
presented gestures were selected as the most useful for this purpose[20]. We
also added an extra class with samples of natural hand movements and called it
“no gesture”. All the images differ in background, lighting, scene, and
subjects. This heterogeneity is achieved by using two crowdsourcing platforms,
namely, Yandex.Toloka333https://toloka.yandex.ru and ABC
Elementary444https://elementary.activebc.ru. All samples in the dataset are
high resolution and collected in the RGB format.

The rest of the paper is structured as follows: in section 2 we review the
related work that describes some of the existing HGR datasets; section 3
provides the whole process of creating the dataset; section 4 presents several
models trained on the dataset and the experimental results. In conclusion, we
describe the main directions for future work.

##  2 Related Work

There are at least 50 hand gesture recognition datasets. They differ by the
number of samples, their resolution, the number of classes, the presence of
negative samples, the homogeneity of scenes, the distance between the camera
and each subject, applied tasks, and the presence of a person in the frame.
This article discusses datasets in the context of solving the classification
problem. Note that some of the described datasets are designed to solve
additional tasks such as detection and pose estimation. Sign language is one
of the categories of gesture styles [21] and the American Sign Language (ASL)
dataset [9] belongs to it. The ASL dataset includes 2,500 images with 40
classes of gestures from 1 subject and only 1 scene. Special attention should
be paid to the main feature of datasets for sign language – the first-person
view approach to HGR dataset collection. Just like the ASL dataset, the
EgoGesture [14] dataset has this feature too. It contains 83 classes of
gestures from 50 subjects and includes samples with dynamic environments. The
ChaLearn Multi-modal Gesture Dataset [11] contains about 15.000 images and can
be useful for solving pose estimation problems. Its use is limited by the fact
that all its gesture samples are from an Italian gesture dictionary. The
Cambridge Hand Gesture Dataset [10] includes 900 image sequences of 9 hand
gesture classes without a person in the frame. The nvGesture dataset [13]
belongs to another of the gesture style types – manipulative gestures. It was
designed specifically to control in-car automotive devices. Therefore, it
contains only 1 scene – a person who sits in a car. This dataset is divided
into 26 classes including the extra class “no gesture”. The IPN Hand [16]
contains more than 4 thousand images from 50 subjects. The main advantages of
the IPN Hand dataset are that it contains continuous gestures without
transition states (same as the ASL dataset) and samples with natural hand
movements similar to target gestures. However, the dataset is limited to
gesture classes, because it was collected for interaction with touchless
screens. One of the biggest datasets, ChaLearn IsoGD [12], is based on the
previously mentioned ChaLearn Multi-modal gesture dataset. It includes 9
different gesture domains, including body language, gesticulations performed
to accompany speech, and others.

The HANDS [17] and the ArASL [15] are the most suitable datasets for our
application. They consist of gestures similar to ours and could potentially be
used by us. However, the HANDS contains only 15 gestures, some of which are
performed with both hands for a total of 29 unique classes. Most of them
differ little from each other, which complicates the use of the HGR system.
The ArASL is designed for Arabic Sign Language and contains about 54.000
images divided into 32 classes of gesture signs corresponding to Arabic
letters. All its images are in grayscale with 64 × 64 dimensions. The
MediaPipe Hands [22] could have been a good variant if it were not collected
from only 18 users with limited variation in the background. In addition, it
is not publicly available.

Some reviewed datasets use their vocabulary of gestures for specific domains
such as sign language, the automotive sector, and others. Even though most
datasets span multiple gesture types [23], this is not enough for our
purposes. The HaGRID is designed to control devices or devices apps. All
dataset gestures raise certain associations due to their possessed meaning.
This allows gestures to solve particular problems such as like/dislike,
play/stop the recording, turn on/off the sound, control the adjustable scale
(e.g. volume scale), etc. In addition, the user can combine some gestures to
create a new gesture that is not included in the dataset (e.g., gestures
“fist” and “palm” can be used to create a gesture “capture”). All gestures are
shown in Figure 1.

Besides the fact that others have gestures from inappropriate domains and do
not have the necessary gestures for us, the collection of the HaGRID was
motivated by a number of other reasons too. First, the resolution of other HGR
datasets images does not correspond to the resolution of the cameras on
particular devices (e.g. SberPortal555https://sberdevices.ru/sberportal/ and
SberTop666https://sberdevices.ru/sberboxtop/), which is FullHD. Second, the
other datasets lack variety in scenes and lighting conditions, which are
necessary for neural networks for good generalization. Finally, the HGR system
requires inputs from different distances to the camera. Notice also that not
all datasets are publicly available.

From Table1 one can see that the proposed dataset HaGRID is the largest in
terms of samples number. It has the highest diversity scores across subjects
and scenes, which helps to avoid intra-class variability. The two last columns
provide the comparison between the HaGRID and described HGR datasets according
to characteristics such as the type of environment and the presence of
continuous gestures.

