# Efficient and Fast Light Field Compression via VAE-Based Spatial and Angular Disentanglement

Soheib Takhtardeshir, Roger Olsson, Christine Guillemot, Mårten Sjöström

► To cite this version:

Soheib Takhtardeshir, Roger Olsson, Christine Guillemot, Mårten Sjöström. Efficient and Fast Light Field Compression via VAE-Based Spatial and Angular Disentanglement. IEEE Access, 2025, 13, pp.18594-18607. 10.1109/ACCESS.2025.3532608. hal-05233427

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Submitted on 1 Sep 2025

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Distributed under a Creative Commons Attribution 4.0 International License
Received 19 November 2024, accepted 14 January 2025, date of publication 22 January 2025, date of current version 29 January 2025.

Digital Object Identifier 10.1109/ACCESS.2025.3532608

RESEARCH ARTICLE

# Efficient and Fast Light Field Compression via VAE-Based Spatial and Angular Disentanglement

SOHEIB TAKHTARDESHIR<sup>1,2</sup>, ROGER OLSSON<sup>1</sup>, (Member, IEEE),

CHRISTINE GUILLEMOT<sup>1,2</sup>, (Fellow, IEEE), AND MÅRTEN SJÖSTRÖM<sup>1,1</sup>, (Senior Member, IEEE)

Corresponding author: Soheib Takhtardeshir (Soheib.Takhtardeshir@miun.se)

This work was supported by the European Joint Doctoral Program on Plenoptic Imaging (PLENOPTIMA) through the European Union's Horizon 2020 Research and Innovation Program under the Marie Skłodowska-Curie Grant under Agreement 956770.

**ABSTRACT** Light field (LF) imaging captures both spatial and angular information, which is essential for applications such as depth estimation, view synthesis, and post-capture refocusing. However, the efficient processing of this data, particularly in terms of compression and encoding/decoding time, presents challenges. We propose a Variational Autoencoder (VAE)-based framework to disentangle the spatial and angular features of light field images, focusing on fast and efficient compression. Our method uses two separate sub-encoders—one for spatial and one for angular features—to allow for independent processing in the latent space, which facilitates more streamlined compression workflows. Evaluations on standard light field datasets demonstrate that our approach reduces encoding and decoding time significantly, with a slight trade-off in Rate-Distortion (RD) performance, making it suitable for real-time applications.

**INDEX TERMS** Light field, compression, disentangling, variational auto-encoder.

## I. INTRODUCTION

Light field (LF) imaging has emerged as a critical area of research due to its capacity to capture both spatial and angular information simultaneously, offering a far more comprehensive depiction of visual scenes than traditional 2D imaging methods. This technology expands the concept of image capture by recording not only the intensity of light rays but also their direction as they intersect the imaging sensor, a property that conventional cameras do not possess [1], [2]. This additional angular information enables several advanced post-capture functionalities, including refocusing, view synthesis, and precise depth estimation, enhancing both the flexibility and quality of visual data manipulation [3], [4], [5]. These characteristics have made light field imaging applicable across a broad range of domains, such as computational photography [2], [6], virtual and augmented reality [7], [8], medical imaging [9], [10], and autonomous driving systems [11], [12].

The associate editor coordinating the review of this manuscript and approving it for publication was Yun Zhang<sup>1, ∗</sup>.

The widespread adoption of light field imaging technology across various industries is limited by the vast amount of data generated by light field cameras. Efficient compression techniques are crucial to address this challenge, ensuring manageable storage and computational demands [13], [14], [15]. Compression methods vary in their suitability depending on the application. For instance, in streaming applications such as virtual and augmented reality, fast decoding is essential for real-time rendering and interaction [16]. In contrast, medical imaging prioritizes encoding efficiency to compress high-resolution light field images for storage and diagnostic purposes, where data integrity and storage space are critical, while encoding time may be less relevant [9], [17]. Similarly, autonomous driving applications require efficient encoding and decoding speeds to process light field data in real-time, enabling prompt decision-making for navigation and safety while minimizing computational overhead [11], [18].

Traditional compression methods typically handle light field data holistically, treating spatial and angular information as inseparable [19], [20], [21], [22]. These methods reduce storage requirements but often result in longer decoding times, making them less ideal for real-time applications.

<footnote n="1">¹Department of Computer and Electrical Engineering, Mid Sweden University, 852 30 Sundsvall, Sweden</footnote>

<footnote n="2">²INRIA, 35042 Rennes, France</footnote>
<figure><img src="image_2.png" /><figcaption>FIGURE 1. Overall architecture of the proposed method.</figcaption></figure>

More recently, Implicit Neural Representations (INRs), such as Neural Radiance Fields (NeRF) [23], have emerged as promising approaches that can compactly encode light field data. INRs, however, require long encoding times due to the need for scene-specific training, making them impractical for real-time compression tasks, though they excel in decoding speed [24], [25]. This makes INRs more suitable for applications like view synthesis, where decoding time is prioritized over encoding [26], [27]. Moreover, INR methods can easily be adapted for tasks beyond compression, such as novel view generation and 3D reconstruction [28], [29].

In contrast, our VAE-based network provides an efficient alternative by learning a transform that reduces the dimensionality of light field data without requiring scene-specific training. Unlike INRs, which directly encode scene information, the VAE learns a transform that can generalize across different scenes, resulting in faster encoding times [30], [31]. This makes the VAE-based approach particularly well-suited for applications such as real-time video streaming, remote sensing, or virtual environments, where speed and efficiency are more critical than scene-specific reconstruction accuracy [32]. However, unlike INR-based methods, the VAE does not support random access, which limits its use in applications requiring direct access to specific views, such as interactive video or some medical imaging tasks [33]. Despite this limitation, the VAE's ability to balance compression efficiency and fast execution time makes it ideal for many real-time and large-scale applications [16], [34].

