Jiahao Pang

CV
h-index9
22papers
1,743citations
Novelty56%
AI Score50

22 Papers

IVSep 9, 2022Code
GRASP-Net: Geometric Residual Analysis and Synthesis for Point Cloud Compression

Jiahao Pang, Muhammad Asad Lodhi, Dong Tian

Point cloud compression (PCC) is a key enabler for various 3-D applications, owing to the universality of the point cloud format. Ideally, 3D point clouds endeavor to depict object/scene surfaces that are continuous. Practically, as a set of discrete samples, point clouds are locally disconnected and sparsely distributed. This sparse nature is hindering the discovery of local correlation among points for compression. Motivated by an analysis with fractal dimension, we propose a heterogeneous approach with deep learning for lossy point cloud geometry compression. On top of a base layer compressing a coarse representation of the input, an enhancement layer is designed to cope with the challenging geometric residual/details. Specifically, a point-based network is applied to convert the erratic local details to latent features residing on the coarse point cloud. Then a sparse convolutional neural network operating on the coarse point cloud is launched. It utilizes the continuity/smoothness of the coarse geometry to compress the latent features as an enhancement bit-stream that greatly benefits the reconstruction quality. When this bit-stream is unavailable, e.g., due to packet loss, we support a skip mode with the same architecture which generates geometric details from the coarse point cloud directly. Experimentation on both dense and sparse point clouds demonstrate the state-of-the-art compression performance achieved by our proposal. Our code is available at https://github.com/InterDigitalInc/GRASP-Net.

85.5CLMay 28
HEART-Bench: Do LLM Agents Exhibit Human-like Psychology?

Weihan Peng, Chenxu Zhang, Qianao Wang et al.

While LLM agents have demonstrated remarkable task-oriented abilities such as planning, reasoning, and action, few works have treated them as complete human personalities where emotional dimensions hold equal importance. In this paper, we introduce a novel benchmark to systematically assess whether LLM agents can simulate coherent, human-like psychology. Specifically, our benchmark constructs 11 diverse human characters grounded in orthogonal Big Five personality traits, with each profile deeply integrated with 1,000 structured autobiographical-style episodic memories distributed across theory-grounded developmental life stages. To rigorously evaluate the psychological manifestations of LLMs, we designed a curated suite of 64 decision-making scenarios, guided by the DIAMONDS taxonomy, a psychological framework that characterizes situations along eight dimensions: Duty, Intellect, Adversity, Mating, pOsitivity, Negativity, Deception, and Sociality. By subjecting agents to varying scenarios, the benchmark evaluates whether they can consolidate their innate personality traits and autobiographical memories to make behavioral decisions that are consistent with their specific psychological profiles. After systematic human validation and filtering, we obtained a benchmark consisting of 673 multiple-choice questions (MCQs). We believe this benchmark provides a principled and scalable testbed for studying human-like emotions, personality consistency, and value-consistent behavioural decision-making in LLM-based agents.

CVAug 29, 2023
WrappingNet: Mesh Autoencoder via Deep Sphere Deformation

Eric Lei, Muhammad Asad Lodhi, Jiahao Pang et al.

There have been recent efforts to learn more meaningful representations via fixed length codewords from mesh data, since a mesh serves as a complete model of underlying 3D shape compared to a point cloud. However, the mesh connectivity presents new difficulties when constructing a deep learning pipeline for meshes. Previous mesh unsupervised learning approaches typically assume category-specific templates, e.g., human face/body templates. It restricts the learned latent codes to only be meaningful for objects in a specific category, so the learned latent spaces are unable to be used across different types of objects. In this work, we present WrappingNet, the first mesh autoencoder enabling general mesh unsupervised learning over heterogeneous objects. It introduces a novel base graph in the bottleneck dedicated to representing mesh connectivity, which is shown to facilitate learning a shared latent space representing object shape. The superiority of WrappingNet mesh learning is further demonstrated via improved reconstruction quality and competitive classification compared to point cloud learning, as well as latent interpolation between meshes of different categories.

CVFeb 11, 2024
PIVOT-Net: Heterogeneous Point-Voxel-Tree-based Framework for Point Cloud Compression

Jiahao Pang, Kevin Bui, Dong Tian

The universality of the point cloud format enables many 3D applications, making the compression of point clouds a critical phase in practice. Sampled as discrete 3D points, a point cloud approximates 2D surface(s) embedded in 3D with a finite bit-depth. However, the point distribution of a practical point cloud changes drastically as its bit-depth increases, requiring different methodologies for effective consumption/analysis. In this regard, a heterogeneous point cloud compression (PCC) framework is proposed. We unify typical point cloud representations -- point-based, voxel-based, and tree-based representations -- and their associated backbones under a learning-based framework to compress an input point cloud at different bit-depth levels. Having recognized the importance of voxel-domain processing, we augment the framework with a proposed context-aware upsampling for decoding and an enhanced voxel transformer for feature aggregation. Extensive experimentation demonstrates the state-of-the-art performance of our proposal on a wide range of point clouds.

CVOct 13, 2024
Towards Reproducible Learning-based Compression

Jiahao Pang, Muhammad Asad Lodhi, Junghyun Ahn et al.

A deep learning system typically suffers from a lack of reproducibility that is partially rooted in hardware or software implementation details. The irreproducibility leads to skepticism in deep learning technologies and it can hinder them from being deployed in many applications. In this work, the irreproducibility issue is analyzed where deep learning is employed in compression systems while the encoding and decoding may be run on devices from different manufacturers. The decoding process can even crash due to a single bit difference, e.g., in a learning-based entropy coder. For a given deep learning-based module with limited resources for protection, we first suggest that reproducibility can only be assured when the mismatches are bounded. Then a safeguarding mechanism is proposed to tackle the challenges. The proposed method may be applied for different levels of protection either at the reconstruction level or at a selected decoding level. Furthermore, the overhead introduced for the protection can be scaled down accordingly when the error bound is being suppressed. Experiments demonstrate the effectiveness of the proposed approach for learning-based compression systems, e.g., in image compression and point cloud compression.

CVAug 13, 2025
EntropyGS: An Efficient Entropy Coding on 3D Gaussian Splatting

Yuning Huang, Jiahao Pang, Fengqing Zhu et al.

As an emerging novel view synthesis approach, 3D Gaussian Splatting (3DGS) demonstrates fast training/rendering with superior visual quality. The two tasks of 3DGS, Gaussian creation and view rendering, are typically separated over time or devices, and thus storage/transmission and finally compression of 3DGS Gaussians become necessary. We begin with a correlation and statistical analysis of 3DGS Gaussian attributes. An inspiring finding in this work reveals that spherical harmonic AC attributes precisely follow Laplace distributions, while mixtures of Gaussian distributions can approximate rotation, scaling, and opacity. Additionally, harmonic AC attributes manifest weak correlations with other attributes except for inherited correlations from a color space. A factorized and parameterized entropy coding method, EntropyGS, is hereinafter proposed. During encoding, distribution parameters of each Gaussian attribute are estimated to assist their entropy coding. The quantization for entropy coding is adaptively performed according to Gaussian attribute types. EntropyGS demonstrates about 30x rate reduction on benchmark datasets while maintaining similar rendering quality compared to input 3DGS data, with a fast encoding and decoding time.

CVNov 9, 2021
Graph-Based Depth Denoising & Dequantization for Point Cloud Enhancement

Xue Zhang, Gene Cheung, Jiahao Pang et al.

A 3D point cloud is typically constructed from depth measurements acquired by sensors at one or more viewpoints. The measurements suffer from both quantization and noise corruption. To improve quality, previous works denoise a point cloud \textit{a posteriori} after projecting the imperfect depth data onto 3D space. Instead, we enhance depth measurements directly on the sensed images \textit{a priori}, before synthesizing a 3D point cloud. By enhancing near the physical sensing process, we tailor our optimization to our depth formation model before subsequent processing steps that obscure measurement errors. Specifically, we model depth formation as a combined process of signal-dependent noise addition and non-uniform log-based quantization. The designed model is validated (with parameters fitted) using collected empirical data from a representative depth sensor. To enhance each pixel row in a depth image, we first encode intra-view similarities between available row pixels as edge weights via feature graph learning. We next establish inter-view similarities with another rectified depth image via viewpoint mapping and sparse linear interpolation. This leads to a maximum a posteriori (MAP) graph filtering objective that is convex and differentiable. We minimize the objective efficiently using accelerated gradient descent (AGD), where the optimal step size is approximated via Gershgorin circle theorem (GCT). Experiments show that our method significantly outperformed recent point cloud denoising schemes and state-of-the-art image denoising schemes in two established point cloud quality metrics.

