A multiresolution framework for local similarity based image denoising

In this paper, we present a generic framework for denoising of images corrupted with additive white Gaussian noise based on the idea of regional similarity. The proposed framework employs a similarity function using the distance between pixels in a multidimensional feature space, whereby multiple feature maps describing various local regional characteristics can be utilized, giving higher weight to pixels having similar regional characteristics. An extension of the proposed framework into a multiresolution setting using wavelets and scale space is presented. It is shown that the resulting multiresolution multilateral (MRM) filtering algorithm not only eliminates the coarse-grain noise but can also faithfully reconstruct anisotropic features, particularly in the presence of high levels of noise

Graph Spectral Image Processing

Recent advent of graph signal processing (GSP) has spurred intensive studies of signals that live naturally on irregular data kernels described by graphs (e.g., social networks, wireless sensor networks). Though a digital image contains pixels that reside on a regularly sampled 2D grid, if one can design an appropriate underlying graph connecting pixels with weights that reflect the image structure, then one can interpret the image (or image patch) as a signal on a graph, and apply GSP tools for processing and analysis of the signal in graph spectral domain. In this article, we overview recent graph spectral techniques in GSP specifically for image / video processing. The topics covered include image compression, image restoration, image filtering and image segmentation

초점 스택에서 3D 깊이 재구성 및 깊이 개선

학위논문 (박사) -- 서울대학교 대학원 : 공과대학 전기·컴퓨터공학부, 2021. 2. 신영길.Three-dimensional (3D) depth recovery from two-dimensional images is a fundamental and challenging objective in computer vision, and is one of the most important prerequisites for many applications such as 3D measurement, robot location and navigation, self-driving, and so on. Depth-from-focus (DFF) is one of the important methods to reconstruct a 3D depth in the use of focus information. Reconstructing a 3D depth from texture-less regions is a typical issue associated with the conventional DFF. