# AxiomVision: Accuracy-Guaranteed Adaptive Visual Model Selection for
Perspective-Aware Video Analytics

Xiangxiang Dai  https://orcid.org/0000-0003-0179-196X The Chinese University
of Hong Kong, Hong Kong, China<EMAIL_ADDRESS>,  Zeyu Zhang
https://orcid.org/0009-0002-4508-671X Huazhong University of Science and
Technology, Wuhan, China<EMAIL_ADDRESS>,  Peng Yang
https://orcid.org/0000-0001-8964-0597 Huazhong University of Science and
Technology, Wuhan, China<EMAIL_ADDRESS>,  Yuedong Xu
https://orcid.org/0000-0003-4168-3998 Fudan University,Shanghai, China
<EMAIL_ADDRESS>,  Xutong Liu  https://orcid.org/0000-0002-8628-5873 The
Chinese University of Hong Kong, Hong Kong, China<EMAIL_ADDRESS>and
John C.S. Lui  https://orcid.org/0000-0001-7466-0384 The Chinese University of
Hong Kong, Hong Kong, China<EMAIL_ADDRESS>
(2024)

###### Abstract.

The rapid evolution of multimedia and computer vision technologies requires
adaptive visual model deployment strategies to effectively handle diverse
tasks and varying environments. This work introduces AxiomVision, a novel
framework that can guarantee accuracy by leveraging edge computing to
dynamically select the most efficient visual models for video analytics under
diverse scenarios. Utilizing a tiered edge-cloud architecture, AxiomVision
enables the deployment of a broad spectrum of visual models, from lightweight
to complex DNNs, that can be tailored to specific scenarios while considering
camera source impacts. In addition, AxiomVision provides three core
innovations: (1) a dynamic visual model selection mechanism utilizing
continual online learning, (2) an efficient online method that efficiently
takes into account the influence of the camera’s perspective, and (3) a
topology-driven grouping approach that accelerates the model selection
process. With rigorous theoretical guarantees, these advancements provide a
scalable and effective solution for visual tasks inherent to multimedia
systems, such as object detection, classification, and counting. Empirically,
AxiomVision achieves a 25.7% improvement in accuracy.

Video analytics, model selection, online learning, camera perspective, neural
networks

††journalyear: 2024††copyright: rightsretained††conference: Proceedings of the
32nd ACM International Conference on Multimedia; October 28-November 1, 2024;
Melbourne, VIC, Australia††booktitle: Proceedings of the 32nd ACM
International Conference on Multimedia (MM ’24), October 28-November 1, 2024,
Melbourne, VIC, Australia††doi: 10.1145/3664647.3681269††isbn:
979-8-4007-0686-8/24/10††ccs: Information systems Multimedia streaming††ccs:
Theory of computation Online learning algorithms

##  1\. Introduction

Video analytics plays a pivotal role in a multitude of tasks in a smart city,
including vehicle license tracking, facial recognition, and traffic monitoring
(Hung et al., 2018; Lin et al., 2022). This variety of applications highlights
the necessity for customized visual models designed to cater to the unique
requirements of different visual tasks. Yet, the application of such models,
particularly those based on deep neural networks (DNNs), faces formidable
challenges. These include the highly diverse requirements of video analytics
tasks, fluctuating environmental conditions, and the imperative for real-time
operation (Chen et al., 2015; Canel et al., 2019). The complexity and
computational intensity of cutting-edge visual models in multimedia systems
further complicate their application in resource-limited settings (Lin et al.,
2023; Zhao et al., 2022). Bandwidth constraints, for example, limit the
feasibility of transmitting high-resolution video for analysis (Zhou et al.,
2023), highlighting a bottleneck in the practical utility of these complex
technologies.

The first challenge in video analytics centers on which visual model to apply
that caters to application-specific requirements under a dynamic environment,
especially in light of phenomena like data drift (Dai et al., 2024a; Bhardwaj
et al., 2022), where live video data’s characteristics stray from the training
dataset, as demonstrated in our Section 2. Despite a wide range of
advancements targeting various specific requirements, efforts to modify
existing models or customize visual models remain predominantly focused on the
static and single scenario. For instance, works such as model pruning and
compression (Han et al., 2020; Kang et al., 2017; Rivas et al., 2022), while
effective at streamlining complex models for resource-limited environments,
face significant performance degradation under adverse conditions like poor
lighting or extreme weather (Kong et al., 2023; He et al., 2023). Given the
above analysis, we advocate for the strategic combination of existing models
to navigate the complexities of real-world scenarios, instead of solely
relying on a singular model or the pursuit of a one-size-fits-all visual model
for universal video analytics.

The complexity further escalates with the second challenge, as the video
analytic system transitions from single-camera sources to multi-camera feeds.
Independent decision-making for each camera regarding model selection would
cause the computational load to increase linearly, which is unsustainable and
retards the model selection process. Strategies such as the “ _follow-the-
leader_ ” (Jiang et al., 2018), _Spatula_ ’s camera correlation prioritization
(Jain et al., 2020), and the _CrossRoI_ system’s re-identification algorithm
(Guo et al., 2021) offer potential solutions for managing multi-camera setups.
Nevertheless, these offline, periodically preset camera groupings, which
depend exclusively on static search clustering and similar approaches, lack
the essential flexibility needed to adapt to the dynamic nature of real-world
environments and the process of continual learning for improvement.

Moreover, the significance of camera deployment in video analytics has been
largely overlooked, with attention primarily focused on enhancing visual
models on the server side, whether in the context of automated surveillance or
user-controlled VR cameras. Nevertheless, for specialized tasks such as the
creation of holographic stereogram portraits (DeCamp and Roy, 2009; Lee et
al., 2023), it is essential to investigate the additional effects arising from
different camera perspectives, particularly when the perspective is altered.
Additionally, due to declining costs, the popularity of cameras with
adjustable viewpoints has surged (for instance, in 2020, the global market
value of pan-tilt-zoom (PTZ) cameras reached $3 billion (Wong et al., 2024;
Insights, 3 11)). Current methodologies, such as configuration adjustments in
inference settings (Zhang et al., 2022; Jiang et al., 2018), optimizing
encoding (Zhou et al., 2023; Wang et al., 2022), and filtering out superfluous
details (Dai et al., 2022; Li et al., 2020), presuppose an immutable scene
captured by cameras. However, the variation of camera contents, application-
specific requirements, and adjustable perspective necessitate moving beyond
exclusively relying on pre-established offline learning methods, to understand
the effects of camera perspectives for the accurate selection of visual models
(the third challenge).

To address these challenges, this paper introduces AxiomVision, a novel
framework designed to guarantee the accuracy of video analytics through the
dynamic selection of visual models. Contrary to systems limited to data center
or cloud environments (Zhang et al., 2017; Shen et al., 2019) that introduce
issues like increased central load and the risk of congestion (Yang et al.,
2019), AxiomVision leverages edge computing (Yang et al., 2019; Zheng et al.,
2024) to decentralize processing, utilizing efficient lightweight DNN models
which are deployed close to data sources. With its tiered edge-cloud
architecture, AxiomVision strikes a balance between leveraging currently
effective visual models and exploring promising, yet untapped models. This is
achieved by continually analyzing observation feedback that includes camera
perspective effects, even in the absence of prior knowledge about these
perspectives. Furthermore, recognizing the potential for correlation among
camera groups, AxiomVision incorporates a graph-based grouping method based on
the natural camera network topology. This approach enables flexible and
continual adjustment for camera groups for various visual tasks. To conclude,
the manners in which this paper tackles the aforementioned third challenges
can be summarized as follows:

C1, Dynamic Visual Model Selection. We enhance task-specific visual
performance by employing an “online learning strategy” to select the optimal
visual model dynamically. This method is different from previous work that
relies solely on a single model or focuses on model enhancement. By
incorporating continual feedback, our strategy employs a dynamic selection
mechanism to identify the best-suited model adaptively. This mechanism is
based on a tiered edge-cloud architecture, which is designed for deploying a
diverse range of visual models, thus ensuring a wide selection availability.

C2, Camera Network Topology Utilization. Recognizing the common practice of
deploying cameras in groups, we leverage the inherent network topology of
these groups to develop a group-based mechanism to expedite the model
selection process, especially in scenarios where there is no clear data to
determine the optimal model or the impact of perspective. We demonstrate that
this approach significantly alleviates the demands of continual learning,
streamlining the operation in grouped camera environments.

C3, Camera Perspective Consideration. In response to the increasingly
adjustable function of the modern camera (Wong et al., 2024) and our
observation of measurement, we develop a “perspective-aware learning method”
for cameras. This method goes beyond the conventional approaches which merely
focus on improving visual models, but we uniquely account for the impact of
the source-side model selection, namely, “camera perspectives”, through online
sensing estimation during the visual model selection process.

Our code is publicly accessible at: Code Link. Additionally, this work does
not raise any ethical issues.

##  2\.  Background and Motivation

We start with a discussion on related works. Then we present our experimental
results to illustrate how visual models’ performance varies under external
environmental conditions and across different visual tasks, underscoring the
necessity of dynamic adaptation. Finally, we present the effects of the camera
perspective.

(a) Different environmental conditions

(b) Model performance with snowfall

(c) Dynamic performance shifts

(d) Environment and model correlation

Figure 1.  Comparative analysis of visual model performance across different
environmental conditions.

(a) Variability in perspective

(b) Varying segmentation accuracy

Figure 2. Role of camera perspective in object detection and semantic
segmentation visual tasks.

###  2.1. Related Work

In video analytics, video frames are continuously streamed from one or more
cameras to servers for processing. This often involves multiple visual models
to support a multitude of video analytics applications, particularly those
based on diverse architectures and weights of DNNs enabling them to
accommodate an extensive array of scenes and vision tasks (Qi et al., 2020;
Guo et al., 2021). However, the growing complexity of DNN architectures has
resulted in increased prediction latency, presenting a considerable challenge
for resource-limited end devices (Tan and Le, 2019; Li et al., 2018). To
handle this, significant efforts have been devoted to leveraging lightweight
models with streamlined architectures and fewer parameters (Han et al., 2020;
Zhang et al., 2018). Yet, despite their efficiency under specific conditions
or in tailored environments, these lightweight models often fall short in
dynamic object distributions or challenging environmental conditions.
Furthermore, the high costs of dynamically retraining model methods (Kong et
al., 2023; Bhardwaj et al., 2022) for specific scenarios make real-time
maintenance challenging under changing conditions (Han et al., 2024). Faced
with this, our method focuses on how to adapt to dynamic environments through
the prioritization of continuous online visual model selection, moving away
from the reliance on a few static models. More importantly, we demonstrate the
importance of “camera perspectives” on the model selection.

Regarding model selection, we implement the strategy derived from multi-armed
bandit (MAB), which performs online section of one or more options from a set
of alternatives based on feedback from previous choices (Lattimore and
Szepesvári, 2020). MAB has been widely applied in various domains, including
recommendation systems (Hill et al., 2017; Dai et al., 2024b), content
delivery (Yang et al., 2018; Liu et al., 2023b), and DNN design (You et al.,
2023; Zhang et al., 2021). Although some previous works on clustering bandits
have explored grouping human users (Gentile et al., 2014; Liu et al., 2022; Li
and Zhang, 2018; Wang et al., 2024b), its application in the intricate domain
of machine-centric video analytics remains under-explored, which uniquely
focuses on maximizing inference accuracy and handling issues such as frame
drops, provided the analytics’ integrity is maintained (Zhang et al., 2022).

###  2.2. Motivation Experiments

To investigate the variability of various models across different scenarios
and the impact of camera perspectives, we conduct a thorough comparative
analysis encompassing a range of models such as the YOLOv5 series (Jocher et
al., 2022), RTM detection (Lyu et al., 2022), SSD (Liu et al., 2016), and
Faster R-CNN (Ren et al., 2015). In particular, object detection and semantic
segmentation are selected as the visual tasks in our experiments.

Dataset. To assess the performance of visual models under different
environmental conditions, we compile five representative video datasets, each
covering a specific real-world scenario. These datasets are sourced from
publicly available videos on YouTube, identified by searching for specific
keywords (e.g., “live stream webcams”) and selecting those pertinent to
traffic conditions. To explore the effects of varying camera perspectives,
four videos with distinct perspectives are selected at the same time from the
above sources (SeeJH.com, 2024a, d, b, c). Furthermore, the free-viewpoint
videos are also utilized for evaluating perspectives, where videos of various
human movements on an indoor stage are recorded using 12 cameras positioned at
equal perspective intervals (Guo et al., 2024).

Evaluation Metrics. For object detection, performance is assessed using the
recall and F1 score metrics. We run the YOLOv5-x model as the ground truth,
with the detection confidence score set to 0.25, and the intersection over the
union threshold for calculating recall set at 0.5 aligning with (Zhang et al.,
2017; Du et al., 2020). For semantic segmentation, pixel accuracy is applied
as the metric, and the complex PP-HumanSegV1-Server (Liu et al., 2021) model
is run as the ground truth (Long et al., 2015).

Performance Variability of Visual Models. Fig. 1(a) reveals image examples
across daytime, nighttime, snowy, and dusky scenarios. The F1 scores of
YOLOv5-n demonstrate fluctuations across these four environments. In Fig.
1(b), a 135-second video depicting a sudden heavy snowfall is analyzed,
revealing a decline in performance across all models as the intensity of the
snowfall increases. The images on T = 20s and T = 100s show a clear difference
before and after the snowfall. Figs. 1(a) and 1(b) effectively illustrate our
argument with extensive examples across diverse environments and utilizing
various visual models: a single universal model faces significant challenges
when attempting to perform consistently in dynamic environments. The models
show performance fluctuations of varying magnitudes depending on the
environmental conditions.

Furthermore, we pre-retrain the YOLOv5-s model on a snowy-day traffic road
dataset(Pitropov et al., 2021) using four different learning rates and
training parameters under 100 epochs. we apply these models to a scenario
where snowfall gradually begins at 30 seconds and intensifies by 45 seconds.
As illustrated in Fig. 1(c), models pre-trained for snowy conditions show
improved performance as the snowfall increases. However, their performance
under normal weather conditions is inferior to that of the standard YOLOv5-s
model, likely due to overtraining on snowy data. In Fig. 1(d), we further pre-
train models on the COCO dataset for 100 epochs under various lighting
conditions and evaluate them using the same YouTube dataset. Although models
specifically pre-trained for certain environments show enhanced performance,
performance fluctuations also exist (the second row). Moreover, the challenge
of accurately quantifying light levels in dynamic real-world environments
complicates the direct matching of these conditions with an appropriate visual
model. This underscores the complexity involved in dynamically adapting visual
models to suit changing environmental conditions.

Impact of Camera Perspective.

(a) Perspective 1 (0°)

(b) Perspective 2 (30°)

(c) Perspective 3 (60°)

Figure 3. Semantic segmentation across diverse camera perspectives for the
same dancer.

We now turn our attention to the significant effects of camera perspective on
model selection. Initially, we evaluate the F1 scores for object detection
tasks using videos taken from different perspectives at the same traffic
intersection at the same time. Fig. 2(a) reveals that the F1 scores
significantly vary with the camera’s viewpoint. For instance, a direct frontal
view achieves an F1 score of 0.85, which drops to 0.61 when the camera is
positioned laterally. Furthermore, for the semantic segmentation task, we
explore the effects of camera perspective through multi-angle videos of
activities such as dancing, playing badminton, and throwing a frisbee in an
indoor environment, with a specific example of dancing showcased in Fig. 3.
According to Fig. 2(b), a frontal capture of a dancer yields a segmentation
accuracy of 0.81, which surprisingly increases to 0.87 from a side angle.
Additional analysis of two other movements shows similar patterns of accuracy
variation. The intrinsic relationship between perspective and model selection
lies in the fact that certain perspectives may pose challenges for a task,
e.g., distant blurred perspective in object recognition, requiring the use of
more sophisticated models, whereas other perspectives can be addressed using
simpler visual models (Another example is in Appendix B). Therefore, the
influence of perspective on model selection is a crucial factor that must be
considered.

##  3\. Model and Problem Formulation

Figure 4. Overview of AxiomVision framework.

In this section, we present the system model and the problem setting of our
proposed AxiomVision framework. Our framework focuses on the adaptive
selection of visual models under dynamic environmental changes and specific
task demands, which utilizes a hierarchical architecture for camera groups,
edge nodes, and cloud resources, and a continual video analytics pipeline to
enhance visual task performance. Fig. 4 depicts our overall framework design.

###  3.1. System Model

Tiered Edge-Cloud Architecture. Traditional methods typically put all visual
tasks, denoted as $\mathcal{Q}$, to the cloud for centralized processing,
which results in higher loads and longer response times on the cloud servers.
To address these issues and also for the deployment of multiple visual models,
we propose a hierarchical architecture, which consists of three levels: (a)
the video server, (b) the edge nodes, and (c) the end camera groups.
AxiomVision introduces a tailored combination set $\mathcal{M}_{q}$ of visual
model models for each distinct visual task $q\in\mathcal{Q}$ to better
accommodate external variables such as lighting conditions and movement
dynamics. Taking the object detection task as an example, lightweight models
such as MobileNet (Howard et al., 2017) are implemented on the resource-
limited edge nodes (Zhou et al., 2024), while the deployment of more
sophisticated models is designated for the cloud center. The total set of
cameras in our system is represented by $\mathcal{N}$ with cardinality
$|\mathcal{N}|$.

Online Video Analytics Pipeline. Our system is designed to adeptly handle the
non-continuous and varied visual tasks through a sequential, discrete-time
round approach. To accommodate the varied nature and frequency of task
demands, we define the sequence of rounds for each visual task
$q\in\mathcal{Q}$ as $\mathcal{T}_{q}$. For a specific visual task like facial
temperature recognition, the duration between consecutive rounds may differ
due to customer flow rates. Similar to (Yang et al., 2019), we assume that
individual tasks do not interfere with one another, permitting each to operate
in its designated round independently. Within this, the operational cycle of
the online video analytics pipeline at each round involves the scheduling
agent selecting visual models, obtaining feedback on their outcomes, and
subsequently updating the evaluations for these models.

Visual Payoff Feedback. To dynamically adapt to evolving conditions and task-
specific demands, we propose a visual payoff feedback mechanism, where payoff
can be interpreted as the likelihood of meeting certain criteria, such as
accuracy, recall, or F1 score. This process mainly focuses on the adjustment
of perspective weights $\boldsymbol{\theta}_{n}$ for each camera
$n\in\mathcal{N}$ in response to task feedback of the selected visual model,
thus enabling the online optimization of visual model efficacy.111For notation
clarity, we initially focus on the impact characteristics related to model
selection from a singular camera perspective. Nonetheless, our forthcoming
strategy for evaluating and categorizing perspective impacts is readily
scalable to accommodate the diverse impact characteristics of changeable
camera perspectives (see Section 5). For any given task $q\in\mathcal{Q}$, the
expected payoff $r_{m_{t},t}$ of the selected visual model $m_{t}$ is
expressed as:

(1)
$\mathbb{E}[r_{m_{t},t}|{m_{t}}]=\mu(\boldsymbol{x}_{m_{t}}^{\top}\boldsymbol{\theta}_{n}),$

where $\mu$ establishes a nonlinear connection between the payoff
$r_{m_{t},t}$ and the feature vector $\mathbf{x}_{m_{t}}$ of the visual model
$m_{t}$ at round $t$, incorporating the influence of the camera perspective
through the weight vector $\mathbf{\theta}_{n}$ (Kveton et al., 2020; Filippi
et al., 2010). An example of such a link function is a neural network, wherein
a final layer equipped with either a sigmoid or ReLU activation function
transforms the intricate features derived into meaningful results (Wu et al.,
2023; Lai et al., 2019).

Combinatorial Model Selection. Unlike conventional works that may only offer a
single model choice per task, we develop a “combinatorial model selection
strategy” from a wide range of model candidates, which increases the
probability of meeting the task’s requirements under diverse environmental
conditions. Specifically, a set of visual model options
$\mathcal{M}_{t}=\\{m_{1},\ldots,m_{|\mathcal{K}_{t}|}\\}\subseteq\mathcal{M}_{q}$
is presented for each task $q$ at every round $t$. $\mathcal{K}_{t}$ with the
size of $|\mathcal{K}_{t}|$ represents the selected visual model index at
round $t$, determined by the first selected model with $r_{t}=1$. Here, if the
accuracy of the selected visual model surpasses the predefined threshold, the
resulting payoff value $r_{t}$ will be assigned a value of 1. Initially, to
conserve resources and ensure rapid response, priority is given to models
deployed at the edge. If these models fall short of the task’s required
accuracy threshold, the scheduling agent will choose more complex models in
the cloud. More importantly, the selection of visual models is continually
refined based on payoff feedback. Thus, at each round $t$, the aggregate
payoff from these combinatorial usages of visual models $\mathcal{M}_{t}$ for
camera $n$ is calculated as:

$R(\mathcal{M}_{n,t})=1-\prod_{k=1}^{|\mathcal{K}_{t}|}(1-r_{m_{k,t},t}(m_{k,t})),\text{
where }k\in\mathcal{K}_{t},m_{k,t}\in\mathcal{M}_{t}.$

Note that we provide a combination of visual models based on the tiered
architecture to ensure accuracy. Moreover, we also strive to ensure that the
initially chosen visual model meets the requirements as much as possible (see
Section 4 for details).

Perspective-Based Grouping. For visual tasks that necessitate inputs from
multiple cameras, such as person tracking, the process entails more than just
evaluating how camera perspectives influence the choice of visual models. It
also presents a potential opportunity to group cameras based on their
overlapping perspective weights, where the increasing deployment of camera
network topologies inherently leads to a common occurrence of overlapping
perspectives (Chen et al., 2017). Recognizing this, we propose to group
cameras with similar influence of perspective $\boldsymbol{\theta}_{n}$ to
adopt a similar visual model selection. To distinguish cameras that cannot be
grouped together, we evaluate the dissimilarity between cameras using the
distance between the feature vectors representing camera perspective effects.
This evaluation involves establishing a “dispersion” criterion: cameras $j,k$
are considered for separate groups if:

(2)
$\vspace{-0.02in}\|\boldsymbol{\theta}_{j}-\boldsymbol{\theta}_{k}\|_{2}\geq\gamma_{q},\forall
j,k\in\mathcal{N},\vspace{-0.02in}$

where $\gamma_{q}$ signifies a predetermined positive dispersion constant
specific to task $q$. Based on the above criterion, the collective set of
cameras $\mathcal{N}$ can be divisible into smaller subsets, and we label them
as $G_{1},G_{2},\ldots,G_{g}$, wherein cameras within the same subset adhere
to a unified visual model selection strategy. Note that neither which camera
belongs to which group, nor the precise number of grouped cameras $g$ can be
not known beforehand in our model.

###  3.2. Problem Formulation

The selection of an optimal visual model is influenced by the diverse visual
tasks, external environment, and internal deployment factors, namely camera
perspectives. As a result, the scheduling agent must continually adapt the
choice of visual model $m_{t}\in\mathcal{M}$ for each processed camera
$n_{t}\in\mathcal{N}$ at the round $t\in\mathcal{T}_{q}$ for visual task $q$,
in alignment with the video analytics payoff. In this work, we propose to
dynamically adapt visual models in an online manner to maximize the overall
payoff across all rounds for any given visual task $q\in\mathcal{Q}$. This
objective is mathematically expressed as:

(3)
$\displaystyle\max\mathbb{E}\left[\sum_{t\in\mathcal{T}}\sum_{n\in\mathcal{N}}\mathbf{1}\\{n_{t}=n\\}R(\mathcal{M}_{n_{t},t})\right],$

where $\boldsymbol{1}\\{\cdot\\}$ denotes the indicator function. Given the
limited bandwidth and computing resources, it is not possible to select the
most resource-intensive visual model option (Jiang et al., 2018). Furthermore,
with the growing deployment of extensive camera networks by various entities,
an exploration into the impact of perspective similarity among cameras is
needed. By analyzing these perspective weight similarities, we aim to identify
and group cameras with similar perspective influences, thereby reducing the
number of subgroups needed for visual model sharing. Nevertheless, this
endeavor introduces several challenges, including complex search spaces,
varying effects of camera perspectives, zero prior knowledge of optimal visual
models, and the strategic deployment of camera groups. Addressing these issues
requires an adaptive algorithm capable of learning and adjusting visual models
online for diverse visual tasks, transcending the limitations of static,
offline model selection strategies.

##  4\. Continual Learning of AxiomVision

In this section, we first present the algorithm design of AxiomVision,
followed by a performance analysis. Specifically, a flexible graph-based
structure is utilized to mirror the natural undirected connectivity found in
camera cluster networks.222For brevity, we focus on the algorithmic procedures
for a singular visual task $q\in Q$, noting that the procedures can be
executed in parallel for multiple visual tasks $Q$.

###  4.1. Algorithm Design

Algorithm 1 Continual Online Learning of AxiomVision

1:Set of cameras $\mathcal{N}$; Parameter $\alpha$, $\beta$; Random
$p_{0}\in(0,1)$.

2:Visual model selection for all visual tasks.

3:Initialization: A complete graph $U_{0}$= ($\mathcal{N},E_{0}$); $g_{1}=1$;
$T_{n,0}=0,\forall n\in\mathcal{N}$.

4:for each $q\in\mathcal{Q}$, $t\in\mathcal{T}_{q}$, independently  do

5: Receive processed camera index $n_{t}$;

6: Identify group $G_{i_{t}}$ that contains $n_{t}$;

7: Estimate perspective weight $\hat{\boldsymbol{\theta}}_{i_{t},t-1}$ based
on Eq. (4);

8: Select the combinotorial model set $\mathcal{M}_{t}\in\mathcal{M}_{q}$
according

9: to Eq. (5) until the predetermined threshold is satisfied;

10: Record payoff $r_{m_{k},t}$ of the selected visual model
$m_{k},k\in\mathcal{K}_{t}$;

11: Increment count of processed camera $n_{t}$:
$T_{n_{t},t+1}=T_{n_{t},t}+1$;

12: Delete from $E_{t}$ all $\left(n_{t},\ell\right)$ if Eq. (6) holds and get
the resulting

13: graph $U_{t+1}=\left(\mathcal{N},E_{t+1}\right)$;

14: Update graph parameter: $p_{t}=p_{0}/t^{2}$;

15: Reconnect all edges in $E_{t+1}$ with probability $p_{t}$;

16:end for

Assigning Inferred Groups for Processed Cameras. Initially, we employ some
common clustering methods, e.g., $K$-means, to group cameras with similar
perspective impact weights. Within each cluster, a fully connected graph is
first established, reflecting camera connectivity symmetry and dynamic
adaptability for network topology, facilitating continual online updates. In
the absence of initial perspective impact weight information, the entire
camera cluster can be initialized as an undirected fully connected graph
$U_{0}=\left(\mathcal{N},E_{0}\right)$, maintained for visual task
$q\in\mathcal{Q}$, where each camera $m\in\mathcal{N}$ represents a node in
the graph. Cameras sharing similar learned perspective impact weights are
interconnected via edges in $E_{0}$. At each round $t$, the connected
components within graph $U_{t}$ signify the inferred groups
$G_{1},G_{2},\ldots,G_{g_{t}}$ with $g_{t}$ denoting the the number of camera
groups at $t$. Initially, graph $U_{1}$ is a complete graph, with $g_{1}=1$.
For the processed camera $n_{t}$, AxiomVision determines camera $n_{t}$’s
group index $i_{t}$ by identifying $U_{t}=\left(\mathcal{N},E_{t}\right)$ to
find the group that camera $n_{t}$ belongs to, i.e., $n_{t}\in G_{i_{t}}$.

Perspective-aware Weight Estimation. To maximize the payoff as defined in Eq.
(1), we propose to use the maximum likelihood estimator
$\hat{\boldsymbol{\theta}}_{i_{t},t}$ to test whether cameras belonging to
group $i_{t}$. This estimator is designed to yield a unique solution,
expressed as:

(4) $\sum_{j=1}^{t-1}\boldsymbol{1}\\{n_{j}\in
G_{i_{t}}\\}\sum_{k=1}^{|{\mathcal{K}}_{j}|}\left(r_{m_{k},j}-\mu(\boldsymbol{x}_{m_{k},j}^{\top}\hat{\boldsymbol{\theta}}_{i_{t},t})\right)\boldsymbol{x}_{m_{k},j}=0.$

Eq. (4) represents the condition for optimality, where the cumulative
discrepancy between the predicted payoff and actual payoff sums to zero, as
estimated by the membership indicator of cameras within the same group
$i_{t}$. We use Newton’s method which allows for efficient computation of the
solution (Li and Zhang, 2018; Filippi et al., 2010). The historical feedback
data from all cameras in the same group, not just camera $n_{t}$, are used to
update the estimation, emphasizing the value of grouping for process
acceleration. For the cases where the exact value of $\mu$ is unknown, the
process can be reduced to an estimation process using
$\boldsymbol{x}_{m_{k},j}^{\top}\hat{\boldsymbol{\theta}}_{i_{t},t}$ (The
subsequent visual model selection component following the same method).

Selecting Visual Model with Optimistic Approach. Following group assigning and
estimation, the currently processed camera undergoes optimization and reward
feedback observations on the selected visual model. Note that the greedy
visual model selection strategy, i.e., $\mathrm{argmax}_{m\in\mathcal{M}_{q}}$
$\mu(\boldsymbol{x}_{m}^{\top}\boldsymbol{\theta}_{n_{t}})$, might result in
insufficient exploration of undiscovered visual models, thereby failing to
ensure optimal model selection. We propose to address this challenge by
adopting an “optimistic approach to encourage exploration” among different
visual models (Lattimore and Szepesvári, 2020; Wang et al., 2023).
Specifically, for any processed camera $n\in\mathcal{N}$, we define the
Gramian matrix as $\boldsymbol{M}_{n,t}=$ $\sum_{\begin{subarray}{c}j\leq t\\\
n_{j}=n\end{subarray}}$
$\sum_{k=1}^{|\mathcal{K}_{j}|}\boldsymbol{x}_{m_{k},j}\boldsymbol{x}_{m_{k},j}^{\top}$,
and for the belonging group index $i$ of camera $n$, denote
$\boldsymbol{M}_{i,t}=$ $\zeta I_{d}+\sum_{n\in G_{i}}\boldsymbol{M}_{n,t}$,
where $\zeta I_{d}$ is a regularization term added to improve stability. Based
on the estimated $\hat{\boldsymbol{\theta}}_{i_{t,t-1}}$ for group
$G_{i_{t}}$, the visual model for round $t$ is selected via the upper
confidence bound strategy:

(5)
$m_{t}=\underset{m\in\mathcal{M}_{q}}{\operatorname{argmax}}\left(\mu(\boldsymbol{x}_{m}^{\top}\hat{\boldsymbol{\theta}}_{i_{t},t-1})+\alpha\left\|\boldsymbol{x}_{m}\right\|_{\boldsymbol{M}_{i_{t},t-1}^{-1}}\right),$

where
$\|\boldsymbol{x}\|_{\boldsymbol{M}}\coloneqq\sqrt{\boldsymbol{x}^{\top}\boldsymbol{M}\boldsymbol{x}}$
and $\alpha$ is a positive parameter. Note that Eq. (5) incorporates both
empirical payoff exploitation from the first term, as well as exploration of
different visual models through the upper confidence bound. The observed
payoff $r_{m_{t},t}$ is then recorded so to update the evaluated performance
of visual model $m_{t}$.

Optimizing Selection for Adaptive Accuracy. Subsequently, the agent selects a
set of visual models $\mathcal{M}_{t}=(m_{1},\ldots,m_{|{\mathcal{K}}_{t}|})$
for the processed cameras using the above optimistic selection strategy. It
initially prioritizes visual models based on Eq. (5), by consideration of
their deployment on edge nodes and in the cloud. If the accuracy does not meet
the predetermined threshold, the process continues with the next model, until
a stopping criterion is met. This strategy enables us to prioritize
potentially high-performing and lightweight models while ensuring accuracy
even under unforeseen circumstances, such as sudden snowy weather.
Additionally, the scheduling agent updates its estimation of visual models
based on the received payoff feedback of each selected visual model, to ensure
that subsequent selections meet the accuracy requirements on the first attempt
as much as possible. Through this approach, our proposed method can achieve
rapid visual model adaptation while ensuring adaptive accuracy across
different conditions.

Updating Dynamic Graph for Grouping. For any processed camera
$n\in\mathcal{N}$, we define $T_{n,t}=$ $\sum_{\begin{subarray}{c}j\leq t\\\
n_{j}=n\end{subarray}}|\mathcal{K}_{j}|$ as the number of effective feedbacks
up to round $t$. The dynamic graph structure is then updated to reflect
changes in camera grouping, particularly adjusting based on the current
inferred similarity in perspective weights. An edge $\left(n_{t},\ell\right)$
is removed if:

(6)
$\left\|\boldsymbol{\theta}_{n_{t},t-1}-\boldsymbol{\theta}_{\ell,t-1}\right\|_{2}>\beta\left(f(T_{n_{t},t-1})+f(T_{\ell,t-1})\right),$

with $f(x)=\sqrt{\frac{1+\log\left(1+x\right)}{1+x}},x\geq 0$. This deleting
function stems from a theoretical optimal graph structure threshold, modified
here for computational feasibility while still maintaining theoretical
validity (Gentile et al., 2014). Further comparisons will be illustrated in
Section 5. The updated graph $U_{t}$ is utilized in the subsequent round.

Adaptive Graph Reconstruction Strategy. To avoid mistakenly removing edges
that might be correct, the scheduling agent reinstates the undirected complete
graph at a certain probability. As more payoff feedback is gathered, the
accuracy of the estimated groupings improves the perspective influence on
visual models. Consequently, there is a diminished need for frequent graph
reconstructions, and this motivates us to have a design where the probability
$p_{t}$ decreases over time. Initially, $p_{0}$, set within the range (0,1),
is determined randomly (Line 14-15).

Note that our continual online design complements, rather than competes with
traditional offline methods. For example, if prior knowledge exists about the
effects of camera perspectives or the choice of models via the offline
methods, it can be easily assimilated into our strategy and progressively
refined based on AxiomVision.

###  4.2. Performance Analysis

For the ease of presenting our theoretical analysis, let
$\|\boldsymbol{x}_{m_{t}}\|_{2}\leq 1$ and
$\|\boldsymbol{\theta}_{n_{t}}\|_{2}\leq 1$, $m_{t}\in\mathcal{M}_{q}$ for all
rounds. At each round $t$, a camera is randomly processed from $\mathcal{N}$
with uniform probability for fairness, independently of selections in previous
rounds. For every visual task $q\in\mathcal{Q}$, we evaluate our algorithms by
measuring the greatest difference in payoff between the theoretically ideal
visual model (not known beforehand) and the visual model actually chosen. This
difference is defined as “regret” (Lattimore and Szepesvári, 2020; Liu et al.,
2023a), expressed as:

(7)
$Reg(T_{q})=\mathbb{E}[\sum_{t\in\mathcal{T}_{q}}\sum_{n\in\mathcal{N},n_{t}=n}R(\mathcal{M}^{*}_{n_{t}})-R(\mathcal{M}_{n_{t},t})],$

where $T_{q}$ denotes the cardinality of $\mathcal{T}_{q}$ and
$\mathcal{M}^{*}_{n_{t}}$ denotes the ”unknown” optimal combinatorial set of
visual models for task $q$.

In line with (Gentile et al., 2014; Liu et al., 2022; Li and Zhang, 2018), we
posit that
$\mathbb{E}\left[\boldsymbol{x}_{m_{t}}\boldsymbol{x}_{m_{t}}^{\top}\right]$
is full rank, with a minimum eigenvalue $\lambda>0$, and that
$x_{m_{t}}^{\top}\boldsymbol{\theta}_{n_{t}}$ exhibits a sub-Gaussian tail
with a variance not exceeding $\sigma^{2}$. Furthermore, following (Li and
Zhang, 2018; Filippi et al., 2010), we consider $\mu$ to be a strictly
increasing, continuously differentiable link function that is Lipschitz
continuous with constant $L$. We denote
$m_{\mu}=\inf_{a\in[-2,2]}\mu^{\prime}(a)$ and assume $m_{\mu}>0$. Defining
$\tilde{\lambda}$ as the integral
$\int_{0}^{\lambda}(1-e^{-\frac{(\lambda-x)^{2}}{2\sigma^{2}}})^{K}dx$ with
$K$ indicating the maximum number of selected combinatorial visual models
across all rounds (Wang et al., 2024a), we set the tuning parameters $\alpha$
and $\beta$ as follows:
$\alpha=\frac{1}{m_{\mu}}\sqrt{\frac{8}{\tilde{\lambda}}+d\ln(T/d)+2\ln(4gT)}$
and $\beta=\sqrt{32d/(\tilde{\lambda}m_{\mu}^{2})}$, where $d$ and $g$
represent the dimension of the vector and the maximum number of camera groups
under all adjustable perspectives, respectively. Then, we give the following
performance guarantee.

######  Theorem 1 (Regret Upper Bound).

The regret of AxiomVision throughout $\mathcal{T}_{q}$ is bounded by
$Reg(T_{q})\leq O\left(\frac{Ld}{m_{\mu}}\sqrt{gKT_{q}}\ln(T_{q})\right)$.

Remark: Theorem 1 suggests that the payoff from video analytics can approach
near-optimal performance asymptotically over rounds, signifying that
$\lim_{T_{q}\to\infty}\frac{Reg(T_{q})}{T_{q}}=0$. The expected regret of
video analytics payoff, defined in Eq. (7), arises from two primary factors
for a given visual task $q$: the rounds needed to gather sufficient
information for accurate camera attribute estimation and grouping, and the
practice of sharing the visual model within the same group instead of making
independent selections. Compared to the ideal scenario where camera grouping
is known and cameras have equal adjustable perspectives, the theoretical
convergence of AxiomVision is nearly optimal. This scenario is analogous to
managing $g$ independent groups, each undergoing $T_{q}/g$ learning rounds,
resulting in a regret lower bound of $\Omega(\frac{L}{m_{\mu}}\sqrt{dgT_{q}})$
(Dani et al., 2008).

Proof Sketch: For any camera $n$ with group index $i$, denote the frequency
associated with group $G_{i}$ up to round $t$ as $T_{i,t}=\sum_{n\in
G_{i}}T_{n,t}$, and
$g_{i_{t},t}(\boldsymbol{\theta})=\sum_{j=1}^{t-1}\boldsymbol{1}\\{n_{j}\in
G_{i_{t}}\\}\sum_{k=1}^{|{\mathcal{K}}_{j}|}\mu(\boldsymbol{x}_{m_{k},j}^{\top}\boldsymbol{\theta})\boldsymbol{x}_{m_{k},j}.$
With Eq. (4), then
$g_{i_{t},t}(\hat{\boldsymbol{\theta}}_{i_{t},t-1})=\sum_{s=1}^{t}$
$\boldsymbol{1}\\{i_{s}\in
I\\}\sum_{k=1}^{|\mathcal{K}_{j}|}r_{m_{k},j}\boldsymbol{x}_{m_{k},j}$. With
probability at least $1-\delta$, for some $j\leq t$ with
$\boldsymbol{M}_{i_{t},j}$ invertible:

$\vspace{-0.1in}\left\|g_{i_{t},t}(\hat{\boldsymbol{\theta}}_{i_{t},t})-g_{i_{t},t}(\boldsymbol{\theta}_{i_{t}})\right\|_{\boldsymbol{M}_{i_{t},t}^{-1}}^{2}\leq
T_{i_{t},j}\lambda_{\min}(\boldsymbol{M}_{i_{t},t})^{-1}+d\ln\frac{T_{i_{t},t}}{d}+2\ln\frac{1}{\delta}$

Here, $\lambda_{\min}(M)$ denotes the minimum eigenvalue of matrix $M$. Then,
$\boldsymbol{\alpha}(t,\delta)=$$\frac{1}{m_{\mu}}\sqrt{\frac{8}{\tilde{\lambda}}+d\ln\frac{t}{d}+2\ln\frac{1}{\delta}}$,
by the property of Lipschitz, we can assert that the currently estimated group
index $i_{t}$ for camera $n_{t}$ is correct. Consequently, the correct
grouping can be formed based on the deleting rule of Eq. (6). Consider the
instantaneous regret $Reg_{t}$ at round $t$ for the selected visual model
$m_{t}$ under task $q$. Given the correct grouping, we obtain:
$Reg_{t}=$$\mu(x_{m^{\star}}^{\top}\boldsymbol{\theta}_{n_{t}})-\mu(\boldsymbol{x}_{m_{t}}^{\top}\boldsymbol{\theta}_{n_{t}})$$\leq
2\alpha
L\left\|\boldsymbol{x}_{m_{t}}\right\|_{\boldsymbol{M}_{i_{t},t-1}^{-1}}.$
Finally, we derive:
$Reg(T_{q})=\mathbb{E}\left[\sum_{t=1}^{T_{q,0}}\mathbb{E}_{t}\left(Reg_{t}\right)\right]+\mathbb{E}\left[\sum_{t=T_{q,0}+1}^{T_{q}}\mathbb{E}_{t}\left(Reg_{t}\right)\right]\leq$
$O\left(\frac{Ld}{m_{\mu}}\sqrt{gKT_{q}}\ln(T_{q})\right).$

##  5\. Performance Evaluation

Figure 5. Comparison when perspective is not considered.

