arXiv subjects

Philip A. Chou

Publications and source records attributed to Philip A. Chou.

At least 19 recordsLinked to original sources

arXiv2026

Transforming harmonic coefficients for 3D splat compression

We address the problem of color attribute compression for 3D splats. We show that all images generated by 3D splats are linear in the coefficients for each color channel, each spherical harmonic, and each splat, and we identify a basis for the space of all such images. We identify an inner product for the coefficient space that induces the squared error loss on images. We show that orthonormalizing the coefficients with respect to this innner product before coding can yield over 2 dB gain.

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arXiv2026

Deep Unrolling of Sparsity-Induced RDO for 3D Point Cloud Attribute Coding

Given encoded 3D point cloud geometry available at the decoder, we study the problem of lossy attribute compression in a multi-resolution B-spline projection framework. A target continuous 3D attribute function is first projected onto a sequence of nested subspaces $\mathcal{F}^{(p)}_{l_0} \subseteq \cdots \subseteq \mathcal{F}^{(p)}_{L}$, where $\mathcal{F}^{(p)}_{l}$ is a family of functions spanned by a B-spline basis function of order $p$ at a chosen scale and its integer shifts. The projected low-pass coefficients $F_l^*$ are computed by variable-complexity unrolling of a rate-distortion (RD) optimization algorithm into a feed-forward network, where the rate term is the sparsity-promoting $\ell_1$-norm. Thus, the projection operation is end-to-end differentiable. For a chosen coarse-to-fine predictor, the coefficients are then adjusted to account for the prediction from a lower-resolution to a higher-resolution, which is also optimized in a data-driven manner.

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arXiv2025

Sandwiched Compression: Repurposing Standard Codecs with Neural Network Wrappers

We propose sandwiching standard image and video codecs between pre- and post-processing neural networks. The networks are jointly trained through a differentiable codec proxy to minimize a given rate-distortion loss. This sandwich architecture not only improves the standard codec's performance on its intended content, but more importantly, adapts the codec to other types of image/video content and to other distortion measures. The sandwich learns to transmit ``neural code images'' that optimize and improve overall rate-distortion performance, with the improvements becoming significant especially when the overall problem is well outside of the scope of the codec's design. We apply the sandwich architecture to standard codecs with mismatched sources transporting different numbers of channels, higher resolution, higher dynamic range, computer graphics, and with perceptual distortion measures. The results demonstrate substantial improvements (up to 9 dB gains or up to 30\% bitrate reductions) compared to alternative adaptations. We establish optimality properties for sandwiched compression and design differentiable codec proxies approximating current standard codecs. We further analyze model complexity, visual quality under perceptual metrics, as well as sandwich configurations that offer interesting potentials in video compression and streaming.

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arXiv2024

Learned Nonlinear Predictor for Critically Sampled 3D Point Cloud Attribute Compression

We study 3D point cloud attribute compression via a volumetric approach: assuming point cloud geometry is known at both encoder and decoder, parameters $θ$ of a continuous attribute function $f: \mathbb{R}^3 \mapsto \mathbb{R}$ are quantized to $\hatθ$ and encoded, so that discrete samples $f_{\hatθ}(\mathbf{x}_i)$ can be recovered at known 3D points $\mathbf{x}_i \in \mathbb{R}^3$ at the decoder. Specifically, we consider a nested sequences of function subspaces $\mathcal{F}^{(p)}_{l_0} \subseteq \cdots \subseteq \mathcal{F}^{(p)}_L$, where $\mathcal{F}_l^{(p)}$ is a family of functions spanned by B-spline basis functions of order $p$, $f_l^*$ is the projection of $f$ on $\mathcal{F}_l^{(p)}$ represented as low-pass coefficients $F_l^*$, and $g_l^*$ is the residual function in an orthogonal subspace $\mathcal{G}_l^{(p)}$ (where $\mathcal{G}_l^{(p)} \oplus \mathcal{F}_l^{(p)} = \mathcal{F}_{l+1}^{(p)}$) represented as high-pass coefficients $G_l^*$. In this paper, to improve coding performance over \cite{do2023volumetric}, we study predicting $f_{l+1}^*$ at level $l+1$ given $f_l^*$ at level $l$ and encoding of $G_l^*$ for the $p=1$ case (RAHT($1$)). For the prediction, we formalize RAHT(1) linear prediction in MPEG-PCC in a theoretical framework, and propose a new nonlinear predictor using a polynomial of bilateral filter. We derive equations to efficiently compute the critically sampled high-pass coefficients $G_l^*$ amenable to encoding. We optimize parameters in our resulting feed-forward network on a large training set of point clouds by minimizing a rate-distortion Lagrangian. Experimental results show that our improved framework outperforms the MPEG G-PCC predictor by $11\%$--$12\%$ in bit rate.

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arXiv2024

One-Click Upgrade from 2D to 3D: Sandwiched RGB-D Video Compression for Stereoscopic Teleconferencing

Stereoscopic video conferencing is still challenging due to the need to compress stereo RGB-D video in real-time. Though hardware implementations of standard video codecs such as H.264 / AVC and HEVC are widely available, they are not designed for stereoscopic videos and suffer from reduced quality and performance. Specific multiview or 3D extensions of these codecs are complex and lack efficient implementations. In this paper, we propose a new approach to upgrade a 2D video codec to support stereo RGB-D video compression, by wrapping it with a neural pre- and post-processor pair. The neural networks are end-to-end trained with an image codec proxy, and shown to work with a more sophisticated video codec. We also propose a geometry-aware loss function to improve rendering quality. We train the neural pre- and post-processors on a synthetic 4D people dataset, and evaluate it on both synthetic and real-captured stereo RGB-D videos. Experimental results show that the neural networks generalize well to unseen data and work out-of-box with various video codecs. Our approach saves about 30% bit-rate compared to a conventional video coding scheme and MV-HEVC at the same level of rendering quality from a novel view, without the need of a task-specific hardware upgrade.

cs.CV↗

arXiv2023

Volumetric 3D Point Cloud Attribute Compression: Learned polynomial bilateral filter for prediction

We extend a previous study on 3D point cloud attribute compression scheme that uses a volumetric approach: given a target volumetric attribute function $f : \mathbb{R}^3 \mapsto \mathbb{R}$, we quantize and encode parameters $θ$ that characterize $f$ at the encoder, for reconstruction $f_{\hatθ}(\mathbf(x))$ at known 3D points $\mathbf(x)$ at the decoder. Specifically, parameters $θ$ are quantized coefficients of B-spline basis vectors $\mathbfΦ_l$ (for order $p \geq 2$) that span the function space $\mathcal{F}_l^{(p)}$ at a particular resolution $l$, which are coded from coarse to fine resolutions for scalability. In this work, we focus on the prediction of finer-grained coefficients given coarser-grained ones by learning parameters of a polynomial bilateral filter (PBF) from data. PBF is a pseudo-linear filter that is signal-dependent with a graph spectral interpretation common in the graph signal processing (GSP) field. We demonstrate PBF's predictive performance over a linear predictor inspired by MPEG standardization over a wide range of point cloud datasets.

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arXiv2023

Sandwiched Video Compression: Efficiently Extending the Reach of Standard Codecs with Neural Wrappers

We propose sandwiched video compression -- a video compression system that wraps neural networks around a standard video codec. The sandwich framework consists of a neural pre- and post-processor with a standard video codec between them. The networks are trained jointly to optimize a rate-distortion loss function with the goal of significantly improving over the standard codec in various compression scenarios. End-to-end training in this setting requires a differentiable proxy for the standard video codec, which incorporates temporal processing with motion compensation, inter/intra mode decisions, and in-loop filtering. We propose differentiable approximations to key video codec components and demonstrate that, in addition to providing meaningful compression improvements over the standard codec, the neural codes of the sandwich lead to significantly better rate-distortion performance in two important scenarios.When transporting high-resolution video via low-resolution HEVC, the sandwich system obtains 6.5 dB improvements over standard HEVC. More importantly, using the well-known perceptual similarity metric, LPIPS, we observe 30% improvements in rate at the same quality over HEVC. Last but not least, we show that pre- and post-processors formed by very modestly-parameterized, light-weight networks can closely approximate these results.

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arXiv2023

Volumetric Attribute Compression for 3D Point Clouds using Feedforward Network with Geometric Attention

We study 3D point cloud attribute compression using a volumetric approach: given a target volumetric attribute function $f : \mathbb{R}^3 \rightarrow \mathbb{R}$, we quantize and encode parameter vector $θ$ that characterizes $f$ at the encoder, for reconstruction $f_{\hatθ}(\mathbf{x})$ at known 3D points $\mathbf{x}$'s at the decoder. Extending a previous work Region Adaptive Hierarchical Transform (RAHT) that employs piecewise constant functions to span a nested sequence of function spaces, we propose a feedforward linear network that implements higher-order B-spline bases spanning function spaces without eigen-decomposition. Feedforward network architecture means that the system is amenable to end-to-end neural learning. The key to our network is space-varying convolution, similar to a graph operator, whose weights are computed from the known 3D geometry for normalization. We show that the number of layers in the normalization at the encoder is equivalent to the number of terms in a matrix inverse Taylor series. Experimental results on real-world 3D point clouds show up to 2-3 dB gain over RAHT in energy compaction and 20-30% bitrate reduction.

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arXiv2023

Two Channel Filter Banks on Arbitrary Graphs with Positive Semi Definite Variation Operators

We propose novel two-channel filter banks for signals on graphs. Our designs can be applied to arbitrary graphs, given a positive semi definite variation operator, while using arbitrary vertex partitions for downsampling. The proposed generalized filter banks (GFBs) also satisfy several desirable properties including perfect reconstruction and critical sampling, while having efficient implementations. Our results generalize previous approaches that were only valid for the normalized Laplacian of bipartite graphs. Our approach is based on novel graph Fourier transforms (GFTs) given by the generalized eigenvectors of the variation operator. These GFTs are orthogonal in an alternative inner product space which depends on the downsampling and variation operators. Our key theoretical contribution is showing that the spectral folding property of the normalized Laplacian of bipartite graphs, at the core of bipartite filter bank theory, can be generalized for the proposed GFT if the inner product matrix is chosen properly. In addition, we study vertex domain and spectral domain properties of GFBs and illustrate their probabilistic interpretation using Gaussian graphical models. While GFBs can be defined given any choice of a vertex partition for downsampling, we propose an algorithm to optimize these partitions with a criterion that favors balanced partitions with large graph cuts, which are shown to lead to efficient and stable GFB implementations. Our numerical experiments show that partition-optimized GFBs can be implemented efficiently on 3D point clouds with hundreds of thousands of points (nodes), while also improving the color signal representation quality over competing state-of-the-art approaches.

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arXiv2021

LVAC: Learned Volumetric Attribute Compression for Point Clouds using Coordinate Based Networks

We consider the attributes of a point cloud as samples of a vector-valued volumetric function at discrete positions. To compress the attributes given the positions, we compress the parameters of the volumetric function. We model the volumetric function by tiling space into blocks, and representing the function over each block by shifts of a coordinate-based, or implicit, neural network. Inputs to the network include both spatial coordinates and a latent vector per block. We represent the latent vectors using coefficients of the region-adaptive hierarchical transform (RAHT) used in the MPEG geometry-based point cloud codec G-PCC. The coefficients, which are highly compressible, are rate-distortion optimized by back-propagation through a rate-distortion Lagrangian loss in an auto-decoder configuration. The result outperforms RAHT by 2--4 dB. This is the first work to compress volumetric functions represented by local coordinate-based neural networks. As such, we expect it to be applicable beyond point clouds, for example to compression of high-resolution neural radiance fields.