The primary challenge in light field image processing stems from the inherently high dimensionality of the data, which is typically represented as a 4D structure combining two spatial dimensions with two angular dimensions [1], [6]. This 4D representation captures both the appearance and geometry of the scene, enabling applications like refocusing and view synthesis [3], [35]. However, this additional complexity significantly increases computational and storage demands [6], [13]. Traditional compression methods have sought to reduce data complexity by compressing light field data holistically, without explicitly separating the spatial and angular components [14], [36]. While these approaches can reduce storage requirements, they often fail to efficiently exploit the distinct redundancies in spatial and angular data, leading to suboptimal compression ratios and higher execution times [19], [37]. Recent methods, such as

Mukati et al. [50], have focused on low-complexity hybrid approaches, which emphasize simplicity but do not address real-time execution challenges that our method overcomes.

A significant limitation of existing light field compression techniques is their treatment of spatial and angular information as inseparable, despite the distinct roles these components play. Spatial data captures the texture and structure of objects in the scene, while angular data encodes viewpoint changes and directionality. Combining these components in a unified approach can lead to inefficiencies, particularly in tasks that require fine-tuned processing for one domain over the other [38], [39]. For example, compression schemes that focus solely on spatial or angular redundancies without harmonizing both dimensions can result in unbalanced performance, where one aspect is compressed effectively, while the other suffers [35]. This issue becomes more apparent as scene complexity increases or in applications demanding high-quality reconstructions, such as virtual reality or medical imaging [7], [11].

The disentanglement of spatial and angular information offers a promising solution to these challenges. By separating these components early in the processing pipeline, we enable more targeted and adaptive processing, which improves both compression efficiency and execution speed [31], [37]. Traditional methods that treat spatial and angular data as inseparable often struggle to reduce redundancies in both dimensions, leading to inefficiencies. In contrast, our method independently compresses spatial and angular features, enabling better exploitation of redundancies in each dimension [38], [39]. Furthermore, by separating these dimensions, we can generalize our approach across diverse datasets, accounting for variations in scene complexity, lighting conditions, and geometry [30], [32]. This results in faster processing and higher overall compression performance, particularly in real-time applications [37].

In this paper, we propose a novel framework for light field image compression that explicitly disentangles spatial and angular information using a VAE-based architecture. Unlike conventional approaches, which treat light field data as a unified entity, our method introduces two specialized sub-encoders: one designed for extracting spatial features and the other for angular information. By separating these domains at the encoder stage, we provide a more flexible latent space representation that can be optimized for specific tasks such
<figure><img src="image_3.png" /><figcaption>**FIGURE 2.** Illustration of the macropixel input structure and its role in the proposed method. Here, *N* represents the number of sub-aperture views in each dimension (e.g., *N* = 3 for a 3 × 3 light field configuration). *W* and *H* denote the width and height of each sub-aperture image, respectively. The labels A, B, C, ..., *I* correspond to individual pixel values taken from each sub-aperture image at a specific position. These pixel values are combined into a macropixel, which is organized into a (*N* × *W*) × (*N* × *H*) array to encode both spatial and angular information effectively.</figcaption></figure>

as super-resolution, scene reconstruction, and compression. This approach reduces the redundancy in the latent space, enabling a more compact and efficient representation of light field data without sacrificing the quality of the reconstructed images [30], [37]. Additionally, the disentangled latent space allows us to prioritize spatial or angular information based on task-specific requirements, reducing computational overhead and improving execution speed [31].

The contributions of this paper are twofold. First, we introduce a novel method for disentangling spatial and angular features in light field images, providing a flexible framework for more adaptive and efficient processing across various tasks. Second, we demonstrate the effectiveness of our approach through comprehensive evaluations on standard light field datasets, with a particular focus on improving compression efficiency and execution speed. By leveraging the inherent structure of spatial and angular information, our approach allows for more accurate and computationally efficient light field data processing.

## A. CONTRIBUTIONS

Our primary contributions are as follows:

* We propose a novel VAE-based framework that explicitly disentangles spatial and angular information in light field images, creating independent latent space representations.

* The disentangled representation enables more adaptive and efficient processing, significantly improving both compression efficiency and execution time, while providing a foundation for future research in light field compression.

* We demonstrate the effectiveness of our method through evaluations on standard light field datasets, showing substantial improvements in compression ratios and processing speeds compared to existing methods.

## II. METHODOLOGY

In this section, we describe the architecture of our VAE-based network, which is designed to disentangle spatial and angular features in light field images. The model incorporates two specialized sub-encoders to process spatial and angular information independently. Disentanglement is achieved within the latent space, enabling better reconstruction fidelity and separable feature representations. While this paper focuses on feature disentanglement, the network architecture is flexible and can be adapted for future tasks such as view synthesis, super-resolution, and other applications requiring efficient latent space representations.

### A. MACROPIXEL INPUT STRUCTURE

The input to the network is in the form of macropixels, which encode both spatial and angular information from the
light field image. A macropixel is constructed by combining corresponding pixels from each sub-aperture image in the light field. For example, in a $N \times N$ light field configuration with $W \times H$ pixels for each view, each macropixel is a $(N \times W) \times (N \times H)$ array, where $W$ and $H$ represent the width and height of each sub-aperture image. As shown in Figure 2, which is an example for:

$$N = W = H = 3$$

the first pixel from each sub-aperture view (labeled A, B, C, ..., I) is arranged in a $3 \times 3$ grid format. This is followed by the second pixel, and so on, effectively capturing both spatial and angular variations within the macropixel.

The macropixel structure allows both the spatial and angular sub-encoders to independently extract domain-specific features using appropriate kernel sizes, strides, and dilation rates. This formulation captures the relationship between the spatial and angular domains in an organized manner, ensuring efficient feature extraction by each sub-encoder. Additionally, this design supports scalability to higher angular resolutions, such as $15 \times 15$, by processing them as $25$ sequential $3 \times 3$ patches, enabling efficient handling of larger light field datasets without architectural modifications.