##  3 HaGRID Dataset

The need for a combination of such characteristics as (1) high-resolution
images, (2) heterogeneity across the image scene, subjects, their age and
gender, lighting, distance from the camera to subjects, and (3) number of
samples became the motivation for creating the HaGRID. The dataset consists of
about half a million FullHD (1920 × 1080) RGB images with 18 gestures and a
“no gesture” class. It has at least 34,730 unique scenes. Keep in mind that
the proposed dataset contains some gestures in two positions: the front and
the back of the hand. This allows interpreting dynamic gestures using two
static gestures. For example, with gestures “stop” and “stop inverted” you can
design dynamic gestures “swipe up” (“stop thumbs down”, i.e. “stop” rotated by
180 degrees, as the start of the row and “stop inverted” as the end) and
“swipe down” (“stop” as the start of the row and “stop inverted thumbs down”,
i.e. “stop inverted” rotated by 180 degrees, as end). Also, you can get 2 more
dynamic gestures, “swipe right” and “swipe left”, with 90-degree rotation
augmentation. All examples of designed dynamic gestures are shown in Figure 2.

In addition to gestures classification, the HaGRID can be used for hand
detection problem (each image has $n$ corresponding bounding boxes for $n$
hands in a frame) and two binary classification problems: (1) gesture/non-
gesture and (2) right/left leading hand777“Leading hand” is the hand that
shows the gesture.. Figure 3 provides the example of markup for one sample in
the dataset.

Figure 2: Examples of designed swipes.

###  3.1 Crowdsourcing

The dataset was collected in 4 stages: (1) gesture image collection stage
called mining, (2) validation stage where mining rules and some conditions are
checked, (3) filtration of inappropriate images, (4) annotation stage for
markup bounding boxes and leading hands. The classification stage is built
into the mining and validation pipelines by splitting pools for each gesture
class. We use two Russian crowdsourcing platforms: Yandex.Toloka (1, 2, and 4
steps) and ABC Elementary (3 and 4 steps) to complete these stages. Note that,
tasks on the ABC Elementary platform are performed only by employees of our
company – this is necessary at the filtration stage. Usage of two platforms at
the annotation stage allows us to increase the confidence of the final
annotation because two different annotator domains mark up images. The
platforms are similarly organized. Thus, the description below is valid for
both of them. The details of each of the steps are the follows:

Figure 3: Example of sample and its annotation.

1\. Mining. The crowd workers’ task was to take a photo of themselves with the
particular gesture indicated in the task description. We define the following
criteria: (1) the annotator must be at a distance of 0.5 – 4 meters from the
camera, and (2) the hand with gesture (i.e. leading hand) must be completely
in the frame. An example of the mining task can be found in Figure 6 of
Appendix A. Sometimes, subjects receive a task to take a photo in low light
conditions or against a bright light source to make the neural network
resilient to extreme conditions. We blocked performers for fast answers (less
than 3 seconds) at the mining stage and all others. All received images were
also checked for duplicates using image hash comparison [24]. The mining tasks
were accompanied by instructions with a warning about the further publication
of the crowd workers’ photos.

2\. Validation. We implemented the validation stage to achieve high confidence
images because users tried to cheat the system at the mining stage. It was
possible to establish that for some time they sent false information and used
cheating tactics, for example, sending a template photo from the task
description, a duplicate photo from one of their previous tasks, a third party
picture, a photo with wrong gesture or a photo with a hand that is not
completely in the frame. There are also a few detected accidents when a worker
uploaded a rotated image by mistake or a photo with an invalid gesture. In
Figure 4, it is described how much data remains after each of the stages.

The goal of the validation stage is a selection of correctly executed images
at the mining stage, i.e. classify with classes “correct”, “incorrect”,
“rotated”, “third party photo” and “photo did not load”. Only “correct” images
get into the dataset. See Figure 6 for the validation task example. Lighting
conditions and the distance from the camera to subjects are not checked due to
the implicitness of these characteristics. No doubt the resulting dataset is
heterogeneous in these parameters since all subjects took photos in different
places.

For each image at this stage we set in the system the dynamic overlap of 3 to
5 performers, i.e. each assignment was completed by at least 3 crowd workers
depending on their skill. Based on the majority rule, some photos were
rejected. Otherwise, the image is considered correct, and then it will be
passed to the filtration stage.

The workers were required to complete a training pool of 10 assignments and an
examination pool with 10 assignments as well. Crowd workers are required to
complete the training pool with no less than 80% accuracy and the exam pool
with no less than 75% accuracy to get access to the exam pool and the
validation tasks, respectively. It is worth noting that the main validation
pool contains tasks to prevent crowd workers from cheating. Those who achieved
low performance on the control tasks are excluded and their annotations are
rejected automatically.

3\. Filtration. Images of children, people without clothes and images with
inscriptions were removed from the HaGRID at this stage due to ethical
reasons. The filtration stage is carried out only on the ABC Elementary
platform. All employees of our company are aware of the prohibition on the
transfer of personal data to third parties and the presence of dubious
content. We use a very strong rule for the filtration stage – 5 workers should
filter each of the images (the filtration task example is shown in Figure 6 of
Appendix A). An answer is accepted if at least 4 workers vote positively for
it. Similar to the validation stage, annotators pass a thorough exam,
training, and control tasks at the filtration stage.

4\. Annotation. At this stage, crowd workers should draw a red border box
around the gesture on each image, and a green border box around the hand
without the gesture if it is completely in the frame (an example is shown in
Figure 7). Different colors are needed for their further translation into
labels. The two platforms allow us to save bounding boxes in COCO
format888https://cocodataset.org with normalized relative coordinates.

The crowd workers were required to complete the examination pool with 75%
success same as in the validation stage. Control tasks are used at this stage
too. Here the correctness of execution is checked by the intersection over
union (IoU).

Annotation overlap is placed dynamically on Yandex.Toloka from 3 to 5 and it
always equals 5 on the ABC Elementary platform. This is used to reduce the
chance of incorrect markup. Variants that were not aggregated after the
maximum overlap will not be used in the dataset. All markups, the number of
which varies from 8 to 10, are collected from two platforms and aggregated by
two schemes – hard and soft aggregation.

For hard aggregation, the next algorithm is implemented. The main rule for
this stage is that we skip aggregation and lose the ability to find a
resulting bounding box if one of the following steps is not satisfied (each
image corresponds to several markups that will be compared):

  * 1)

Check the number of the bounding boxes for equality.

  * 2)

Find centroids by using the Means Shift for all bounding boxes and merge the
closest objects to the groups. Then check the number of boxes in each group
(at least $0.7n$ should stay in the group, where $n$ \- number of markups).

  * 3)

Check labels for bounding boxes in each group for equality.

  * 4)

Check IoU for each group and compare with a threshold (by default 0.7).

If all steps of the hard pipeline are successfully passed, the final markups
are averaged. Thus, the aggregation result for each image consists of a list
of bounding boxes and their labels. If all image markups do not have bounding
boxes, then the image is removed from the dataset. For the hard aggregation
example and pipeline scheme, see the top of Figure 8 and the left of Figure 9,
respectively.

The soft aggregation pipeline is used if the hard aggregation algorithm fails.
Soft aggregation can be understood as preprocessing before hard aggregation.
It does not require conditions such as the same number of boxes and hand
labels. The soft aggregation steps are as follows:

  * 1)

Remove close to dots boxes (i.e. too small, probably randomly drawn),
duplicates within one option out of $n$.

  * 2)

Find centroids the same as in hard aggregation.

  * 3)

Remove “outliers” (i.e. boxes that were not included in the group).

  * 4)

Check labels for each bounding box in the group. The goal of this is to find
the correct label in the group and change incorrect labels to correct ones.
The label is considered correct if it matches 70 percent of the subjects’
answers or more.

  * 5)

Check the number of bounding boxes for equality in the each group: if the
number of boxes in the group is less than $n$, then we attempt to add the
missing boxes by aggregating the remaining, which must be at least 70% of $n$.
The aggregate result is put in place of the missing box.

  * 6)

Hard aggregation is attempted one more time.

  * 7)

If it fails, we iteratively eliminate some of the $n$ markup variants (70% of
$n$ should remain) and try to hard aggregate the rest.

See the bottom of Figure 8 and the right of Figure 9 for the soft aggregation
example and its pipeline scheme, respectively. Note that, we do not pay a
worker if his variant of markup is incorrect 999The answer is incorrect if at
least 70% of workers are unanimous in favor of choosing another option. (i.e.
a box is missing in the markup or there is an extra box or boxes of the wrong
color).

We also asked subjects on the ABC Elementary platform to annotate a leading
hand for each image to solve the task of determining the side of the hand. The
reason for this is that to be able to interpret dynamic gestures with static
ones. As discussed above, dynamic gestures “swipe up” and “swipe down” can be
shown with one hand, while gestures “swipe right” and “swipe left” are hard to
show without using a second hand. If the horizontal static gestures “stop” and
“stop inverted” are shown with the left hand, then it is the dynamic gesture
“swipe right”, otherwise – “swipe left”. Leading hand labels can be used to
design two different gestures from one as in [17]. For example, right “three”
and left “three” can be two different gestures “right three” and “left three”.

###  3.2 Dataset Characteristics

HaGRID size is approximately 716 GB – it includes more than 550 thousand
images divided into 18 classes of gestures: “call”, “dislike”, “fist”, “four”,
“like”, “mute”, “ok”, “one”, “palm”, “peace”, “peace inverted”, “rock”,
“stop”, “stop inverted”, “three”, “three2”, “two up”, “two up inverted” (shown
in Figure 1). Each gesture class contains more than 30.000 high resolution RGB
images10101030.000 samples per class may seem redundant for architectures such
as ResNets [25]. However, this can be an important advantage for large models
e.g. visual transformers [26].. Each image has a bounding box with a gesture.
Also, some images have “no gesture” bounding box if there is a second hand in
the frame. This extra class contains 123,589 samples.

The dataset contains 34,730 unique faces and at least that many unique scenes.
The subjects are people from 18 to 65 years old. The ratio of women to men is
about 27 to 20. The dataset was collected mainly indoors with considerable
variation in lighting, including artificial and natural light. Besides, the
dataset includes images taken in extreme conditions such as facing and backing
to a window. Also, the subjects had to demonstrate gestures at different
distances from the camera (Figure 4).

Figure 4: Distribution of the bounding box area relative to the whole image.
The boxes take up 5 to 25% of the image, which means the camera is mostly far
from the person.

###  3.3 Dataset Splitting

The data were splitted into training (92%), and testing (8%) sets by subject,
with on average 28,300 images per class (509,323 total) and 2,400 images per
class (43,669 total), respectively. Detailed information about the number of
images is provided in Table 2. The numbers of subjects in training and testing
sets equal are 31,952 and 2,778, respectively. In addition, the anonymized
user ID hash has been added to the annotation file. This will allow the
dataset user to split the train-val dataset himself. Since the size of the
dataset is large, we designed a small version (100 samples per class) of the
HaGRID with annotations for preview at the link for your comfort.

Gesture | Train + Val | Test | Total
---|---|---|---
call | 28,193 | 2,436 | 30,629
dislike | 28,537 | 2,551 | 31,088
fist | 27,764 | 2,506 | 30,270
four | 28,880 | 2,492 | 31,372
like | 27,721 | 2,415 | 30,136
mute | 28,971 | 2,438 | 31,409
ok | 27,999 | 2,391 | 30,390
one | 28,444 | 2,462 | 30,906
palm | 28,326 | 2,427 | 30,753
peace | 28,303 | 2,477 | 30,780
peace inverted | 27,864 | 2,278 | 30,142
rock | 27,782 | 2,413 | 30,195
stop | 27,963 | 2,400 | 30,363
stop inverted | 28,857 | 2,469 | 31,326
three | 28,015 | 2,408 | 30,423
three2 | 27,789 | 2,332 | 30,121
two up | 29,679 | 2,545 | 32,224
two up inverted | 28,236 | 2,229 | 30,465
total images | 509,323 | 43,669 | 552,992
no gesture | 112,740 | 10,849 | 123,589
total boxes | 622,063 | 54,518 | 676,581

Table 2: HaGRID separation into trainval and test sets. Note that, the number
of images is not equal to the number of bounding boxes, because the image can
contain two hands and, therefore, two boxes.

##  4 Benchmark Evaluation

Model | Model size (MB) | Parameters (M) | Inference time (ms) | Metrics
---|---|---|---|---
Gestures | Leading hand | mAP
ResNet-18 | 44.8 | 11.19 | 64.5 | 98.72 | 99.27 | -
ResNet-152 | 233.7 | 58.19 | 411.5 | 99.11 | 99.45 | -
ResNeXt-50 | 92.5 | 23.02 | 136.1 | 98.99 | 99.39 | -
ResNeXt-101 | 348.2 | 86.79 | 581.4 | 99.28 | 99.28 | -
MobileNetV3 small | 8.7 | 2.13 | 8.9 | 96.78 | 98.28 | -
MobileNetV3 large | 22.0 | 5.46 | 16.9 | 97.88 | 98.58 | -
ViT-B/32 pretrained | 353.1 | 88.24 | 166.4 | 98.49 | 99.13 | -
MobileNetV3 large + SSDLite | 10.1 | 2.46 | 51.1 | - | - | 71.49

Table 3: Models training results on the HaGRID. F1-score was chosen as the
classification metric. Intel(R) Core(TM) i9-9880H CPU @ 2.30GHz is used for
computing inference time.

To test the efficiency of the dataset, 8 popular architectures are evaluated
for the 2 HGR tasks: hand detection and hand gesture classification. We chose
SSDLite [27] as a detector and set of 7 architectures consisting of ResNet-18,
ResNet-152 [25], ResNeXt-50, ResNeXt-101 [28], MobileNetV3 small, MobileNetV3
large [29], and ViT-B/32 [26] as classifiers.

###  4.1 Detection Experiment Setup

SSDLite model with MobileNetV3 large [29] backbone was used to solve the hand
detection problem.

Due to the large size of the dataset, the model was trained from scratch,
using an SGD with a momentum of 0.9 and a weight decay of 0.0005 as an
optimizer. The learning rate starts from 0.005 with a learning rate step decay
of 3 epochs. The detector achieved the highest metric on epoch 67.

###  4.2 Classification Experiment Setup

All classifiers are trained on cropped images with a random scale from 1 to 2.
All the metrics below were calculated on the testing set, which contains
43,669 images (about 2,400 per gesture class111111Note that, one image may
include two hands – one with gesture and the other without it.).

Two heads were added to each model backbone: for the hand gesture
classification into 19 classes and for the leading hand binary classification
into 2 classes. The model predicts gesture (or “no gesture”) class and arm
side for each hand to simplify the pipeline. We sum the Cross-Entropy Loss
function outputs for the corresponding tasks:

$Loss=CE(h,\hat{h})+CE(g,\hat{g})\\\
=-(\sum_{c=1}^{N}h_{c}\log(\hat{h}_{c})+\sum_{c=1}^{M}g_{c}\log(\hat{g}_{c})),$
(1)

where $h,\hat{h}\in{[0,1]}$ are the true and predicted labels for leading hand
side classification, $N$ – the number of the leading hand classes, $g,\hat{g}$
are the true and predicted labels for gestures classification, and $M$ – the
number of gesture classes.

Classification models were trained from scratch except for the ViT32. Other
learning parameters are similar to the detection model, but LinearLR with a
learning rate decay of 0.001 is used instead of StepLR. The classifiers are
trained for up to 100 epochs. Our experiments are conducted on a single Nvidia
Tesla V100 GPU with a batch size of 64.

###  4.3 Results

Table 3 presents the evaluation results of the selected model architectures
for solving three problems – hand detection, gestures, and leading hand
classification tasks. The best gesture classification result is obtained by
the ResNeXt-101 model and the best leading hand classification result by the
ResNet-152. Despite the decline in metrics, MobileNetV3 architectures are the
most suitable models for us due to their lightweight and speed.

In addition, in Figure 5, the confusion matrix of the best hand gestures
classification result obtained by ResNeXt-101 is represented. We can conclude
that all classes are well separated from each other. As expected, there are
pairs of similar gestures, e.g., “like” and “call”, “three” and “four”, “stop”
and “palm”, which generate several mistakes in the prediction. The problem of
reducing the number of errors with class “no gesture” will be solved by adding
samples with natural hand movements similar to target gestures to the dataset.

Demo version of the gesture recognition system with one of the most
lightweight and fastest classifier MobileNetV3 large can be found in our
repository.

Figure 5: Confusion matrix of gesture classification on the HaGRID using
ResNeXt-101 model.

##  5 Discussion

Models. We did not have a goal to train the best models given the dataset, as
this paper proposed to present the HaGRID and its creation pipeline. The
results are a starting point for research of the dataset possibilities to
influence the performance of the HGR system. But even now the metrics show the
high quality of the dataset.

One of the directions of the next studies is adding data augmentations to
include rare cases of gesturing. It is necessary to try such augmentations as
translation and rotation. We expect that these manipulations will complicate
the task, but at the same time reduce restrictions on the use of the HGR
system. Another line of research is a quantization of models due to it is
important to run the HGR system on devices. Quantization-aware training (QAT)
and neural architecture search (NAS) are considered promising research
directions too.

Dataset. The HaGRID is meant to be used in hand gesture recognition systems.
Besides, the dataset can be used for leading hand searching. The use of the
leading hand can also allow for a 2x increase in the number of gestures to
match with a large number of computer responses. Our following work on this
topic consists of increasing the dataset size by adding new static gestures
and samples with natural behaviors of users’ hands similar to the target
gestures. Important to mention that we are planning to expand the markup with
additional annotations such as gender, segmentation masks, keypoints, and so
on. Also, we are soon going to introduce new datasets for image & video
recognition and some popular computer vision tasks.

In addition, we hope that HaGRID, with any additional markup, can be a useful
dataset for many computer vision tasks such as pose estimation, face
detection, and others.

##  6 Conclusion

In this paper, we introduce the HAnd Gesture Recognition Dataset called
HaGRID, which is one of the largest and the most diverse in terms of subjects
and collection conditions. The gesture dataset is mainly intended to be used
in system control devices, but the potential for its application is quite
vast. HaGRID is the most complex dataset compared to others since it was
collected from about 35.000 scenes with different lighting and distance to the
camera. Besides, the baselines for HGR tasks evaluation are provided. The
whole dataset, the trial version with 100 images per class, pre-trained
models, and the demo are publicly available in the
repository121212https://github.com/hukenovs/hagrid or the
mirror131313https://gitlab.aicloud.sbercloud.ru/rndcv/hagrid.

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## Appendices

##  Appendix A Data collection information

Figure 6: The web interface for mining tasks (left), validation tasks
(middle), and filtration tasks (right). Figure 7: The web interface for
annotation tasks. Yandex.Toloka interface (left). ABC Elementary interface
(right).

Gesture | Mining | Validation | Filtration | Annotation
---|---|---|---|---
call | 55,502 | 36,516 | 32,325 | 30,629
dislike | 53,889 | 39,752 | 33,252 | 31,088
fist | 48,157 | 39,724 | 32,215 | 30,270
four | 50,590 | 39,376 | 33,408 | 31,372
like | 49,674 | 37,964 | 32,457 | 30,136
mute | 49,056 | 38,782 | 33,725 | 31,409
ok | 63,017 | 37,305 | 32,460 | 30,390
one | 47,566 | 37,666 | 32,819 | 30,906
palm | 47,507 | 38,299 | 32,954 | 30,753
peace | 47,870 | 38,228 | 32,874 | 30,780
peace inverted | 52,800 | 36,711 | 31,676 | 30,142
rock | 48,374 | 37,175 | 32,157 | 30,195
stop | 50,564 | 38,120 | 32,888 | 30,363
stop inverted | 54,468 | 36,811 | 32,647 | 31,326
three | 47,616 | 37,373 | 32,423 | 30,423
three2 | 54,479 | 36,319 | 31,012 | 30,121
two up | 55,433 | 38,276 | 33,591 | 32,224
two up inverted | 48,183 | 36,287 | 31,892 | 30,465
total | 924,745 | 680,684 | 586,775 | 552,992

Table 4: The number of samples which remain after each of the stage. Figure 8:
Hard and soft aggregation examples. (top) Hard aggregation: the image has
three variants of markup with the same number of boxes that belong to the same
group; all boxes are marked with one class and their group $IoU>0.7$. (bottom)
Soft aggregation: the first three variants of the image were not averaged
using the hard aggregation, so the 4th variant was added. “Outliers” bounding
box with the gesture label from the third variant was removed. After this,
variants 1 and 3 have one missing box each. Missing boxes were added to the
variants. The hard aggregation was applied again and the result was positive.

Figure 9: Hard and soft aggregation pipelines. (left) Hard aggregation: the
result is aggregated only after the successful passing of all checks. (right)
Soft aggregation: after each failed check, a corrective action is taken.


Nearly Static Magnetized Kerr Black-hole in Non-linear Electrodynamics

K. G. Managave, H. A. Redekar, R. B. Kumbhar, S. P. Das 111Email:
<EMAIL_ADDRESS>and K. Y. Rajpure
Department of Physics, Shivaji University,
Kolhapur-416004, Maharashtra, India.

###### Abstract

We have analyzed the thermodynamics of slowly rotating magnetized Kerr black-
hole, with typical spin parameter $a\leq 0.1$ (nearly static) in the
background of non-linear electrodynamics. In particular we have studied the
Bekenstein-Hawking entropy, Hawking temperature, angular momentum, specific
heats and identified regions of parameters for possible phase-transitions. It
turns out that once the stability lost the black-hole never come back to its
original stable position.

##  1 Introduction

The solutions of Black-hole (BH) are natural outcome of the General theory of
Relativity(GTR). Generally the BH characterized by their radius, masses,
charges, angular momentum etc. Depending upon the parameter choices BH could
have very different types, e.g., the Schwarzschild, Kerr, Kerr-Newman,
Reissner Nordström[1], [2] . In our analysis we considered the Kerr solutions,
i.e., the BH with rotation parameters.

The evolution of the different composite stars estimates that the rotation
parameters could have varied ranges of 0.01 to 0.60 with very different
characteristics features [3]. The nearly static in our consideration is with
spin parameter $a$ is 0.1 or less.

Nonlinear electrodynamics (NLED) has been attracted attention to
astrophysicists since sometime back. NLED could have combined with General
theory of relativity(GTR) – we called as NLED-GTR. This theory has some
remarkable features, e.g., consistent theory of inflationary model of the
Universe [4, 5, 6, 7, 8, 9, 10].

This NLED-GTR model has few characteristic features, e.g., absence of initial
singularities, putting an upper limit on the Electric field at the origin of
point-like particles, the finite self-energy of the charged particles [8],
[11] [12].

It is to be noted that in Quantum Electrodynamics(QED) the non-linear terms
arises due to the loop corrections [14, 15, 16]. The NLED-GTR model follows
the correspondence principle, i.e., in the weak-field limit we get the linear
electrodynamics.

The physics of BH (both electrically and magnetically charged) in presence of
NLED has been studied since some time [12], [17], [18]. We have studied the
thermodynamics properties of the slowly rotating magnetized Kerr BH in NLED-
GTR scenario.

The paper is organized as follows: we briefly outline the NLED-GTR model in
section 2. In section 3 we discussed the Kerr BH relevant for the NLED-GTR and
estimated the magnetized mass density that affects the relevant thermodynamic
parameters for slowly rotating (with spin parameter $a$) for
$\gamma=\frac{1}{2},\frac{4}{5}$ and $1$. We conclude in Section 6.

We adopted natural units, i.e., $c=\hbar=1$, $\varepsilon_{0}=\mu_{0}=1$ and
with metric signature $\eta=\mbox{diag}(-1,1,1,1)$

##  2  Non-linear Electrodynamics (NLED)-model

The Lagrangian density is as (following [12]):

${\cal L}=-\frac{{\cal F}}{1+(\beta{\cal F})^{\gamma}},$ (1)

where the parameter $\beta$ has the dimensions of 4D-volume (manifests the
strength of the coupling), and $\gamma$ (manifests the order of interaction)
is the dimensionless parameter [12]. The ${\cal
F}=(1/4)F_{\mu\nu}F^{\mu\nu}=(\textbf{B}^{2}-\textbf{E}^{2})/2$, where
$F_{\mu\nu}=\partial_{\mu}A_{\nu}-\partial_{\nu}A_{\mu}$ is the field strength
tensor, with $A_{\mu}=(\phi,\vec{A})$ the $\phi$ and $\vec{A}$ are the scalar
and vector potential respectively.

One can obtain the field equations

$\partial_{\mu}\left({\cal L}_{\cal F}F^{\mu\nu}\right)=0,$ (2)

where ${\cal L}_{\cal F}=\partial{\cal L}/\partial{\cal F}$ by using the
Euler-Lagrange (EL) equations.

The EL equation on Lagrangian density leads to

${\cal L}_{\cal F}=\frac{(\gamma-1)(\beta{\cal F})^{\gamma}-1}{(1+(\beta{\cal
F})^{\gamma})^{2}}.$ (3)

The group velocity over the background is less than photon speed requires
${\cal L}_{\cal F}\leq 0$ [19] so that the causality principle holds and
confirm the absence of tachyon. In our analysis we imply that $0\leq\gamma\leq
1$ and we consider only magnetized black holes (E=0, ${\cal
F}=\textbf{B}^{2}/2$). For simplicity in our analysis we set $\beta=1$.

The symmetrical energy-momentum tensor (is obtained from Eqn. 1 ) is:

$T_{\mu\nu}=\frac{(\gamma-1)(\beta{\cal F})^{\gamma}-1}{[1+(\beta{\cal
F})^{\gamma}]^{2}}F_{\mu}^{~{}\alpha}F_{\nu\alpha}-g_{\mu\nu}{\cal L}.$ (4)

The trace of the energy-momentum tensor Eqn.4 leads to

${\cal T}\equiv T^{\mu}_{\mu}=\frac{4\gamma{\cal F}(\beta{\cal
F})^{\gamma}}{[1+(\beta{\cal F})^{\gamma}]^{2}}.$ (5)

The trace of Eqn.LABEL:trace2 is non-zero due to the presence of dimensional
parameter $\beta=1$(as we considered throughout our analysis) and it leads the
breaking of scale invariance.