cs.GR↗

arXiv2021

3D Scene Compression through Entropy Penalized Neural Representation Functions

Some forms of novel visual media enable the viewer to explore a 3D scene from arbitrary viewpoints, by interpolating between a discrete set of original views. Compared to 2D imagery, these types of applications require much larger amounts of storage space, which we seek to reduce. Existing approaches for compressing 3D scenes are based on a separation of compression and rendering: each of the original views is compressed using traditional 2D image formats; the receiver decompresses the views and then performs the rendering. We unify these steps by directly compressing an implicit representation of the scene, a function that maps spatial coordinates to a radiance vector field, which can then be queried to render arbitrary viewpoints. The function is implemented as a neural network and jointly trained for reconstruction as well as compressibility, in an end-to-end manner, with the use of an entropy penalty on the parameters. Our method significantly outperforms a state-of-the-art conventional approach for scene compression, achieving simultaneously higher quality reconstructions and lower bitrates. Furthermore, we show that the performance at lower bitrates can be improved by jointly representing multiple scenes using a soft form of parameter sharing.

cs.CV↗

arXiv2020

Nonlinear Transform Coding

We review a class of methods that can be collected under the name nonlinear transform coding (NTC), which over the past few years have become competitive with the best linear transform codecs for images, and have superseded them in terms of rate--distortion performance under established perceptual quality metrics such as MS-SSIM. We assess the empirical rate--distortion performance of NTC with the help of simple example sources, for which the optimal performance of a vector quantizer is easier to estimate than with natural data sources. To this end, we introduce a novel variant of entropy-constrained vector quantization. We provide an analysis of various forms of stochastic optimization techniques for NTC models; review architectures of transforms based on artificial neural networks, as well as learned entropy models; and provide a direct comparison of a number of methods to parameterize the rate--distortion trade-off of nonlinear transforms, introducing a simplified one.

cs.IT↗

arXiv2020

Spectral folding and two-channel filter-banks on arbitrary graphs

In the past decade, several multi-resolution representation theories for graph signals have been proposed. Bipartite filter-banks stand out as the most natural extension of time domain filter-banks, in part because perfect reconstruction, orthogonality and bi-orthogonality conditions in the graph spectral domain resemble those for traditional filter-banks. Therefore, many of the well known orthogonal and bi-orthogonal designs can be easily adapted for graph signals. A major limitation is that this framework can only be applied to the normalized Laplacian of bipartite graphs. In this paper we extend this theory to arbitrary graphs and positive semi-definite variation operators. Our approach is based on a different definition of the graph Fourier transform (GFT), where orthogonality is defined with the respect to the Q inner product. We construct GFTs satisfying a spectral folding property, which allows us to easily construct orthogonal and bi-orthogonal perfect reconstruction filter-banks. We illustrate signal representation and computational efficiency of our filter-banks on 3D point clouds with hundreds of thousands of points.

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arXiv2020

Region adaptive graph fourier transform for 3d point clouds

We introduce the Region Adaptive Graph Fourier Transform (RA-GFT) for compression of 3D point cloud attributes. The RA-GFT is a multiresolution transform, formed by combining spatially localized block transforms. We assume the points are organized by a family of nested partitions represented by a rooted tree. At each resolution level, attributes are processed in clusters using block transforms. Each block transform produces a single approximation (DC) coefficient, and various detail (AC) coefficients. The DC coefficients are promoted up the tree to the next (lower resolution) level, where the process can be repeated until reaching the root. Since clusters may have a different numbers of points, each block transform must incorporate the relative importance of each coefficient. For this, we introduce the $\mathbf{Q}$-normalized graph Laplacian, and propose using its eigenvectors as the block transform. The RA-GFT achieves better complexity-performance trade-offs than previous approaches. In particular, it outperforms the Region Adaptive Haar Transform (RAHT) by up to 2.5 dB, with a small complexity overhead.

cs.CV↗

arXiv2020

Deep Implicit Volume Compression

We describe a novel approach for compressing truncated signed distance fields (TSDF) stored in 3D voxel grids, and their corresponding textures. To compress the TSDF, our method relies on a block-based neural network architecture trained end-to-end, achieving state-of-the-art rate-distortion trade-off. To prevent topological errors, we losslessly compress the signs of the TSDF, which also upper bounds the reconstruction error by the voxel size. To compress the corresponding texture, we designed a fast block-based UV parameterization, generating coherent texture maps that can be effectively compressed using existing video compression algorithms. We demonstrate the performance of our algorithms on two 4D performance capture datasets, reducing bitrate by 66% for the same distortion, or alternatively reducing the distortion by 50% for the same bitrate, compared to the state-of-the-art.