## B. NETWORK ARCHITECTURE

Our architecture consists of two primary components: (1) a spatial sub-encoder and (2) an angular sub-encoder. These sub-encoders extract distinct features from the input macropixel light field image and output a joint latent representation. This latent space, which disentangles spatial and angular features, is subsequently passed to a decoder for decoding, which is shown in detail in Figure 3.

### 1) SPATIAL AND ANGULAR SUB-ENCODERS

The spatial and angular sub-encoders use convolutional layers with specific kernel sizes, dilation rates, and strides to extract features from the macropixels. The spatial sub-encoder focuses on capturing local textures and object structures, while the angular sub-encoder processes directional information and viewpoint variations. We adopt a similar strategy as proposed by Wang et al. [40] in the design of the first convolutional layers for the spatial and angular sub-encoders, ensuring efficient feature extraction tailored to each domain.

In the spatial sub-encoder, convolutional layers are designed to handle the spatial relationships across different sub-aperture images. Similarly, the angular sub-encoder uses layers that capture angular relationships between different perspectives. Both sub-encoders utilize dilated convolutions to efficiently capture larger receptive fields while maintaining computational efficiency. Figure 4 illustrates the first convolutional layer of both sub-encoders, showing how specific kernel sizes, dilation rates, and strides are applied to extract features from the macropixel structure.

The feature extraction process can be formulated as follows:

$$\mathbf{F}_{\text{spatial}} = f_{\text{spatial}}(\mathbf{X}_{\text{spatial}}) = \text{Conv}(\mathbf{X}_{\text{spatial}}; k_s, d_s, c_s), \quad (1)$$

$$\mathbf{F}_{\text{angular}} = f_{\text{angular}}(\mathbf{X}_{\text{angular}}) = \text{Conv}(\mathbf{X}_{\text{angular}}; k_a, d_a, c_a), \quad (2)$$

where $\mathbf{F}_{\text{spatial}}$ and $\mathbf{F}_{\text{angular}}$ are the extracted feature maps, $k_s$ and $k_a$ are the kernel sizes, $d_s$ and $d_a$ are dilation rates, and $c_s$ and $c_a$ are the output channels for the spatial and angular sub-encoders, respectively. The specific design of these convolutional layers ensures that spatial and angular features are disentangled early in the processing pipeline, enabling independent manipulation in the latent space.

Once the spatial and angular features are extracted, they are concatenated to form the joint latent representation:

$$\mathbf{Z} = [\mathbf{F}_{\text{spatial}}, \mathbf{F}_{\text{angular}}], \quad (3)$$

where $\mathbf{Z}$ encodes the disentangled spatial and angular features and serves as the input to the decoder.

### 2) DECODER

The decoder reconstructs the original light field data from the disentangled latent representation $\mathbf{Z}$ using transposed convolutional layers. These layers are designed to restore both the spatial and angular information while preserving the disentanglement achieved in the encoding process. The reconstruction can be expressed as:

$$\hat{\mathbf{X}} = f_{\text{decoder}}(\mathbf{Z}) = \text{Conv}^{\top}(\mathbf{Z}; k_d, d_d, c_d), \quad (4)$$

where $\hat{\mathbf{X}}$ denotes the reconstructed light field image, and $k_d$, $d_d$, and $c_d$ are the kernel size, dilation rate, and output channels for the decoder. The decoder ensures that the spatial and angular characteristics are reintroduced coherently, maintaining the separation between these components throughout the reconstruction process.

## C. DETAILED LAYER ARCHITECTURE

In Table 1, we provide the detailed layer configurations of the spatial and angular sub-encoders, as well as the decoder. These specifications are important for reimplementing the architecture and ensuring the network's precise behavior across different implementations.

## D. LOSS FUNCTION AND LATENT SPACE ENTROPY MODELING

To ensure high-fidelity reconstruction and effective disentanglement, we employ a loss function that balances reconstruction accuracy and latent space efficiency. The loss function is defined as:

$$\mathcal{L} = R(\mathbf{Z}) + \lambda \cdot D(\mathbf{X}, \hat{\mathbf{X}}), \quad (5)$$

where $R(\mathbf{Z})$ is the rate term representing the entropy of the latent representation, and $D(\mathbf{X}, \hat{\mathbf{X}})$ is the distortion term
<figure><img src="image_4.png" /><figcaption>FIGURE 3. The overall architecture of the proposed method, highlighting the spatial and angular sub-encoders. The latent representations from both are concatenated and then passed to the decoder for reconstruction.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>FIGURE 4. Illustration of the initial layers in the spatial (a) and angular (b) sub-encoders. The figure details how kernels, dilation rates, and strides are applied to the macropixels, with (a) focusing on spatial feature extraction and (b) targeting angular information extraction. These configurations ensure that each sub-encoder processes its respective domain effectively for subsequent concatenation and decoding.</figcaption></figure>

measuring the reconstruction error. The Lagrange multiplier $\lambda$ balances the trade-off between reconstruction fidelity and the entropy of the latent space.

To explicitly represent the rate term $R(Z)$, we define it as the estimated entropy of the latent code. This can be expressed as:

$$R(Z) = -\mathbb{E}_Z[\log P_{\theta}(Z)], \qquad (6)$$

where $P_{\theta}(Z)$ represents the probability of the latent code under the entropy model with parameters $\theta$. These parameters are optimized during training to adapt to the distribution of the latent codes, enhancing compression efficiency by allowing the network to assign shorter codes to more probable values. The distortion term, $D(X, \hat{X})$, quantifies the reconstruction

quality as the mean squared error (MSE) between the original and reconstructed light field macropixels:

$$D(X, \hat{X}) = \frac{1}{N} \sum_{i=1}^{N} (X_i - \hat{X}_i)^2, \qquad (7)$$

where $N$ represents the number of macropixels. The combination of these two terms ensures that the network achieves both high reconstruction quality and an efficient latent representation.

E. TRAINING PROCEDURE

The network is trained end-to-end using the Adam optimizer, which dynamically adjusts learning rates during training.
<table><caption>TABLE 1. Detailed layer architecture of the VAE network.</caption><thead><tr><th>Layer Name</th><th>Input Size</th><th>Output Size</th><th>Kernel Size / Stride / Padding</th><th>Activation / Special Layer</th></tr></thead><tbody><tr><td colspan="5" style="text-align: center; font-weight: bold;">Spatial Encoder</td></tr><tr><td>Conv2d</td><td>3 × H<sub>s</sub> × W<sub>s</sub></td><td>128 × H'<sub>s</sub> × W'<sub>s</sub></td><td>5 × 5/1/1 (dilation=3)</td><td>GDN</td></tr><tr><td>Conv2d</td><td>128 × H'<sub>s</sub> × W'<sub>s</sub></td><td>128 × H''<sub>s</sub> × W''<sub>s</sub></td><td>5 × 5/2/1</td><td>GDN</td></tr><tr><td>Conv2d</td><td>128 × H''<sub>s</sub> × W''<sub>s</sub></td><td>128 × H'''<sub>s</sub> × W'''<sub>s</sub></td><td>5 × 5/2/1</td><td>GDN</td></tr><tr><td>Conv2d</td><td>128 × H'''<sub>s</sub> × W'''<sub>s</sub></td><td>128 × H''''<sub>s</sub> × W''''<sub>s</sub></td><td>5 × 5/2/1</td><td>GDN</td></tr><tr><td>Conv2d</td><td>128 × H''''<sub>s</sub> × W''''<sub>s</sub></td><td>64 × H<sub>f</sub> × W<sub>f</sub></td><td>5 × 5/3/1</td><td>GDN</td></tr><tr><td colspan="5" style="text-align: center; font-weight: bold;">Angular Encoder</td></tr><tr><td>Conv2d</td><td>3 × H<sub>a</sub> × W<sub>a</sub></td><td>128 × H'<sub>a</sub> × W'<sub>a</sub></td><td>3 × 3/3/1</td><td>GDN</td></tr><tr><td>Conv2d</td><td>128 × H'<sub>a</sub> × W'<sub>a</sub></td><td>128 × H''<sub>a</sub> × W''<sub>a</sub></td><td>5 × 5/2/1</td><td>GDN</td></tr><tr><td>Conv2d</td><td>128 × H''<sub>a</sub> × W''<sub>a</sub></td><td>128 × H'''<sub>a</sub> × W'''<sub>a</sub></td><td>5 × 5/2/1</td><td>GDN</td></tr><tr><td>Conv2d</td><td>128 × H'''<sub>a</sub> × W'''<sub>a</sub></td><td>64 × H<sub>f</sub> × W<sub>f</sub></td><td>5 × 5/2/1</td><td>GDN</td></tr><tr><td colspan="5" style="text-align: center; font-weight: bold;">Concatenation Layer</td></tr><tr><td>Concat</td><td>64 × H<sub>f</sub> × W<sub>f</sub> + 64 × H<sub>f</sub> × W<sub>f</sub></td><td>128 × H<sub>f</sub> × W<sub>f</sub></td><td>-</td><td>-</td></tr><tr><td colspan="5" style="text-align: center; font-weight: bold;">Decoder</td></tr><tr><td>ConvTranspose2d</td><td>128 × H<sub>f</sub> × W<sub>f</sub></td><td>128 × H'<sub>f</sub> × W'<sub>f</sub></td><td>5 × 5/3/0</td><td>Inverse GDN</td></tr><tr><td>ConvTranspose2d</td><td>128 × H'<sub>f</sub> × W'<sub>f</sub></td><td>128 × H''<sub>f</sub> × W''<sub>f</sub></td><td>4 × 4/2/0</td><td>Inverse GDN</td></tr><tr><td>ConvTranspose2d</td><td>128 × H''<sub>f</sub> × W''<sub>f</sub></td><td>128 × H'''<sub>f</sub> × W'''<sub>f</sub></td><td>4 × 4/2/1</td><td>Inverse GDN</td></tr><tr><td>ConvTranspose2d</td><td>128 × H'''<sub>f</sub> × W'''<sub>f</sub></td><td>3 × H<sub>s</sub> × W<sub>s</sub></td><td>4 × 4/2/1</td><td>Sigmoid</td></tr></tbody></table>

Adam is well-suited for complex architectures like VAEs due to its adaptive learning rate mechanism, which helps stabilize the training process, particularly in high-dimensional data. The model is trained for 500 epochs, with batch sizes of 32 macropixel patches. Early stopping based on validation loss prevents overfitting. The effectiveness of the disentangled representations is evaluated on standard light field datasets.

### III. EXPERIMENTAL SETUP

In this section, we provide a detailed description of the datasets used for training, validation, and testing, along with the hyperparameters and hardware configuration utilized during the training of our VAE-based model for disentangling spatial and angular features in light field images.

#### A. DATASETS

We employed two different datasets for our experiments: the PINet dataset for training and validation, and the EPFL dataset for testing.

##### 1) PINet DATASET

For training and validation, we used the PINet dataset [41], a large-scale image dataset captured using a Lytro Illum hand-held light field camera. This dataset contains 7,549 light field images (LIs) that were captured under various conditions and cover a wide range of categories, such as animals (e.g., cats, camels), objects (e.g., bottles, fans), and other common scenes. The images are categorized into 178 distinct classes based on the WordNet hierarchy, and registered depth maps are provided for each image. Each light field image in the dataset has a spatial resolution of 625 × 434 pixels and an angular resolution of 15 × 15 views. The images are processed from the raw light field data through

the Light Field Toolbox v0.4, which applies demosaicing and devnetting corrections.