Figure 6. Different deleting function $f(x)$ on regret.

###  5.1. Implementation and Setup

Testbed. Leveraging public 360° VR camera feeds from (4K Urban Life, 2024a, b,
c, d), our setup involves NVIDIA Jetson TX2, Nano, and TX2 NX end devices
handling $|\mathcal{N}|=308$ video segments from different perspectives, with
ENs powered by NVIDIA GeForce RTX 4060 and HPC Dell PowerEdge R930 servers as
the cloud center. Rectilinear images are extracted from panorama to function
as adjustable perspectives (Lenjani et al., 2020). Beyond the DNN model used
in Section 2, we employ the lightweight YOLOv5-s, trained on the COCO dataset
under diverse lighting, finally containing a total of 17 optional visual
models. Visual tasks, in line with (Li et al., 2020; Wong et al., 2024),
include Classification, Counting, Detection, and Aggregation. Utilizing
approaches from (Liu et al., 2022; Li et al., 2019; Wu et al., 2023), we
construct and decompose a performance payoff matrix for these tasks across all
video segments, extracting feature vectors for visual model index
representation. Camera bandwidth varies between 1 and 2 Mb/s, with EN to
server uplink around 10 Mb/s (Lin et al., 2023; Hung et al., 2018).

Metrics. We evaluate the following performance metrics: (a) Accuracy: Assessed
for the four visual tasks outlined in (Li et al., 2020; Wong et al., 2024).
(b) Round: As described in Section 3. (c) Regret: Detailed in Eq. (7). (d)
Time: Encompasses the algorithm’s execution time, visual model inference time
(e.g., YOLOv5-s), and initial transmission time. Notably, transmission and
analysis are not sequential; initial data upload incurs a startup latency,
followed by continuous and parallel transmission and analysis. (e) Bandwidth:
Normalized bandwidth usage for transmitting encoded video segments. Through
both theoretical and empirical analysis, AxiomVision parameters are set to
$(\alpha,\beta)=(0.25,0.1)$. Note that we periodically run YOLOV5-x to acquire
true bounding boxes for accuracy assessment (included in the total consumption
measurements), and additional extended experiments can be found in Appendix B.

###  5.2. In-depth Analysis of Exploring Results

In pursuit of evaluating the effectiveness and rationale of certain components
within our AxiomVision design, we conduct a comprehensive series of
experiments under the object detection task.

Perspective Effects. To underscore the importance of camera perspective
alongside server-side models, we design an AxiomVision variant without
perspective consideration, w/o Perspective, and compared it with a version
integrating camera perspective, w/ Perspective, plus a greedy method providing
fixed-perspective optimal model across all feeds. As depicted in Fig. 6,
results show w/ Perspective improves mean accuracy by 2.7% over w/o
Perspective. Moreover, both w/o Perspective and w/ Perspective by facilitating
online model selection, surpass the greedy strategy by 2.3% and 5.6% in
accuracy.

Deleting Function Evaluation. Based on (Nagaraj et al., 2016; Low, 2003), we
assess various deleting functions: $f_{1}(x)=\sqrt{\frac{1+\ln(1+x)}{1+x}}$
(ours), $f_{2}(x)=$ $\frac{1}{(1+x)^{2}}$, $f_{3}(x)=$ $\frac{1}{\sqrt{1+x}}$,
$f_{4}(x)=$ $\frac{1}{\sqrt[4]{1+x}}$, $f_{5}(x)=$ $1+\ln(1+x)$, and
$f_{6}(x)=$ $\sqrt{1+\ln(1+x)}$. We evaluate the regret incurred by different
functions at 15, 50, 200, and 850 rounds for each camera, with the optimal
strategy determined through the YOLOv5-x model. Fig. 6 shows that the function
$\sqrt{\frac{1+\log(1+x)}{1+x}}$ consistently delivers optimal performance
across various rounds with minimal regret.

Figure 7. Influence of grouping cameras on acceleration.

Figure 8. The benefit of increased camera count.

Grouping Impact on Acceleration. Exploring the effect of camera grouping on
acceleration within the AxiomVision framework, we compare performances between
ungrouped (w/o Grouping) and grouped (w/ Grouping) setups, as illustrated in
Fig. 8. By setting accuracy thresholds from 0.8 to 0.87, w/ Grouping
significantly reduces the total number of rounds across all cameras by at
least 1.27$\times$, achieving an average acceleration of 3.23$\times$ and a
median of 2.18$\times$. Additionally, we observe that increasing the number of
cameras leads to a reduction in the required rounds while achieving a similar
level of accuracy, as shown in Fig. 8.

Figure 9. Evaluating usage of combinatorial set of models.

Figure 10. Set-based vs. graph-based on executing time.

Combinatorial Set Benefits. Referring to Section 3, we address dynamic
accuracy needs by assembling a combinatorial set of visual models for
selection, as illustrated in Fig. 10. Highlighting this design’s benefits, we
compare it with a non-combinatorial system (w/o Combing), which, after
applying w/ Combing, would run subsequent high-load models at equal
probability. The cumulative distribution function (CDF) for accuracy of object
detection in Fig. 10 shows that using the combinatorial set (w/ Combing)
achieves a median precision improvement over the non-combinatorial method (w/o
Combing) by 2.3%, with an average increase of 2.6%.

Graph Grouping Efficiency. In Algorithm 1, we implement a graph-based camera
grouping strategy, and a set-based AxiomVision algorithm is designed here.
Through testing execution time across various accuracy thresholds of 308
camera feeds, as depicted in Fig. 10, the graph-based approach significantly
reduces execution time by factors of 1.13$\times$, 3.62$\times$, 9.82$\times$,
and 10.50$\times$. Particularly in high-round scenarios, this graph-based
grouping method notably surpasses the set-based grouping in time efficiency.

###  5.3. Benchmarking against State-of-the-Art

Benchmarks. Our comparison includes the following schemes. (1) Chameleon,
capable of dynamically selecting the visual model based on temporal and
spatial correlations (Jiang et al., 2018). (2) Dual-MS, inspired by (Du et
al., 2020), categorizes visual models into two layers: a simpler model and a
more complex model, for effective model selection. (3) EAMU, standing for
edge-assisted on model update in adverse environments (Kong et al., 2023). (4)
Greedy, which, during the initial short segment of analysis for all video
sources offline, runs all models to identify the one offering the highest
average accuracy.

Figure 11. Accuracy on fixed and adjustable perspectives.

Figure 12. Decomposition of total time overhead.

Figure 13. Accuracy with varying bandwidth.

Accuracy on Fixed & Adjustable Perspectives. The average accuracy of 2000
rounds is illustrated in Fig. 11. Across different visual tasks for fixed
perspectives, AxiomVision, which employs a continuous online model selection,
consistently outperforms EAMU, Chameleon, Dual-MS and Greedy. Furthermore,
under adjustable perspectives, EAMU and Chameleon experience a deterioration
in accuracy due to their lack of consideration about the impact of source-side
camera perspectives.

Decomposition of Total Time. We compare our approach under $T_{q}=2000,\forall
q\in\mathcal{Q}$ with Chameleon (setting its parameter interval $=5$ and
top-$k=5$ for re-profiling video pipelines, referred to as execution time),
and EAMU (calculating its average training cost for retraining, also denoted
as execution time). Fig. 13 indicate that although our method leads to an
increase in inference time due to the adoption of a combinatorial design, it
efficiently reduces execution time by eliminating the need for the re-
profiling in Chameleon and the retraining process in EAMU. In comparison,
Chameleon allocates nearly identical time for spatial-temporal profiling; EAMU
incurs a significant additional time cost due to its retraining process.
Moreover, the initiation time for transmission is markedly the smallest in
scale under 200 kbps bandwidth constraint.

Impact of Bandwidth Condition. In Fig. 13, we benchmark our methodology
against Chameleon across the above tasks (abbreviated as $q1,q2,q3,q4$). EAMU
is omitted owing to its retraining architecture, which diverges from the
context of bandwidth. The outcomes demonstrate that the strategic approach of
AxiomVision, which involves selectively deploying complex models for tasks
where accuracy is compromised, significantly boosts performance across all
visual tasks. This advantage becomes particularly prominent in scenarios of
limited bandwidth, underscoring our method’s efficiency in bandwidth-
restricted video analytics.

##  6\. Conclusion

We propose AxiomVision, an innovative framework guaranteeing performance for a
wide range of environments and visual tasks. AxiomVision leverages dynamic
model selection and a tiered edge-cloud architecture. With experiments based
on extensive real-world camera videos, AxiomVision introduces a novel approach
to consider camera perspective and unveils a group-based acceleration strategy
that capitalizes on camera cluster topology. Furthermore, AxiomVision is
designed with a theoretical performance guarantee even under the worst-case
scenarios, that is, AxiomVision can asymptotically converge to the optimal
model section policy. Tested on a built platform, AxiomVision demonstrates
superior performance over existing works, and greatly improves adaptability
and efficiency across various video analytics applications.

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## Appendix

##  Appendix A Proof of Theorem 1

###### Proof.

For any processed camera $n\in\mathcal{N}$, we define the Gramian matrix and
the number of effective feedbacks for camera $n$ up to round $t$,
respectively, as follows:

$\displaystyle\boldsymbol{M}_{n,t}=\sum_{\begin{subarray}{c}j\leq t\\\
n_{j}=n\end{subarray}}\sum_{k=1}^{|\mathcal{K}_{j}|}\boldsymbol{x}_{m_{k},j}\boldsymbol{x}_{m_{k},j}^{\top}\,,\quad
T_{n,t}=\sum_{\begin{subarray}{c}j\leq t\\\
n_{j}=n\end{subarray}}|\mathcal{K}_{j}|$

Subsequently, for any camera $n$ belonging to group index $i$, denote

(8) $\begin{split}&\boldsymbol{M}_{i,t}=\zeta I_{d}+\sum_{n\in
G_{i}}\boldsymbol{M}_{n,t},\quad T_{i,t}=\sum_{n\in G_{i}}T_{n,t}\end{split}$

be the regularized Gramian matrix, and the frequency associated with belonging
group $G_{i}$, respectively, incorporating the regularization parameter
$\zeta>0$ up to round $t$.

Consider the gradient function defined for any camera within group $G_{i_{t}}$
at time $t$ as:

$g_{i_{t},t}(\boldsymbol{\theta})=\sum_{j=1}^{t-1}\boldsymbol{1}\\{n_{j}\in
G_{i_{t}}\\}\sum_{k=1}^{|{\mathcal{K}}_{j}|}\mu(\boldsymbol{x}_{m_{k},j}^{\top}\boldsymbol{\theta})\boldsymbol{x}_{m_{k},j}.$

Recall that $\hat{\boldsymbol{\theta}}{i_{t},t}$ is identified as the unique
solution of the equation:

$\sum_{j=1}^{t-1}\boldsymbol{1}\\{n_{j}\in
G_{i_{t}}\\}\sum_{k=1}^{|{\mathcal{K}}_{j}|}\left(r_{m_{k},j}-\mu(\boldsymbol{x}_{m_{k},j}^{\top}\hat{\boldsymbol{\theta}}_{i_{t},t})\right)\boldsymbol{x}_{m_{k},j}=0.$

Then, it is possible to express
$g_{i_{t},t}(\hat{\boldsymbol{\theta}}_{i_{t},t-1})$, which captures the
cumulative response adjusted by the previous estimate of
$\boldsymbol{\theta}$, as follows:
$g_{i_{t},t}(\hat{\boldsymbol{\theta}}_{i_{t},t-1})=\sum_{s=1}^{t-1}\boldsymbol{1}\\{n_{j}\in
G_{i_{t}}\\}\sum_{k=1}^{|\mathcal{K}_{j}|}r_{m_{k},j}\boldsymbol{x}_{m_{k},j}$.
This formulation integrates the feedback up to round $t-1$, weighted by the
membership of the cameras in the group $G_{i_{t}}$, to refine the estimation
of the parameter $\boldsymbol{\theta}$.

Next, we introduce a lemma that provides a theoretical guarantee for the
accuracy of the ridge regression estimate in approximating the true weight
vector of camera perspective influence. This lemma is critical for
understanding the bounds of estimation error in linear models with ridge
regression.

######  Lemma 0 (Theorem 1 in (Abbasi-Yadkori et al., 2011)).

Consider a sequence of data points
$\left(x_{1},y_{1}\right),\ldots,\left(x_{t},y_{t}\right)$ are generated
sequentially from a linear model such that $\left\|x_{t}\right\|\leq 1$ for
all $t,\mathbb{E}\left[y_{t}\mid x_{t}\right]=\theta_{*}^{\top}x_{t}$ for
fixed but unknown $\theta_{*}$ with norm at most 1 , and
$\left\\{y_{t}-\theta_{*}^{\top}x_{t}\right\\}_{t=1,2,\ldots}$ have $1$-sub-
Gaussian tails. Let $M_{t}=\zeta
I+\sum_{s=1}^{t}x_{s}x_{s}^{\top},b_{t}=\sum_{s=1}^{t}x_{s}y_{s}$, and
$\delta>0$. If $\hat{\theta}_{t}=M_{t}^{-1}b_{t}$ is the ridge regression
estimator of $\theta_{*}$, then with probability at least $1-\delta$, for all
$t\geq 0$,

$\displaystyle\left\|\hat{\theta}_{t}-\theta_{*}\right\|_{M_{t}}$
$\displaystyle\leq\sqrt{d\ln\left(1+\frac{t}{\zeta
d}\right)+2\ln\frac{1}{\delta}}+\sqrt{\zeta}.$

Furthermore, we examine the determinant of the matrix $\boldsymbol{M}_{t}$ and
its relationship with its eigenvalues and trace, leading to:

$\displaystyle
det(\boldsymbol{M}_{t})\leq\big{(}\frac{\sum_{i=1}^{d}\lambda_{i}}{d}\big{)}^{d}=\big{(}\frac{trace(\boldsymbol{M}_{t})}{d}\big{)}^{d}\leq\big{(}\frac{t+\zeta
d}{d}\big{)}^{d}\,,$

where $\lambda_{i},(i=1,2,\ldots,d)$ denotes the eigenvalues of the matrix
$\boldsymbol{M}_{t}$, $trace(\boldsymbol{M}_{t})$ denotes the trace of
$\boldsymbol{M}_{t}$. By Lemma 1, combined with the inequality:
$\operatorname{det}\left(\boldsymbol{M}_{i,t}\right)\leq\frac{1}{d^{d}}$
$\left(\operatorname{trace}(\boldsymbol{M}_{i,t})+\sum_{j=1}^{t}\left\|x_{t}\right\|_{2}^{2}\right)^{d}$$\leq\left(\zeta+t/d\right)^{d},$
for some $j\leq t$ (will be clarified later) with $\boldsymbol{M}_{i_{t},j}$
invertible, with probability at least $1-\delta$, we have:

$\left\|g_{i_{t},t}(\hat{\boldsymbol{\theta}}_{i_{t},t})-g_{i_{t},t}(\boldsymbol{\theta}_{i_{t}})\right\|_{\boldsymbol{M}_{i_{t},t}^{-1}}^{2}\leq
T_{i_{t},j}\lambda_{\min}(\boldsymbol{M}_{i_{t},t})^{-1}+d\ln\frac{T_{i_{t},t}}{d}+2\ln\frac{1}{\delta},$

Here, $\lambda_{\min}(M)$ denotes the minimum eigenvalue of matrix $M$.

Leveraging the Lipschitz continuity and the properties of the first derivative
for the function $\mu$,
$g_{i_{t},t}(\hat{\boldsymbol{\theta}}_{i_{t},t})-g_{i_{t},t}(\boldsymbol{\theta}_{i_{t}})\succeq
m_{\mu}\boldsymbol{M}_{i_{t},t}$, we assert that the difference between the
gradient functions evaluated at the estimated and true parameter vectors is
bounded by the product of $m_{\mu}$ and the matrix $\boldsymbol{M}_{i_{t},t}$.
Consequently, this relationship yields the following inequality:

$m_{\mu}^{2}\left\|\hat{\boldsymbol{\theta}}_{i_{t},t}-\boldsymbol{\theta}_{i_{t}}\right\|_{\boldsymbol{M}_{i_{t},t}}^{2}\leq
T_{i_{t},j}\lambda_{\min}(\boldsymbol{M}_{i_{t},t})^{-1}+d\ln\frac{T_{i_{t},t}}{d}+2\ln\frac{1}{\delta}.$

From Lemma 1, denoting
$\boldsymbol{\alpha}(t,\delta)=\frac{1}{m_{\mu}}\sqrt{\frac{8}{\tilde{\lambda}}+d\ln\frac{t}{d}+2\ln\frac{1}{\delta}}$,
we can derive that the following inequality holds:

$\displaystyle\left|\mu(x_{m^{\star}_{t}}^{\top}\boldsymbol{\theta}_{i_{t}})-\mu(\boldsymbol{x}_{m_{t}}^{\top}\boldsymbol{\theta}_{i_{t}})\right|\leq$
$\displaystyle
L\left\|x_{m^{\star}_{t}}^{\top}\boldsymbol{\theta}_{i_{t}}-\boldsymbol{x}_{m_{t}}^{\top}\boldsymbol{\theta}_{i_{t}}\right\|$
$\displaystyle\leq~{}$ $\displaystyle
2L\boldsymbol{\alpha}(T_{i_{t},t-1},\delta)\left\|\boldsymbol{x}_{m_{t}}\right\|_{\boldsymbol{M}_{i_{t},t}^{-1}}\,.$

which confirms the accuracy of the estimated group index $i_{t}$ for camera
$n_{t}$. Here, $m^{\star}_{t}$ represents the optimal model at round $t$.

In the context of this analysis, let us consider a scenario where for any
$\omega>0$ and any $m\in\mathcal{M}_{t}$:

$\mathbb{P}_{t}(\boldsymbol{\theta}_{m}<-\omega|\left|\mathcal{M}_{t}\right|)\leq
e^{-\frac{\omega^{2}}{2\sigma^{2}}}\,,$

where $\mathbb{P}_{t}(\cdot)$ is the shorthand for the conditional probability
given the size of the set $\mathcal{M}t$. Given that

$\displaystyle\mathbb{E}_{t}[(\boldsymbol{\theta}^{\top}\boldsymbol{x}_{m,t})^{2}|\left|\mathcal{M}_{t}\right|$
$\displaystyle=\mathbb{E}_{t}[\boldsymbol{\theta}^{\top}\boldsymbol{x}_{m,t}\boldsymbol{x}_{m,t}^{\top}\boldsymbol{\theta}|\left|\mathcal{M}_{t}\right|]$
$\displaystyle\geq\lambda_{\text{min}}(\mathbb{E}_{\boldsymbol{x}\sim\rho}[\boldsymbol{x}\boldsymbol{x}^{\top}])\geq\lambda,$

it follows that

$\mathbb{P}_{t}(\min_{i=1,\ldots,\left|\mathcal{M}_{t}\right|}(\boldsymbol{\theta}^{\top}\boldsymbol{x}_{m,t})^{2}\geq\lambda-\omega|\left|\mathcal{M}_{t}\right|)\geq(1-e^{-\frac{\omega^{2}}{2\sigma^{2}}})^{K}\,.$

From this, we deduce that

$\displaystyle\mathbb{E}_{t}[(\boldsymbol{\theta}^{\top}\boldsymbol{x}_{m_{t}})^{2}|\left|\mathcal{M}_{t}\right|]$
$\displaystyle\geq\mathbb{E}_{t}[\min_{m\in\mathcal{M}_{t}}(\boldsymbol{\theta}^{\top}\boldsymbol{x}_{m,t})^{2}|\left|\mathcal{M}_{t}\right|]$
$\displaystyle\geq\int_{0}^{\infty}\mathbb{P}_{t}(\min_{m\in\mathcal{M}_{t}}(\boldsymbol{\theta}^{\top}\boldsymbol{x}_{m,t})^{2}\geq
x|\left|\mathcal{M}_{t}\right|)dx$
$\displaystyle\geq\int_{0}^{\lambda}(1-e^{-\frac{(\lambda-x)^{2}}{2\sigma^{2}}})^{K}dx\triangleq\tilde{\lambda}$

This establishes a lower bound, $\tilde{\lambda}$, on the expected squared
projection of $\boldsymbol{\theta}$ onto the feature vectors
$\boldsymbol{x}_{m,t}$ for any $m$ in $\mathcal{M}_{t}$,

By Claim 1 of (Gentile et al., 2014), Lemma 7, 8 of (Li and Zhang, 2018), for
each camera $n$, for all
$T_{n,t}\geq\frac{1024}{\tilde{\lambda}^{2}}\ln\frac{512d}{\tilde{\lambda}^{2}\delta}$,
$\lambda_{\min}(\boldsymbol{M}_{n,t})\geq T_{n,t}\tilde{\lambda}/8$ with high
probability. Thus with high probability, for the belonging group index $i$, we
have:

$\displaystyle\left\|\hat{\boldsymbol{\theta}}_{n,t}-\boldsymbol{\theta}_{n}\right\|_{\boldsymbol{M}_{i,t}}$
$\displaystyle\leq\frac{1}{m_{\mu}}\sqrt{\frac{8}{\tilde{\lambda}}+d\ln\frac{T_{n,t}}{d}+2\ln\frac{1}{\delta}}$
$\displaystyle\left\|\hat{\boldsymbol{\theta}}_{n,t}-\boldsymbol{\theta}_{n}\right\|$
$\displaystyle\leq\frac{\sqrt{\frac{8}{\tilde{\lambda}}+d\ln\frac{T_{n,t}}{d}+2\ln\frac{1}{\delta}}}{m_{\mu}\sqrt{\tilde{\lambda}T_{n,t}/8}}.$

When
$T_{n,t}\geq\frac{512d}{(\gamma_{q})^{2}\lambda}\ln\frac{|\mathcal{N}|}{\delta}$
with Lemma 10 in (Li and Zhang, 2018), we have:
$\frac{\boldsymbol{\alpha}\left(T_{n,t},\delta\right)}{m_{\mu}\sqrt{\tilde{\lambda}T_{n,t}/8}}$
$<\frac{\gamma_{q}}{4}.$ According to Lemma 1 in (Wang et al., 2024b), these
conditions are satisfied with a probability of at least $1-\delta$, for
$\delta$ in the interval $(0,1)$, provided that the time $t$ meets or exceeds

(9) $\displaystyle t\geq$ $\displaystyle
4|\mathcal{N}|\max\left\\{\frac{512d}{(\gamma_{q})^{2}\tilde{\lambda}}\ln\frac{|\mathcal{N}|}{\delta},\frac{256}{\tilde{\lambda}^{2}}\ln\frac{32d}{\tilde{\lambda}^{2}\delta}\right\\}$
$\displaystyle+16|\mathcal{N}|\ln\frac{4|\mathcal{N}|T}{\delta}=:T_{q,0},$

With this, we can show that AxiomVision will group all the cameras correctly
after $T_{q,0}$. Let $\alpha=\frac{16\sqrt{d}}{\tilde{\lambda}m_{\mu}}$ and
use $i(n)$ to denote the index of group camera $n$ belongs to (_i.e._ , $n\in
G_{i(n)}$). First, if AxiomVision deletes the edge $(n,\ell)$, then camera $n$
and camera $\ell$ belong to different ground-truth groups, i.e.,
$\left\|\boldsymbol{\theta}_{n}-\boldsymbol{\theta}_{\ell}\right\|_{2}>0$.
This is because by the deletion rule of the algorithm, the concentration
bound, and triangle inequality,
$\left\|\boldsymbol{\theta}_{n}-\boldsymbol{\theta}_{\ell}\right\|_{2}\geq\left\|\hat{\boldsymbol{\theta}}_{n,t}-\hat{\boldsymbol{\theta}}_{\ell,t}\right\|_{2}-\left\|\boldsymbol{\theta}_{i(\ell)}-\boldsymbol{\theta}_{\ell,t}\right\|_{2}-\left\|\boldsymbol{\theta}_{i(n)}-\boldsymbol{\theta}_{n,t}\right\|_{2}>0$.
Second, we show that if
$\left\|\boldsymbol{\theta}_{n}-\boldsymbol{\theta}_{\ell}\right\|\geq\gamma_{q}$,
AxiomVision will delete the edge $(n,\ell)$, where the dispersion condition in
Eq. (2) implies that if the condition of deleting edge in Eq. (6) is met, then
cameras $n,\ell$ indeed belong to different ground-truth groups. This is
because if
$\left\|\boldsymbol{\theta}_{n}-\boldsymbol{\theta}_{\ell}\right\|\geq\gamma_{q}$,
then by the triangle inequality, and
$\left\|\hat{\boldsymbol{\theta}}_{n,t}-\boldsymbol{\theta}_{i(n)}\right\|_{2}<\frac{\gamma_{q}}{4}$,
$\left\|\hat{\boldsymbol{\theta}}_{\ell,t}-\boldsymbol{\theta}_{i(\ell)}\right\|_{2}<\frac{\gamma_{q}}{4}$,
$\boldsymbol{\theta}_{n}=\boldsymbol{\theta}_{i(n)}$,
$\boldsymbol{\theta}_{\ell}=\boldsymbol{\theta}_{i(\ell)}$, we have
$\left\|\hat{\boldsymbol{\theta}}_{n,t}-\hat{\boldsymbol{\theta}}_{\ell,t}\right\|_{2}$
$\geq\left\|\boldsymbol{\theta}_{n}-\boldsymbol{\theta}_{\ell}\right\|-$
$\left\|\hat{\boldsymbol{\theta}}_{n,t}-\boldsymbol{\theta}_{i(n)}\right\|_{2}-$
$\left\|\hat{\boldsymbol{\theta}}_{\ell,t}-\boldsymbol{\theta}_{i(\ell)}\right\|_{2}$
$>\gamma_{q}-$$\frac{\gamma_{q}}{4}-$$\frac{\gamma_{q}}{4}=\frac{\gamma_{q}}{2}$.
Note that the threshold $\beta(f(T_{n_{t},t-1})+f(T_{\ell,t-1}))$ in Eq. (6)
is designed in accordance with the theoretical framework (Gentile et al.,
2014). Moreover, Algorithm 1 reinstates the fully connected graph visual model
as detailed in Line 15. This adjustment ensures that, when applied across all
cameras, the derived groupings are precise.

Once AxiomVision successfully groups all cameras accurately, it follows that
the discrepancy between the estimated parameter vector
$\hat{\boldsymbol{\theta}}_{i{t},t-1}$ for group $i_{t}$ at time $t-1$ and the
true parameter vector $\boldsymbol{\theta}_{n_{t}}$ for camera $n_{t}$ is
bounded by the norm induced by the matrix $\boldsymbol{M}_{i_{t},t-1}$:

(10)
$\left\|\hat{\boldsymbol{\theta}}_{i_{t},t-1}-\boldsymbol{\theta}_{n_{t}}\right\|_{\boldsymbol{M}_{i_{t},t-1}}\leq\boldsymbol{\alpha}(T_{i_{t},t-1},\delta)\leq\boldsymbol{\alpha}(T,\delta).$

Then, applying the Cauchy-Schwarz inequality, we obtain:

$\displaystyle\left|\boldsymbol{x}^{\top}_{m_{t}}\left(\hat{\boldsymbol{\theta}}_{i_{t},t-1}-\boldsymbol{\theta}_{n_{t}}\right)\right|$
$\displaystyle\leq\|x\|_{\boldsymbol{M}_{i_{t},t-1}^{-1}}$
$\displaystyle\left\|\hat{\boldsymbol{\theta}}_{i_{t},t-1}-\boldsymbol{\theta}_{n_{t}}\right\|_{\boldsymbol{M}_{i_{t},t-1}^{-1}}\leq\boldsymbol{\alpha}(T,\delta)\|x\|_{\boldsymbol{M}_{i_{t},t-1}^{-1}}.$

By setting $\delta=1/T$, with probability at least $1-1/T$, for each camera
$n_{t}$ with the selected visual model $m_{t}$ under query $q$, the following
holds:

(11)
$\displaystyle\left|\boldsymbol{x}^{\top}_{m_{t}}\left(\hat{\boldsymbol{\theta}}_{i_{t},t-1}-\boldsymbol{\theta}_{n_{t}}\right)\right|\leq\alpha\|\boldsymbol{x}\|_{\boldsymbol{M}_{i_{t},t-1}^{-1}}.$

This establishes a confidence interval that bridges the gap between group-
based visual model selection and individual selection.

The analysis of instantaneous regret, $Reg_{t}$, at any given round $t$ for
the selected visual model $m_{t}$ under visual task $q$, allows us to assess
the immediate loss due to the choice of the model at that round. For $t\geq
T_{q,0}$, the instantaneous regret is given by:

(12) $\displaystyle Reg_{t}=$
$\displaystyle\mu(x_{m^{\star}_{t}}^{\top}\boldsymbol{\theta}_{n_{t}})-\mu(\boldsymbol{x}_{m_{t}}^{\top}\boldsymbol{\theta}_{n_{t}})$
$\displaystyle\leq$ $\displaystyle
2\boldsymbol{\alpha}L(T_{i_{t},t-1},\delta)\left\|\boldsymbol{x}_{m_{t}}\right\|_{\boldsymbol{M}_{i_{t},t-1}^{-1}}\leq
2\alpha
L\left\|\boldsymbol{x}_{m_{t}}\right\|_{\boldsymbol{M}_{i_{t},t-1}^{-1}}.$

Aggregating all instant regrets under visual task $q$ into a total regret
$Reg(T_{q})$, and applying the Cauchy-Schwarz inequality for summation over
all rounds, we derive:

(13) $\displaystyle Reg(T_{q})$
$\displaystyle=\mathbb{E}\left[\sum_{t=1}^{T_{q,0}}\mathbb{E}_{t}\left(Reg_{t}\right)\right]+\mathbb{E}\left[\sum_{t=T_{q,0}+1}^{T_{q}}\mathbb{E}_{t}\left(Reg_{t}\right)\right]$
$\displaystyle\leq
T_{q,0}+\sum_{t=T_{q,0}+1}^{T_{q}}L\min\left\\{2,2\alpha\left\|\boldsymbol{x}_{m_{t}}\right\|_{\boldsymbol{M}_{i_{t},t-1}^{-1}}\right\\}$
$\displaystyle\stackrel{{\scriptstyle(a)}}{{\leq}}T_{q,0}+2\alpha\sum_{1}^{g_{q}}\sqrt{T_{q}\sum_{t=T_{q,0}+1}^{T_{q}}\min\\{1,\left\|\boldsymbol{x}_{m_{t}}\right\|_{\boldsymbol{M}_{i_{t},t-1}^{-1}}^{2}}\\}$
$\displaystyle\stackrel{{\scriptstyle(b)}}{{\leq}}T_{q,0}+2\alpha
L\sqrt{2g_{q}dT\log\left(1+\frac{T}{\zeta d}\right)},$

where $g_{q}$ denotes the number of ground-truth camera groups under visual
task $q$ and (a) is due to the Cauchy-Schwarz inequality, (b) is by Lemma 11
in (Abbasi-Yadkori et al., 2011). Finally, in the event of failure, which
occurs with a probability of at most $\delta$, the regret remains constant. ∎

##  Appendix B Extended Experiments

###  B.1. Effect of Camera Angles on Model Selection

(a) Camera A

(b) Camera B

(c) Camera C

Figure 14.  The same object from different perspectives.

Fig. 14 demonstrates how the perception of the same object changes from
different camera angles. Camera A, positioned at a greater distance and higher
angle, provides an overview perspective, potentially altering the perception
of size and shape due to increased distance and angle, thereby necessitating a
more complex object detection algorithm. On the other hand, Camera C captures
the object at a low angle and close range, clearly revealing details, which
allows for the use of a more lightweight object detection algorithm. These
variations in perspective significantly impact how surveillance or computer
vision systems detect and recognize objects, underscoring the influence of
different camera perspectives on the selection of visual models.

Table 1. Accuracy under varying bandwidth for classification. Time (s) | 0 | 4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 | 40 | 44 | 48 | 52 | 56
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
Accuracy | 0.922 | 0.922 | 0.924 | 0.916 | 0.920 | 0.918 | 0.920 | 0.921 | 0.919 | 0.913 | 0.925 | 0.930 | 0.928 | 0.931 | 0.933
Bandwidth (Mbps) | 0.407 | 0.365 | 0.365 | 0.267 | 0.232 | 0.203 | 0.147 | 0.161 | 0.168 | 0.098 | 0.168 | 0.182 | 0.175 | 0.196 | 0.224
Table 2. Accuracy under varying bandwidth for counting. Time (s) | 0 | 4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 | 40 | 44 | 48 | 52 | 56
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
Accuracy | 0.923 | 0.923 | 0.929 | 0.921 | 0.920 | 0.926 | 0.960 | 0.962 | 0.965 | 0.969 | 0.967 | 0.928 | 0.898 | 0.902 | 0.890
Bandwidth (Mbps) | 1.024 | 1.270 | 1.228 | 1.094 | 1.144 | 1.144 | 1.508 | 1.768 | 1.789 | 1.726 | 1.628 | 1.186 | 0.779 | 0.954 | 0.730
Table 3. Accuracy under varying bandwidth for detection. Time (s) | 0 | 4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 | 40 | 44 | 48 | 52 | 56
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
Accuracy | 0.913 | 0.912 | 0.910 | 0.906 | 0.907 | 0.942 | 0.979 | 0.972 | 0.978 | 0.976 | 0.880 | 0.835 | 0.845 | 0.830 | 0.843
Bandwidth (Mbps) | 1.515 | 1.593 | 1.501 | 1.431 | 1.557 | 1.985 | 2.540 | 2.392 | 2.526 | 2.441 | 1.256 | 0.702 | 0.898 | 0.695 | 0.716
Table 4. Accuracy under varying bandwidth for aggregation. Time (s) | 0 | 4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 | 40 | 44 | 48 | 52 | 56
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
Accuracy | 0.824 | 0.823 | 0.827 | 0.823 | 0.822 | 0.855 | 0.870 | 0.871 | 0.869 | 0.865 | 0.871 | 0.835 | 0.790 | 0.786 | 0.792
Bandwidth (Mbps) | 0.316 | 0.351 | 0.379 | 0.316 | 0.358 | 0.631 | 0.772 | 0.821 | 0.751 | 0.673 | 0.765 | 0.519 | 0.168 | 0.210 | 0.210

Figure 15. Accuracy v.s. the normalized bandwidth.

Figure 16. Accuracy under varying bandwidth.

(a) $\alpha=0.25,\beta=0.05$

(b) $\alpha=0.25,\beta=0.2$

(c) $\alpha=0.5,\beta=0.05$

(d) $\alpha=0.5,\beta=0.2$

Figure 17. Comparative analysis of AxiomVision performance on fixed
perspectives with different parameters.

(a) $\alpha=0.25,\beta=0.05$

(b) $\alpha=0.25,\beta=0.2$

(c) $\alpha=0.5,\beta=0.05$

(d) $\alpha=0.5,\beta=0.2$

Figure 18.  Comparative analysis of AxiomVision performance on adjustable
perspectives with different parameters.

###  B.2. Accuracy-Bandwidth Trade-off

As illustrated in Fig. 16, our system adeptly achieves a balance between two
pivotal metrics—accuracy and bandwidth—through an online visual model
selection process based on the tiered edge-cloud architecture. In comparison,
both EAMU and Chameleon limit themselves to relatively uniform visual models
which result in either compromised accuracy or excessive bandwidth
consumption. Conversely, by setting combinatorial accuracy thresholds of
$Th=0.7,0.8,0.9$ under various bandwidth scenarios respectively, AxiomVision
consistently achieves higher accuracy with lower bandwidth usage. This
efficiency allows for the conservation of bandwidth resources without
sacrificing accuracy.

###  B.3. Accuracy with Bandwidth Variability

Fig. 16 depicts the behavior of video feeds over a 60-second span, subject to
dynamic and varied bandwidth conditions at ENs. Notably, Fig. 16 highlights
how AxiomVision dynamically adjusts its selection of visual models in response
to a surge in bandwidth availability between 20 and 40 seconds. This
adjustment enables the adoption of more resource-demanding visual models,
resulting in a significant boost in accuracy. Such adaptability demonstrates
AxiomVision’s exceptional responsiveness to changes in bandwidth. For detailed
changes in accuracy for the four specific visual tasks as bandwidth varies,
please refer to Table 1-4.

###  B.4. Ablation Study on Different Parameters

Fig. 17 and Fig. 18 present a detailed comparative analysis on both fixed and
adjustable perspective cameras, illustrating the performance of our proposed
system, AxiomVision, against Dual-MS across four distinct visual tasks. This
thorough comparison, conducted over a wide range of parameter settings,
ensures a comprehensive evaluation of the system’s capabilities. Notably, the
superior accuracy and consistent performance of AxiomVision underscore its
robustness and adaptability to various environmental conditions.

(a) Dataset: People

(b) Dataset: Mixed

(c) Dataset: Cars

(d) Dataset: People

(e) Dataset: Mixed

(f) Dataset: Cars

Figure 19.  Comparison of AxiomVision with multi deployment levels;
AxiomVision (bi-level) with the first and second levels.

(a) Dataset: People

(b) Dataset: Mixed

(c) Dataset: Cars

(d) Dataset: People

(e) Dataset: Mixed

(f) Dataset: Cars

Figure 20.  Comparison of AxiomVision with multi deployment levels;
AxiomVision (bi-level) with the first and third levels.

(a) Dataset: People

(b) Dataset: Mixed

(c) Dataset: Cars

(d) Dataset: People

(e) Dataset: Mixed

(f) Dataset: Cars

Figure 21.  Comparison of AxiomVision with multi deployment levels;
AxiomVision (bi-level) with the second and third levels.

###  B.5. Visual Model Deployment Analysis

We continue to explore deployment strategies for visual models within edge-
cloud architectures. Specifically, we categorize the deployed visual models
into three levels: simple, medium-complexity, and complex visual models. The
simple and medium-complexity models are deployed at the ENs, while the complex
models are deployed in the cloud. This comprehensive tiering strategy for
visual model deployment is named AxiomVision (multi-level). In the main text,
we also introduce a deployment strategy that includes only two levels of
models, referred to as Dual-MS. Here, we explore the comparison between
different dual-level models and multi-level models. Specifically, we have
explored the advantages and disadvantages of models resulting from different
selection methods.

First, we introduce a dual-level deployment strategy that incorporates only
the simple and medium-complexity models, referred to as AxiomVision (bi-
level1). As shown in Fig. 19(a)-(c), we initially assessed the impact of these
two deployment strategies on accuracy. The results indicate that AxiomVision
(multi-level) outperforms AxiomVision (bi-level1) across various object
detection tasks, demonstrating higher accuracy. Additionally, we considered
bandwidth factors, taking into account a trade-off between accuracy and cost,
denoted as $a-\eta b$, where $a$ and $b$ represent normalized accuracy and
bandwidth, respectively, and $\eta=0.5$ is a weighted unit conversion
parameter. Fig. 19(d)-(f) reveals that although AxiomVision (bi-level1), by
not requiring the scheduling of complex cloud-based visual models, saves
bandwidth resources, its inability to handle tasks requiring high accuracy
results in lower overall accuracy, making the overall trade-off less
favorable.

Secondly, we explored another dual-level visual model deployment scheme,
namely deploying only simple and complex models, designated as AxiomVision
(bi-level2). Fig. 20(a)-(c), compared to AxiomVision (multi-level),
AxiomVision (bi-level2), due to covering only simple and complex models, may
more frequently invoke complex visual models, thus exhibiting higher accuracy
under certain conditions. However, as shown in Fig. 20(d)-(f), AxiomVision
(bi-level2) leads to higher resource consumption due to the omission of
medium-complexity models. In contrast, AxiomVision (multi-level) can adopt
medium-complexity models for tasks of medium complexity, ensuring ideal
accuracy while efficiently saving bandwidth resources. Therefore, when
evaluating the trade-off between accuracy and bandwidth, the multi-level
visual model deployment strategy demonstrates significant advantages.

Finally, we examined the deployment scheme of the dual-level visual model,
termed AxiomVision (bi-level3), which incorporates medium-complexity and
complex models. As illustrated in Fig. 21(a)-(c), unlike the AxiomVision
(multi-level) approach, AxiomVision (bi-level3) eschews the use of simple
models and this modification enhances accuracy. However, it is worth noting
that AxiomVision (multi-level) also achieved the threshold targets. However,
when we take into account a trade-off between accuracy and execution time,
denoted as $a-\gamma e$, where $a$ and $e$ represent normalized accuracy and
time, respectively, and $\gamma=0.2$ is a weighted unit conversion parameter.
As shown in Fig. 21(d)-(f), when evaluating the trade-off between accuracy and
execution time, the multi-level visual model deployment strategy demonstrates
significant advantages.

In summary, AxiomVision (bi-level) cannot simultaneously ensure and balance
the three metrics of accuracy, bandwidth, and execution time. In contrast,
AxiomVision (multi-level), when properly structured, can achieve better
results in all three metrics. Through the discussions above, we provide deeper
insights into the effective deployment of visual models and demonstrate that
the multi-level deployment strategy has outstanding adaptability to visual
tasks of varying complexities—capable of maintaining high accuracy, low
latency, and resource consumption, presenting an optimal solution.