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arXiv2018

A Volumetric Approach to Point Cloud Compression

Compression of point clouds has so far been confined to coding the positions of a discrete set of points in space and the attributes of those discrete points. We introduce an alternative approach based on volumetric functions, which are functions defined not just on a finite set of points, but throughout space. As in regression analysis, volumetric functions are continuous functions that are able to interpolate values on a finite set of points as linear combinations of continuous basis functions. Using a B-spline wavelet basis, we are able to code volumetric functions representing both geometry and attributes. Geometry is represented implicitly as the level set of a volumetric function (the signed distance function or similar). Attributes are represented by a volumetric function whose coefficients can be regarded as a critically sampled orthonormal transform that generalizes the recent successful region-adaptive hierarchical (or Haar) transform to higher orders. Experimental results show that both geometry and attribute compression using volumetric functions improve over those used in the emerging MPEG Point Cloud Compression standard.

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arXiv2018

Surface Light Field Compression using a Point Cloud Codec

Light field (LF) representations aim to provide photo-realistic, free-viewpoint viewing experiences. However, the most popular LF representations are images from multiple views. Multi-view image-based representations generally need to restrict the range or degrees of freedom of the viewing experience to what can be interpolated in the image domain, essentially because they lack explicit geometry information. We present a new surface light field (SLF) representation based on explicit geometry, and a method for SLF compression. First, we map the multi-view images of a scene onto a 3D geometric point cloud. The color of each point in the point cloud is a function of viewing direction known as a view map. We represent each view map efficiently in a B-Spline wavelet basis. This representation is capable of modeling diverse surface materials and complex lighting conditions in a highly scalable and adaptive manner. The coefficients of the B-Spline wavelet representation are then compressed spatially. To increase the spatial correlation and thus improve compression efficiency, we introduce a smoothing term to make the coefficients more similar across the 3D space. We compress the coefficients spatially using existing point cloud compression (PCC) methods. On the decoder side, the scene is rendered efficiently from any viewing direction by reconstructing the view map at each point. In contrast to multi-view image-based LF approaches, our method supports photo-realistic rendering of real-world scenes from arbitrary viewpoints, i.e., with an unlimited six degrees of freedom (6DOF). In terms of rate and distortion, experimental results show that our method achieves superior performance with lighter decoder complexity compared with a reference image-plus-geometry compression (IGC) scheme, indicating its potential in practical virtual and augmented reality applications.

cs.MM↗

arXiv2018

Comments on "Compression of 3D Point Clouds Using a Region-Adaptive Hierarchical Transform"

The recently introduced coder based on region-adaptive hierarchical transform (RAHT) for the compression of point clouds attributes, was shown to have a performance competitive with the state-of-the-art, while being much less complex. In the paper "Compression of 3D Point Clouds Using a Region-Adaptive Hierarchical Transform", top performance was achieved using arithmetic coding (AC), while adaptive run-length Golomb-Rice (RLGR) coding was presented as a lower-performance lower-complexity alternative. However, we have found that by reordering the RAHT coefficients we can largely increase the runs of zeros and significantly increase the performance of the RLGR-based RAHT coder. As a result, the new coder, using ordered coefficients, was shown to outperform all other coders, including AC-based RAHT, at an even lower computational cost. We present new results and plots that should enhance those in the work of Queiroz and Chou to include the new results for RLGR-RAHT. We risk to say, based on the results herein, that RLGR-RAHT with sorted coefficients is the new state-of-the-art in point cloud compression.

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