We chose this dataset due to its large scale and diversity, as it contains a variety of objects, scenes, and textures that provide a comprehensive testbed for assessing disentanglement performance across different spatial and angular contexts. For training, we used 80% of the images (6,039 images), while the remaining 20% (1,510 images) were used for validation. During preprocessing, each image was partitioned into smaller macropixels, which contain both spatial and angular information, to serve as inputs to the network. This approach ensures the network learns efficiently from localized patches of the light field data, optimizing memory usage and enabling faster training.

##### 2) EPFL DATASET

For testing and evaluation, we utilized the EPFL Light Field Dataset [42]. The EPFL dataset consists of high-resolution light field images captured using a Lytro Illum camera, which are widely used in light field processing research. The dataset includes a variety of scenes, ranging from indoor to outdoor environments, and provides images at a resolution of 625 × 434 pixels with an angular resolution of 15 × 15 views per image. This dataset was chosen to test generalization because of its diverse scene types, making it ideal for evaluating how well our network generalizes across both familiar and unseen environments. It serves as an unseen test set to evaluate the generalization capabilities of the network and its ability to disentangle spatial and angular information on diverse light field images.

#### B. TRAINING DETAILS AND HYPERPARAMETERS

We trained the network using the Adam optimizer with an initial learning rate of $1 \times 10^{-4}$, which was reduced during training using a learning rate scheduler. The scheduler
decreases the learning rate by a factor of 0.1 when the validation performance plateaued for more than 20 epochs. The model was trained for a total of 500 epochs to ensure convergence, particularly given the complexity of the disentanglement task.

The batch size used during training was 32, with smaller patches of macropixels, each of resolution 312 × 216, extracted from the light field images serving as input to the network. This macropixel-based approach allowed the network to efficiently learn from both the spatial and angular domains in a localized manner, optimizing training speed and memory usage. Furthermore, the convolutional layers in both the spatial and angular sub-encoders were initialized with kernel sizes of 3 and dilation rates tuned for optimal performance based on preliminary experiments.

Regularization techniques, such as early stopping based on validation loss, were applied to prevent overfitting. Additionally, the model was evaluated periodically on the validation set to monitor its ability to maintain disentanglement and reconstruction quality.

## C. HARDWARE CONFIGURATION

The experiments were conducted on the NAISS (National Academic Infrastructure for Supercomputing in Sweden), using NVIDIA V100 GPU and Intel(R) Xeon(R) Gold 6244 CPU. These high-performance GPUs allowed for efficient training of the network over the large-scale dataset, with the distributed computing resources of HPC2N accelerating the training process. The training for 500 epochs required approximately 90-100 hours, taking full advantage of the parallel processing capabilities of the GPUs.

Each training experiment was run with 16 GB of GPU memory, which was sufficient for handling the large batch sizes and the macropixel-based input structure. All experiments were implemented using PyTorch, which allowed for seamless utilization of GPU acceleration and efficient gradient computation during backpropagation.

## D. EVALUATION METRICS

During training, we tracked the reconstruction accuracy using mean squared error (MSE) between the original and reconstructed light field macropixels. Additionally, Peak Signal-to-Noise Ratio (PSNR) was computed as a key quantitative metric to assess the quality of the reconstructed light field images. PSNR provides an objective measure of the compression quality by comparing the fidelity of the reconstructed images to the originals, making it particularly suitable for evaluating the performance of compression algorithms. Higher PSNR values indicate better preservation of image quality after compression, which is critical in assessing the effectiveness of our disentangled framework.

In addition to reconstruction accuracy, we focused on measuring the efficiency of the proposed method. Execution time, specifically the time taken for both encoding and decoding processes, was recorded to evaluate the computational cost of our framework. By tracking the execution time, we aim to

demonstrate the practical benefits of our method, particularly for real-time and large-scale light field applications where computational efficiency is paramount.

For testing on the EPFL dataset, similar evaluation metrics were employed to assess how well the model generalized to unseen light field data. PSNR continued to be a key metric in evaluating the quality of compression, while execution time provided insights into the scalability and practicality of our approach. The disentanglement of spatial and angular components was carefully evaluated through these quantitative metrics to ensure the robustness and efficiency of the model across different datasets.

## IV. RESULTS

In this section, we present the performance of our VAE-based network on the EPFL dataset, focusing on compression efficiency and computational performance. We evaluate the model using both qualitative and quantitative metrics, with an emphasis on compression-related metrics. Specifically, we compare our method to state-of-the-art approaches by analyzing key metrics such as PSNR and structural similarity index measure (SSIM) to assess the quality of reconstruction.

Our method achieves a competitive balance between compression efficiency and computational speed, as demonstrated by the RD graph. Across a range of bitrates, it consistently maintains high visual quality at lower bitrates compared to most existing methods. One method slightly surpasses ours in RD performance; however, our approach significantly excels in terms of execution time, providing much faster encoding and decoding speeds. This underscores the suitability of our method for real-time applications and large-scale processing, where computational efficiency is critical.

Additionally, an ablation study is conducted to assess the impact of varying the latent space distribution between spatial and angular features. This study evaluates the model's adaptability to different compression rates and its effect on both compression efficiency and reconstruction quality.

### A. QUALITATIVE RESULTS

#### 1) ERROR MAP RESULTS

We begin by presenting the average error maps of the reconstructed views for several challenging scenes from the EPFL dataset, including *Fountain*, *Danger*, *Bikes*, and *Pillars*, with a focus on similar bitrates, which is shown in Figure 5. These error maps illustrate the differences between the original and reconstructed light field images, highlighting the artifacts produced by different compression methods at comparable rates. To provide a clearer comparison, we zoom in on specific regions of the error maps to offer better visualization of the artifacts.