CVApr 1, 2021
FESTA: Flow Estimation via Spatial-Temporal Attention for Scene Point Clouds

Haiyan Wang, Jiahao Pang, Muhammad A. Lodhi et al.

Scene flow depicts the dynamics of a 3D scene, which is critical for various applications such as autonomous driving, robot navigation, AR/VR, etc. Conventionally, scene flow is estimated from dense/regular RGB video frames. With the development of depth-sensing technologies, precise 3D measurements are available via point clouds which have sparked new research in 3D scene flow. Nevertheless, it remains challenging to extract scene flow from point clouds due to the sparsity and irregularity in typical point cloud sampling patterns. One major issue related to irregular sampling is identified as the randomness during point set abstraction/feature extraction -- an elementary process in many flow estimation scenarios. A novel Spatial Abstraction with Attention (SA^2) layer is accordingly proposed to alleviate the unstable abstraction problem. Moreover, a Temporal Abstraction with Attention (TA^2) layer is proposed to rectify attention in temporal domain, leading to benefits with motions scaled in a larger range. Extensive analysis and experiments verified the motivation and significant performance gains of our method, dubbed as Flow Estimation via Spatial-Temporal Attention (FESTA), when compared to several state-of-the-art benchmarks of scene flow estimation.

CVAug 5, 2020
Graph Signal Processing for Geometric Data and Beyond: Theory and Applications

Wei Hu, Jiahao Pang, Xianming Liu et al.

Geometric data acquired from real-world scenes, e.g., 2D depth images, 3D point clouds, and 4D dynamic point clouds, have found a wide range of applications including immersive telepresence, autonomous driving, surveillance, etc. Due to irregular sampling patterns of most geometric data, traditional image/video processing methodologies are limited, while Graph Signal Processing (GSP) -- a fast-developing field in the signal processing community -- enables processing signals that reside on irregular domains and plays a critical role in numerous applications of geometric data from low-level processing to high-level analysis. To further advance the research in this field, we provide the first timely and comprehensive overview of GSP methodologies for geometric data in a unified manner by bridging the connections between geometric data and graphs, among the various geometric data modalities, and with spectral/nodal graph filtering techniques. We also discuss the recently developed Graph Neural Networks (GNNs) and interpret the operation of these networks from the perspective of GSP. We conclude with a brief discussion of open problems and challenges.

CVJun 17, 2020
TearingNet: Point Cloud Autoencoder to Learn Topology-Friendly Representations

Jiahao Pang, Duanshun Li, Dong Tian

Topology matters. Despite the recent success of point cloud processing with geometric deep learning, it remains arduous to capture the complex topologies of point cloud data with a learning model. Given a point cloud dataset containing objects with various genera, or scenes with multiple objects, we propose an autoencoder, TearingNet, which tackles the challenging task of representing the point clouds using a fixed-length descriptor. Unlike existing works directly deforming predefined primitives of genus zero (e.g., a 2D square patch) to an object-level point cloud, our TearingNet is characterized by a proposed Tearing network module and a Folding network module interacting with each other iteratively. Particularly, the Tearing network module learns the point cloud topology explicitly. By breaking the edges of a primitive graph, it tears the graph into patches or with holes to emulate the topology of a target point cloud, leading to faithful reconstructions. Experimentation shows the superiority of our proposal in terms of reconstructing point clouds as well as generating more topology-friendly representations than benchmarks.

IVFeb 11, 2020
3D Point Cloud Enhancement using Graph-Modelled Multiview Depth Measurements

Xue Zhang, Gene Cheung, Jiahao Pang et al.

A 3D point cloud is often synthesized from depth measurements collected by sensors at different viewpoints. The acquired measurements are typically both coarse in precision and corrupted by noise. To improve quality, previous works denoise a synthesized 3D point cloud a posteriori after projecting the imperfect depth data onto 3D space. Instead, we enhance depth measurements on the sensed images a priori, exploiting inherent 3D geometric correlation across views, before synthesizing a 3D point cloud from the improved measurements. By enhancing closer to the actual sensing process, we benefit from optimization targeting specifically the depth image formation model, before subsequent processing steps that can further obscure measurement errors. Mathematically, for each pixel row in a pair of rectified viewpoint depth images, we first construct a graph reflecting inter-pixel similarities via metric learning using data in previous enhanced rows. To optimize left and right viewpoint images simultaneously, we write a non-linear mapping function from left pixel row to the right based on 3D geometry relations. We formulate a MAP optimization problem, which, after suitable linear approximations, results in an unconstrained convex and differentiable objective, solvable using fast gradient method (FGM). Experimental results show that our method noticeably outperforms recent denoising algorithms that enhance after 3D point clouds are synthesized.

CVSep 17, 2019
Deep End-to-End Alignment and Refinement for Time-of-Flight RGB-D Module

Di Qiu, Jiahao Pang, Wenxiu Sun et al.

Recently, it is increasingly popular to equip mobile RGB cameras with Time-of-Flight (ToF) sensors for active depth sensing. However, for off-the-shelf ToF sensors, one must tackle two problems in order to obtain high-quality depth with respect to the RGB camera, namely 1) online calibration and alignment; and 2) complicated error correction for ToF depth sensing. In this work, we propose a framework for jointly alignment and refinement via deep learning. First, a cross-modal optical flow between the RGB image and the ToF amplitude image is estimated for alignment. The aligned depth is then refined via an improved kernel predicting network that performs kernel normalization and applies the bias prior to the dynamic convolution. To enrich our data for end-to-end training, we have also synthesized a dataset using tools from computer graphics. Experimental results demonstrate the effectiveness of our approach, achieving state-of-the-art for ToF refinement.

CVSep 26, 2018
DSR: Direct Self-rectification for Uncalibrated Dual-lens Cameras

Ruichao Xiao, Wenxiu Sun, Jiahao Pang et al.

With the developments of dual-lens camera modules,depth information representing the third dimension of thecaptured scenes becomes available for smartphones. It isestimated by stereo matching algorithms, taking as input thetwo views captured by dual-lens cameras at slightly differ-ent viewpoints. Depth-of-field rendering (also be referred toas synthetic defocus or bokeh) is one of the trending depth-based applications. However, to achieve fast depth estima-tion on smartphones, the stereo pairs need to be rectified inthe first place. In this paper, we propose a cost-effective so-lution to perform stereo rectification for dual-lens camerascalled direct self-rectification, short for DSR1. It removesthe need of individual offline calibration for every pair ofdual-lens cameras. In addition, the proposed solution isrobust to the slight movements, e.g., due to collisions, ofthe dual-lens cameras after fabrication. Different with ex-isting self-rectification approaches, our approach computesthe homography in a novel way with zero geometric distor-tions introduced to the master image. It is achieved by di-rectly minimizing the vertical displacements of correspond-ing points between the original master image and the trans-formed slave image. Our method is evaluated on both real-istic and synthetic stereo image pairs, and produces supe-rior results compared to the calibrated rectification or otherself-rectification approaches

CVJul 31, 2018
Deep Graph Laplacian Regularization for Robust Denoising of Real Images

Jin Zeng, Jiahao Pang, Wenxiu Sun et al.

Recent developments in deep learning have revolutionized the paradigm of image restoration. However, its applications on real image denoising are still limited, due to its sensitivity to training data and the complex nature of real image noise. In this work, we combine the robustness merit of model-based approaches and the learning power of data-driven approaches for real image denoising. Specifically, by integrating graph Laplacian regularization as a trainable module into a deep learning framework, we are less susceptible to overfitting than pure CNN-based approaches, achieving higher robustness to small datasets and cross-domain denoising. First, a sparse neighborhood graph is built from the output of a convolutional neural network (CNN). Then the image is restored by solving an unconstrained quadratic programming problem, using a corresponding graph Laplacian regularizer as a prior term. The proposed restoration pipeline is fully differentiable and hence can be end-to-end trained. Experimental results demonstrate that our work is less prone to overfitting given small training data. It is also endowed with strong cross-domain generalization power, outperforming the state-of-the-art approaches by a remarkable margin.

CVMar 20, 2018
3D Point Cloud Denoising using Graph Laplacian Regularization of a Low Dimensional Manifold Model

Jin Zeng, Gene Cheung, Michael Ng et al.

3D point cloud - a new signal representation of volumetric objects - is a discrete collection of triples marking exterior object surface locations in 3D space. Conventional imperfect acquisition processes of 3D point cloud - e.g., stereo-matching from multiple viewpoint images or depth data acquired directly from active light sensors - imply non-negligible noise in the data. In this paper, we adopt a previously proposed low-dimensional manifold model for the surface patches in the point cloud and seek self-similar patches to denoise them simultaneously using the patch manifold prior. Due to discrete observations of the patches on the manifold, we approximate the manifold dimension computation defined in the continuous domain with a patch-based graph Laplacian regularizer and propose a new discrete patch distance measure to quantify the similarity between two same-sized surface patches for graph construction that is robust to noise. We show that our graph Laplacian regularizer has a natural graph spectral interpretation, and has desirable numerical stability properties via eigenanalysis. Extensive simulation results show that our proposed denoising scheme can outperform state-of-the-art methods in objective metrics and can better preserve visually salient structural features like edges.

CVMar 18, 2018
Zoom and Learn: Generalizing Deep Stereo Matching to Novel Domains

Jiahao Pang, Wenxiu Sun, Chengxi Yang et al.

Despite the recent success of stereo matching with convolutional neural networks (CNNs), it remains arduous to generalize a pre-trained deep stereo model to a novel domain. A major difficulty is to collect accurate ground-truth disparities for stereo pairs in the target domain. In this work, we propose a self-adaptation approach for CNN training, utilizing both synthetic training data (with ground-truth disparities) and stereo pairs in the new domain (without ground-truths). Our method is driven by two empirical observations. By feeding real stereo pairs of different domains to stereo models pre-trained with synthetic data, we see that: i) a pre-trained model does not generalize well to the new domain, producing artifacts at boundaries and ill-posed regions; however, ii) feeding an up-sampled stereo pair leads to a disparity map with extra details. To avoid i) while exploiting ii), we formulate an iterative optimization problem with graph Laplacian regularization. At each iteration, the CNN adapts itself better to the new domain: we let the CNN learn its own higher-resolution output; at the meanwhile, a graph Laplacian regularization is imposed to discriminatively keep the desired edges while smoothing out the artifacts. We demonstrate the effectiveness of our method in two domains: daily scenes collected by smartphone cameras, and street views captured in a driving car.

CVMar 7, 2018
Single View Stereo Matching

Yue Luo, Jimmy Ren, Mude Lin et al.

Previous monocular depth estimation methods take a single view and directly regress the expected results. Though recent advances are made by applying geometrically inspired loss functions during training, the inference procedure does not explicitly impose any geometrical constraint. Therefore these models purely rely on the quality of data and the effectiveness of learning to generalize. This either leads to suboptimal results or the demand of huge amount of expensive ground truth labelled data to generate reasonable results. In this paper, we show for the first time that the monocular depth estimation problem can be reformulated as two sub-problems, a view synthesis procedure followed by stereo matching, with two intriguing properties, namely i) geometrical constraints can be explicitly imposed during inference; ii) demand on labelled depth data can be greatly alleviated. We show that the whole pipeline can still be trained in an end-to-end fashion and this new formulation plays a critical role in advancing the performance. The resulting model outperforms all the previous monocular depth estimation methods as well as the stereo block matching method in the challenging KITTI dataset by only using a small number of real training data. The model also generalizes well to other monocular depth estimation benchmarks. We also discuss the implications and the advantages of solving monocular depth estimation using stereo methods.

CVDec 18, 2017
LSTM Pose Machines

Yue Luo, Jimmy Ren, Zhouxia Wang et al.

We observed that recent state-of-the-art results on single image human pose estimation were achieved by multi-stage Convolution Neural Networks (CNN). Notwithstanding the superior performance on static images, the application of these models on videos is not only computationally intensive, it also suffers from performance degeneration and flicking. Such suboptimal results are mainly attributed to the inability of imposing sequential geometric consistency, handling severe image quality degradation (e.g. motion blur and occlusion) as well as the inability of capturing the temporal correlation among video frames. In this paper, we proposed a novel recurrent network to tackle these problems. We showed that if we were to impose the weight sharing scheme to the multi-stage CNN, it could be re-written as a Recurrent Neural Network (RNN). This property decouples the relationship among multiple network stages and results in significantly faster speed in invoking the network for videos. It also enables the adoption of Long Short-Term Memory (LSTM) units between video frames. We found such memory augmented RNN is very effective in imposing geometric consistency among frames. It also well handles input quality degradation in videos while successfully stabilizes the sequential outputs. The experiments showed that our approach significantly outperformed current state-of-the-art methods on two large-scale video pose estimation benchmarks. We also explored the memory cells inside the LSTM and provided insights on why such mechanism would benefit the prediction for video-based pose estimations.

CVAug 30, 2017
Cascade Residual Learning: A Two-stage Convolutional Neural Network for Stereo Matching

Jiahao Pang, Wenxiu Sun, Jimmy SJ. Ren et al.