The models exhibits Maxwell’s Electrodynamics at the weak field limit,
$\beta{\cal F}\ll 1$, ${\cal L}\rightarrow-{\cal F}$, i.e., holds the
correspondence principle.

##  3 Magnetized Kerr black holes

We consider the electromagnetic energy density to be small enough that the
Kerr vacuum solution is valid. We have also considered the rotation parameter
is small enough (consistent with astrophysical evidence of evolution of stars)
that the Kerr-solution is almost nearly static (with rotation parameter $a\leq
0.1$) over the magnetized NLED background.

The geometry of Kerr space-time metric is

$\displaystyle ds^{2}$ $\displaystyle=$ $\displaystyle-
dt^{2}+\frac{2Mr}{\Sigma}\left(dt-a\sin^{2}\theta
d\phi\right)^{2}+\frac{\Sigma}{\Delta}dr^{2}+\Sigma d\theta^{2}$ (6)
$\displaystyle+(r^{2}+a^{2})\sin\theta d\phi^{2}\ ,$

where

$\Sigma=r^{2}+a^{2}\cos^{2}\theta,~{}~{}~{}\Delta=r^{2}+a^{2}-2Mr.$ (7)

Here $M$ is the mass-energy parameter of the BH and $a$ is its rotation
parameter. The thermodynamic quantities of a Kerr BH can be expressed in terms
of its horizon radius $r_{+}=M+\sqrt{M^{2}-a^{2}}$, which is defined by taking
$\Delta=0$.

The magnetic mass of the Kerr BH is

$M(r)=\int_{0}^{r}\rho_{M}(r)r^{2}dr,$ (8)

where $\rho_{M}$ is the magnetic energy density [12]. The magnetic mass of the
BH is $m_{M}=\int_{0}^{\infty}\rho_{M}(r)r^{2}dr$. The magnetic energy density
(E=0), found from Eq.LABEL:trace2, is

$\rho_{M}=T_{0}^{~{}0}=\frac{{\cal F}}{1+(\beta{\cal F})^{\gamma}}.$ (9)

For the magnetized black hole [13] one can find the field-strength with
magnetic charge($q$) and at distance r is ${\cal F}=q^{2}/(2r^{4})$. We set
for simplicity the value of $q=1$.

Similar to [12] we have also considered $\gamma=\frac{1}{2}$. We have cross-
checked our results with rotation parameter $a=0$ and found consistent with
results in [12].

##  4 Thermodynamic Parameters

In this section we are summarizing few important thermodynamic parameters [22]
relevant for our analysis.

$\bullet$ The Bekenstein-Hawking entropy is

$S_{BH}=\pi(r_{+}^{2}+a^{2}),$ (10)

$\bullet$ The Hawking temperature of the black hole horizon is

$T_{H}=\frac{1}{2\pi}\left[\frac{r_{+}}{r_{+}^{2}+a^{2}}-\frac{1}{2r_{+}}\right],$
(11)

$\bullet$ The angular momentum($J$) of the black hole is

$J=\frac{a}{2r_{+}}(r_{+}^{2}+a^{2}),$ (12)

$\bullet$ The specific heat capacity at constant angular momentum is

$C_{J}=T_{H}\left(\frac{\partial S_{BH}}{\partial
T_{H}}\right)_{J}=\frac{2\pi(r_{+}^{2}-a^{2})(r_{+}^{2}+a^{2})^{2}}{3a^{4}+6r_{+}^{2}a^{2}-r_{+}^{4}}\
.$ (13)

##  5 Numerical analysis

In our numerical analysis we have considered three different values of
$\gamma=\frac{1}{2},\frac{4}{5}$ and $1$.

We assume the value of spin parameter ($a$) is slowly rotating or nearly
static. Let us comment briefly on that. Some massive stars especially stars
with initial masses $M>20M_{Sun}$, produce BHs upon core-collapse. The
resulting stellar remnant is a rotating Kerr BH, whose dimensionless spin is
defined as $a=\frac{Jc}{GM^{2}}$, where J is the angular momentum of the BH, c
is the speed of light, G is Newton’s Gravitational constant and M is the mass
of the BH [21]. The values of spin parameter ($a$) can be in wide ranges: from
0.006 to 0.549 [21]. The numerical values of $a=0.1(0.01)$ could be possible
for a BH formed from a single massive star irrespective of the angular
momentum. The BH speed rates are measured in X-ray binaries (XRBs), and
current estimates suggest a broad range of spin-rates $0.1\leq a\leq 1$ [3].

###  5.1 $\gamma=\frac{1}{2}$

We have plotted the entropy (in the left-panel of Fig.1 ) as a function of
radial co-ordinates. The entropy is almost identical for both of the two-spin
parameters under consideration.

We have plotted the Hawking temperature (right-panel of Fig.1) as a function
of radial co-ordinates. It seems that the Hawking temperature is positive
approximate at $r\geq$ 0.02 (0.2) for spin parameter $a=0.01(0.1)$ with solid-
blue(dashed-red).

In the left(right)-panel of Fig.2 we have plotted the angular momentum
(specific heat at constant angular momentum). It reflects the fact that with
low(high) spin parameter the angular momentum is small(large). The specific
heat is discontinuous at $r=0.02(0.2)$ for the spin parameter $a=0.01(0.1)$
and the BH undergoes second order phase-transition. In this region of r the
Heat capacity is negative and the BH is unstable. Moreover for larger r the
specific heat ($C_{J}$) is always negative it suggests that once the BH
undergoes instability it never comes back to its original stable position.

Figure 1:  The Entropy (left) and Hawking temperature (right) for
$\gamma=\frac{1}{2}$

Figure 2:  The angular momentum($J$) and the specific heat at constant angular
momentum ($C_{J}$) for slowly rotating Kerr BH (with spin parameter,
$a$=$0.01$ with solid-blue and $0.1$ with dashed-red) in non-linear
electrodynamics. The value of $\gamma$ is $\frac{1}{2}$

###  5.2 $\gamma=\frac{4}{5}$

We have plotted the Entropy (in the left-panel of Fig.3 ) as a function of
radial co-ordinates for $\gamma=\frac{4}{5}$. The entropy is almost identical
for both of the two-spin parameters. The values of spin parameter for nearly
static Kerr solutions are small enough to show-up any appreciable changes.

We have plotted the Hawking temperature (right-panel of Fig.3) as a function
of radial co-ordinates. It seems that the Hawking temperature is positive
approximate at $r\geq$ 0.225 (0.7) for spin parameter $a=0.01(0.1)$ with
solid-blue (dashed-red). It turns out that the large values of $\gamma$ with
respect to Fig.1 the BH instability occurs for larger values of radial
parameters.

In the left(right)-panel of Fig.4 we have plotted the angular momentum
(specific heat at constant angular momentum). It reflects the fact that with
low(high) spin parameter the angular momentum is small(large). The specific
heat is discontinuous at $r=0.0225(0.7)$ for the spin parameter $a=0.01(0.1)$
and the BH undergoes second order phase-transition. In this region of radial
distance the specific heat capacity ($C_{J}$) is negative and the BH is
unstable.

Figure 3:  The Entropy (left) and Hawking temperature (right) for
$\gamma=\frac{4}{5}$

Figure 4:  The angular momentum($J$) and the specific heat at constant angular
momentum ($C_{J}$) for slowly rotating Kerr BH (with spin parameter,
$a$=$0.01$ with solid-blue and $0.1$ with dashed-red) in non-linear
electrodynamics. The value of $\gamma$ is $\frac{4}{5}$

###  5.3 $\gamma=1$

Figure 5:  The Entropy (left) and Hawking temperature (right) for $\gamma=1$

Figure 6:  The angular momentum($J$) and the specific heat at constant angular
momentum ($C_{J}$) for slowly rotating Kerr BH (with spin parameter,
$a$=$0.01$ with solid-blue and $0.1$ with dashed-red) in non-linear
electrodynamics. The value of $\gamma$ is $1$.

The allowed values of $\gamma$ is $0\leq\gamma\leq 1$ and we considered the
extreme value. We have plotted the Entropy (in the left-panel of Fig.5 ) as a
function of radial co-ordinates. The entropy is almost identical for both of
the two-spin parameters. As the values of spin parameter for near static Kerr
solutions are small enough to show-up any appreciable changes.

We have plotted the Hawking temperature (right-panel of Fig.5) as a function
of radial co-ordinates. It seems that the Hawking temperature is positive
approximate at $r\geq$ 0.31 (0.71) for spin parameter $a=0.01(0.1)$ with
solid-blue (dashed-red). It seems that the large values of $\gamma$ with
respect to Fig.1 the BH instability occurs for the large values of radial
parameters.

In the left(right)-panel of Fig.6 we have plotted the angular momentum
(specific heat at constant angular momentum). It reflects the fact that with
low(high) spin parameter the angular momentum is small(large). The specific
heat is discontinuous approximately at $r=0.31(0.71)$ for the spin parameter
$a=0.01(0.1)$ and the BH undergoes second order phase-transition. For larger r
the specific heat capacity ($C_{J}$) never comeback to positive values so we
can say that BH is unstable.

##  6 Summary and Conclusion

We have analyzed the thermodynamic properties of magnetized Black-hole in
presence of the non-linear electrodynamics with two independent parameters
$\beta$ and $\gamma$. In our numerical analysis we set $\beta=1$ throughout.
We assumed the magnetized Black-hole is rotating very slowly with two values
of rotation parameter ($a$) 0.01 and 0.1 (both normalized to mass), so that
nearly static Kerr metric could be used for the magnetized BH. The
correspondence principle takes place so that for the non-rotational model the
metric is converted into the Schwarzschild metric in the vanishing limits of
$a$-parameter. We have analyzed several thermodynamic parameters, for example
Black-hole entropy, Hawking temperature, angular momentum and specific heat
capacity at constant angular momentum. We have also demarcated the regions
where the Black-holes undergoes second-order phase transitions and regions of
instability.

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