At lower bitrates, noticeable differences in artifact patterns can be observed across the methods. For example, while Jpeg Pleno [43] suffers from prominent block-wise quantization artifacts—clearly visible in the zoomed-in error maps—our method shows fewer and less severe artifacts
<figure><img src="image_6.png" /><figcaption>**FIGURE 5.** Average error maps comparing reconstructed images and ground truth for various scenes in the EPFL dataset [42]: Fountain, Danger, and Bikes. The zoomed-in sections focus on regions where reconstruction artifacts are more prominent. PSNR values are included to quantitatively compare the performance of our method against other state-of-the-art approaches, emphasizing areas of higher reconstruction error.</figcaption></figure>

at the same compression rate. This is especially evident in the zoomed-in cropped regions, where the block-like distortions in Jpeg Pleno reconstructions become particularly pronounced, whereas our approach maintains smoother transitions and fewer visible errors.

In comparison to RLVC [44] and HLVC [45], the artifacts in their reconstructions are more pronounced and similar in nature, with more visible distortions in low-detail regions and along object boundaries. These artifacts become even more noticeable in the zoomed-in error maps, showing higher error concentrations. Our method, by contrast, produces significantly cleaner reconstructions with fewer visual artifacts, even at similar bitrates. This highlights the superior artifact reduction capabilities of our method, particularly in challenging areas where other methods struggle to preserve detail.

When comparing our approach with the method proposed by Shi [46], which is based on implicit neural representations, Shi's method shows slightly better performance in terms of PSNR and error map quality. This is reflected in the reduced number of artifacts in their reconstructed views, particularly in low-bitrate scenarios. However, while Shi's

method offers a slight improvement in terms of visual quality, it comes at the cost of significantly longer encoding times due to its scene-specific training requirements. Our method, by contrast, offers a substantial advantage in terms of speed, making it more suitable for applications where fast execution time is critical. This efficiency, combined with competitive visual quality, highlights its practicality for real-time scenarios, a topic further explored in the Quantitative Results section.

By focusing on the average error maps and zoomed-in crops, we provide a detailed visualization of the performance differences between the methods, demonstrating that our approach consistently produces fewer artifacts across the tested scenes. This qualitative analysis clearly shows that our method outperforms Jpeg Pleno [43], RLVC [44], and HLVC [45] in terms of visual quality, especially in low-bitrate scenarios, while offering a faster and more efficient alternative to Shi's implicit neural representation method [46].

In Figure 6, we show the reconstructed center views from two scenes in the EPFL dataset [42]: Fountain and Bikes. The zoomed-in sections highlight challenging areas where
<figure><img src="image_7.png" /><figcaption>**FIGURE 6.** Reconstructed center views from two scenes in the EPFL dataset [42]: Fountain and bikes. Zoomed-in sections emphasize challenging areas where artifacts are particularly noticeable. The figure provides a comparison between our proposed network and Jpeg-Pleno, showcasing the differences in artifact reduction and overall image quality.</figcaption></figure>

compression artifacts are visible, with comparisons drawn between our network and Jpeg-Pleno at similar bitrates. In the *Fountain* scene, Jpeg-Pleno exhibits visible block-wise artifacts, particularly in the water streams and stone textures. These artifacts disrupt the smoothness of the textures, leading to block-like distortions that degrade the overall visual quality. By contrast, our method produces fewer artifacts, preserving more detail and maintaining smoother transitions in these complex regions.

In the *Bikes* scene, Jpeg-Pleno [43] also struggles with high-frequency details, such as the bike spokes, where artifacts are more pronounced along the edges. Our approach, however, reduces these distortions significantly, delivering cleaner reconstructions and better preserving structural integrity, even at the same bitrate. These visual comparisons illustrate that, despite operating at similar bitrates, our network consistently delivers higher perceptual quality with fewer visible artifacts, particularly in scenes with fine textures and complex patterns. These artifacts at low bitrates are primarily caused by quantization errors in the latent space,

which limit the network's ability to accurately represent high-frequency details. Techniques such as perceptual loss functions, which prioritize visually significant features, and lightweight post-processing filters can be employed to further reduce these distortions.

## B. QUANTITATIVE RESULTS

### 1) RATE-DISTORTION GRAPH

To further evaluate our model's performance, we present the Rate-Distortion (RD) graph for four test scenes from the EPFL dataset, including *Fountain*, *Danger*, *Bikes*, and *Pillars*. In this graph (shown in Figure 7), we compare our method against several state-of-the-art approaches, namely Jpeg Pleno [43], HEVC [47], RLVC [44], HLVC [45], and Shi's [46] method. The graph illustrates the performance of each method based on Peak Signal-to-Noise Ratio (PSNR) as a function of bitrate.

As shown in Figure 7, our method consistently outperforms most of the competing approaches across the tested scenes, achieving higher PSNR at lower bitrates. While Shi's
<figure><img src="image_8.png" /><figcaption>**FIGURE 7.** Rate-Distortion (RD) curve comparing the performance of our proposed VAE-based light field compression method against HEVC [47], RLVC [44], HLVC [45], JPEG-Pleno [43], and Shi's [46] method. Our method consistently outperforms the others across most datasets in terms of compression efficiency and image reconstruction quality, except for Shi's method, which shows superior results on a few specific datasets.</figcaption></figure>

method slightly surpasses ours in RD performance, our approach demonstrates a significant advantage in execution time, making it more efficient and practical for real-time applications. This balance between compression quality and computational efficiency highlights the strengths of our method in various light field tasks.

## 2) EXECUTION TIME

In addition to evaluating compression quality, we analyze the execution time of our method, which was performed using an RTX 3080 GeForce GPU, and compare it against several state-of-the-art approaches, including Jpeg Pleno [43], RLVC [44], and HLVC [45]. Execution time is a crucial factor, particularly for real-time applications and large-scale processing. Our method consistently demonstrates faster encoding and decoding times, while also delivering better compression quality compared to these methods. Specifically, our approach outperforms Jpeg Pleno [43],

RLVC [44], and HLVC [45] in both compression quality and execution time, making it a highly effective and practical solution.