Leveraging on the recent developments in convolutional neural networks (CNNs), matching dense correspondence from a stereo pair has been cast as a learning problem, with performance exceeding traditional approaches. However, it remains challenging to generate high-quality disparities for the inherently ill-posed regions. To tackle this problem, we propose a novel cascade CNN architecture composing of two stages. The first stage advances the recently proposed DispNet by equipping it with extra up-convolution modules, leading to disparity images with more details. The second stage explicitly rectifies the disparity initialized by the first stage; it couples with the first-stage and generates residual signals across multiple scales. The summation of the outputs from the two stages gives the final disparity. As opposed to directly learning the disparity at the second stage, we show that residual learning provides more effective refinement. Moreover, it also benefits the training of the overall cascade network. Experimentation shows that our cascade residual learning scheme provides state-of-the-art performance for matching stereo correspondence. By the time of the submission of this paper, our method ranks first in the KITTI 2015 stereo benchmark, surpassing the prior works by a noteworthy margin.

CVMay 30, 2017
Robust Tracking Using Region Proposal Networks

Jimmy Ren, Zhiyang Yu, Jianbo Liu et al.

Recent advances in visual tracking showed that deep Convolutional Neural Networks (CNN) trained for image classification can be strong feature extractors for discriminative trackers. However, due to the drastic difference between image classification and tracking, extra treatments such as model ensemble and feature engineering must be carried out to bridge the two domains. Such procedures are either time consuming or hard to generalize well across datasets. In this paper we discovered that the internal structure of Region Proposal Network (RPN)'s top layer feature can be utilized for robust visual tracking. We showed that such property has to be unleashed by a novel loss function which simultaneously considers classification accuracy and bounding box quality. Without ensemble and any extra treatment on feature maps, our proposed method achieved state-of-the-art results on several large scale benchmarks including OTB50, OTB100 and VOT2016. We will make our code publicly available.

CVApr 19, 2017
Accurate Single Stage Detector Using Recurrent Rolling Convolution

Jimmy Ren, Xiaohao Chen, Jianbo Liu et al.

Most of the recent successful methods in accurate object detection and localization used some variants of R-CNN style two stage Convolutional Neural Networks (CNN) where plausible regions were proposed in the first stage then followed by a second stage for decision refinement. Despite the simplicity of training and the efficiency in deployment, the single stage detection methods have not been as competitive when evaluated in benchmarks consider mAP for high IoU thresholds. In this paper, we proposed a novel single stage end-to-end trainable object detection network to overcome this limitation. We achieved this by introducing Recurrent Rolling Convolution (RRC) architecture over multi-scale feature maps to construct object classifiers and bounding box regressors which are "deep in context". We evaluated our method in the challenging KITTI dataset which measures methods under IoU threshold of 0.7. We showed that with RRC, a single reduced VGG-16 based model already significantly outperformed all the previously published results. At the time this paper was written our models ranked the first in KITTI car detection (the hard level), the first in cyclist detection and the second in pedestrian detection. These results were not reached by the previous single stage methods. The code is publicly available.

CVApr 27, 2016
Graph Laplacian Regularization for Image Denoising: Analysis in the Continuous Domain

Jiahao Pang, Gene Cheung

Inverse imaging problems are inherently under-determined, and hence it is important to employ appropriate image priors for regularization. One recent popular prior---the graph Laplacian regularizer---assumes that the target pixel patch is smooth with respect to an appropriately chosen graph. However, the mechanisms and implications of imposing the graph Laplacian regularizer on the original inverse problem are not well understood. To address this problem, in this paper we interpret neighborhood graphs of pixel patches as discrete counterparts of Riemannian manifolds and perform analysis in the continuous domain, providing insights into several fundamental aspects of graph Laplacian regularization for image denoising. Specifically, we first show the convergence of the graph Laplacian regularizer to a continuous-domain functional, integrating a norm measured in a locally adaptive metric space. Focusing on image denoising, we derive an optimal metric space assuming non-local self-similarity of pixel patches, leading to an optimal graph Laplacian regularizer for denoising in the discrete domain. We then interpret graph Laplacian regularization as an anisotropic diffusion scheme to explain its behavior during iterations, e.g., its tendency to promote piecewise smooth signals under certain settings. To verify our analysis, an iterative image denoising algorithm is developed. Experimental results show that our algorithm performs competitively with state-of-the-art denoising methods such as BM3D for natural images, and outperforms them significantly for piecewise smooth images.