A significant comparison is with Shi's [46] method. Although their approach achieves slightly better compression quality, as shown in terms of PSNR, this comes with a significant drawback in terms of execution time. Shi's [46] method requires scene-specific training, which involves retraining the network for each new scene, leading to considerably longer encoding times. This performance gap in RD metrics could potentially be reduced by integrating advanced entropy modeling techniques, such as context-based probability models, or by employing adaptive bitrate allocation strategies to maximize bitrate efficiency. In contrast, our method generalizes across different scenes, allowing for much faster encoding without the need for retraining, making it far more efficient and scalable for real-time and large-scale applications.
<figure><img src="image_9.png" /><figcaption>FIGURE 8. Execution time and quality comparison between our methods and other state of the art methods. The left graph shows encoding time for 9 × 9 SAIs of Fountain scene of EPFL dataset [42] and the right graph shows only decoding time per SAI.</figcaption></figure>

As shown in Figure 8, our method demonstrates a clear advantage in execution time across all tested methods, striking an ideal balance between high compression quality and computational efficiency. Although Shi's [46] method achieves slightly better quality, its significantly longer execution time due to scene-specific training limits its practicality compared to our faster, more versatile approach.

### 3) BD-PSNR COMPARISON

We evaluate the performance of our proposed network by comparing it against several state-of-the-art methods, including JPEG Pleno [43], RLVC [44], HLVC [45], VVC [48], DDLF [49], and Shi's [46] using BD-PSNR gains with respect to the HEVC [47] baseline. BD-PSNR, calculated using the Bjøntegaard metric, measures the average PSNR gain over a range of bitrates, where higher values indicate better compression efficiency.

<table><caption>TABLE 2. BD-PSNR gains (dB) of the proposed method with respect to HEVC baselines. The best results are in bold, and the second-best results are underlined.</caption><thead><tr><th>Methods</th><th>Bikes</th><th>Danger</th><th>Pillars</th><th>Fountain</th><th>Average</th></tr></thead><tbody><tr><td>JPEG-Pleno [43]</td><td>0.20</td><td>1.38</td><td>0.58</td><td>0.30</td><td>0.61</td></tr><tr><td>HLVC [45]</td><td>0.01</td><td>0.01</td><td>-0.05</td><td>-0.07</td><td>-1.54</td></tr><tr><td>RLVC [44]</td><td>0.35</td><td>0.29</td><td>0.20</td><td>0.32</td><td>0.29</td></tr><tr><td>VVC [48]</td><td>1.18</td><td>1.41</td><td>1.27</td><td>1.06</td><td>1.23</td></tr><tr><td>DDLF [49]</td><td>0.69</td><td>0.93</td><td>-0.01</td><td>0.90</td><td>0.62</td></tr><tr><td>Shi's [46]</td><td><strong>1.88</strong></td><td><strong>3.20</strong></td><td><strong>1.93</strong></td><td><strong>2.50</strong></td><td><strong>2.37</strong></td></tr><tr><td>Ours</td><td>1.56</td><td>2.95</td><td><strong>1.93</strong></td><td>2.32</td><td>2.20</td></tr></tbody></table>

Table 2 shows the BD-PSNR gains (in dB) for different scenes from the EPFL dataset, including *Bikes*, *Danger*, *Pillars*, and *Fountain*. Our method achieves the best result in one of the scenes and ranks second-best in the other three. Although Shi's method provides slightly better BD-PSNR in

several cases, its significant encoding time requirements due to scene-specific training limit its practicality. In contrast, our approach offers competitive BD-PSNR gains along with significantly faster execution times, making it well-suited for real-time and large-scale applications where efficiency is critical.

In summary, our method strikes a good balance between compression performance and computational efficiency, outperforming other methods in execution time, which is essential for practical use cases.

### 4) PSNR HEAT-MAP AMONG VIEWS

Figure 9 presents the PSNR heatmap for the *Fountain* dataset, illustrating the reconstruction quality across a 9 × 9 grid of views, with each color representing the PSNR value for a specific view. This heatmap demonstrates the performance of our method in terms of compression quality across different views in the light field.

As shown in the figure, our network processes the views in 3 × 3 blocks, and the central view within each 3 × 3 block tends to achieve higher PSNR values, reflecting better reconstruction quality. This behavior is expected, as the central views often contain more consistent spatial and angular information, allowing our method to reconstruct them with higher fidelity. The PSNR heatmap highlights the effectiveness of our approach in preserving high-quality reconstructions, particularly in the central views, while maintaining competitive performance across the entire view set.

### C. ABLATION STUDY

To assess the importance of the spatial and angular disentanglement in the latent space, we performed an ablation
<figure><img src="image_10.png" /><figcaption>FIGURE 9. The PSNR heatmap for fountain dataset for 9 × 9 central views.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>FIGURE 10. The correlation coefficient map between spatial-angular, spatial-spatial and angular-angular which has been shown for 60-40 separation in latent for spatial and angular part.</figcaption></figure>

<table><caption>TABLE 3. Ablation study comparing different latent space distributions between spatial and angular features. We report average PSNR (dB), and SSIM values for four different scenes in the EPFL dataset [42]: Fountain, Danger, Bikes, and Pillars. The 60/40 distribution yields the best overall performance.</caption><thead><tr><td>Latent Space Distribution</td><td>PSNR (dB)</td><td>SSIM</td></tr></thead><tbody><tr><td>50/50 Spatial/Angular</td><td>35.48</td><td>0.960</td></tr><tr><td>75/25 Spatial/Angular</td><td>35.55</td><td>0.965</td></tr><tr><td>25/75 Spatial/Angular</td><td>35.12</td><td>0.943</td></tr><tr><td>40/60 Spatial/Angular</td><td>35.26</td><td>0.952</td></tr><tr><td><b>60/40 Spatial/Angular</b></td><td><b>35.75</b></td><td><b>0.976</b></td></tr></tbody></table>

study by varying the latent space allocation between these two components. Instead of using an equal 50-50% allocation between spatial and angular features, we experimented with different allocations: 25-75%, 75-25%, 40-60%, and 60-40%. These variations allowed us to analyze how the different divisions of the latent space impact compression efficiency and the quality of the reconstructed output.

We also evaluated the correlation between the spatial and angular features in each configuration, analyzing how much energy each component carries in terms of its importance for compression. As shown in Figure 10, the correlation map between spatial and angular parts demonstrates that they are properly separated in our framework, with the correlation mostly appearing between spatial features and between angular features, indicating effective disentanglement.

Additionally, Table 3 shows how the different network configurations affect the quality of the reconstructed output. The table highlights that certain configurations, such as 75-25% or 60-40%, yield more optimal results for compression while maintaining high-quality reconstructions, reflecting the balance between spatial and angular information required for efficient compression.

As shown in Table 3, allocating 60-40% of the latent space to both spatial and angular features provides the best balance between reconstruction quality and feature disentanglement, demonstrating the effectiveness of our default configuration.

## V. CONCLUSION

In this paper, we presented a novel VAE-based framework for light field image compression that explicitly disentangles spatial and angular information. By leveraging two specialized sub-encoders, the proposed method enables a compact yet effective latent space representation, allowing for improved compression efficiency and computational performance. The separation of spatial and angular features facilitates more targeted processing, providing flexibility for adapting the framework to various compression scenarios.

Through extensive evaluations on standard light field datasets, our approach demonstrated competitive performance, achieving significant gains in execution speed while maintaining high-quality reconstructions across a range of bitrates. The results show that our method consistently outperforms state-of-the-art approaches such as JPEG Pleno, RLVC, and HLVC in terms of both visual quality and computational efficiency. Furthermore, although Shi's method achieves slightly better PSNR in certain scenarios, our model's ability to generalize across scenes without retraining underscores its practicality for real-time and large-scale applications.

The modular structure of the proposed framework highlights its potential for adaptation to various tasks. For instance, disentangled spatial and angular representations enable the flexibility to prioritize spatial fidelity for applications like immersive imaging or angular consistency for tasks such as multi-view reconstruction. This flexibility ensures its adaptability to different application-specific requirements.

Future work will focus on refining the framework to address artifact behavior, particularly at low bitrates, to further improve the visual quality of reconstructions. Additionally, we plan to include Quality of Experience (QoE) testing in real-world applications, such as virtual reality (VR)
environments. These refinements aim to align the framework with practical deployment needs, ensuring its relevance for diverse and user-centric scenarios.

The combination of high compression efficiency, low execution time, and adaptability makes our approach a compelling solution for next-generation light field imaging applications.

## ACKNOWLEDGMENT

The authors acknowledge the computational resources provided by the National Academic Infrastructure for Supercomputing in Sweden (NAISS). Additionally, they acknowledge the use of OpenAI's ChatGPT for grammar and style enhancement in certain sections of this manuscript. The AI system was used to refine the clarity and fluency of the text while ensuring technical accuracy, with all content being verified and approved by them.

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<figure><img src="image_12.png" /></figure>

**SOHEIB TAKHTARDESHIR** received the B.Sc. degree in electrical engineering and the M.Sc. degree in digital electronic engineering from Shahid Beheshti University (SBU), Tehran, Iran, in 2013 and 2021, respectively. He is currently pursuing the double degree Ph.D. degree with Mid Sweden University and INRIA, Rennes, France. Since 2022, he has been a Researcher with Mid Sweden University and INRIA, as a part of European Joint Doctoral Program on Plenoptic

Imaging (PLENOPTIMA). His research interests include light field imaging, processing, representation, and compression.

<figure><img src="image_13.png" /></figure>

**ROGER OLSSON** (Member, IEEE) received the M.Sc. degree in electrical engineering and the Ph.D. degree in telecommunication from Mid Sweden University, Sweden, in 1998 and 2010, respectively. He was with the Video Compression and Distribution Industry, from 1997 to 2000. He was a Junior Lecturer with Mid Sweden University, from 2000 to 2004, where he taught courses in telecommunication, signals and systems, and signal and image processing. Since 2010, he has been a Researcher with Mid Sweden University. His research interests include plenoptic and light field imaging, processing, and compression; light field modeling; and depth map capture and processing.

<figure><img src="image_14.png" /></figure>

**CHRISTINE GUILLEMOT** (Fellow, IEEE) received the Ph.D. degree from the École Nationale Supérieure des Télécommunications (ENST), Paris, and the Habilitation degree in research direction from the University of Rennes. From 1985 to October 1997, she was with France Telecom, where she has been involved in various projects in the areas of image and video coding and processing for TV, HDTV, and multimedia. From January 1990 to 1991, she was with Bellcore, NJ, USA, as a Visiting Scientist. She is currently the Director of Research with INRIA. Her research interests include signal and image processing and computer vision. She has served as a Senior Member for the editorial board of *IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING* (2013-2015) and a Senior Area Editor for *IEEE TRANSACTIONS ON IMAGE PROCESSING* (2016-2020). She was served as an Associate Editor for *IEEE TRANSACTIONS ON IMAGE PROCESSING* (2000-2003 and 2014-2016), *IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY* (from 2004-2006), and *IEEE TRANSACTIONS ON SIGNAL PROCESSING* (2007-2009).

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**MÅRTEN SJÖSTRÖM** (Senior Member, IEEE) received the M.Sc. degree in electrical engineering and applied physics from Linköping University, Sweden, in 1992, the Licentiate of Technology degree in signal processing from the KTH Royal Institute of Technology, Stockholm, Sweden, in 1998, and the Ph.D. degree in modeling of nonlinear systems from the École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland, in 2001. He was an Electrical Engineer with ABB, Sweden, from 1993 to 1994; and a fellow with CERN from 1994 to 1996. In 2001, he joined Mid Sweden University, and he was appointed as an Associate Professor and a Full Professor of signal processing, in 2008 and 2013, respectively. He has been the Head of computer and system sciences with Mid Sweden University, since 2013. He founded the Realistic 3-D Research Group, in 2007. His current research interests include multidimensional signal processing and imaging and system modeling and identification.

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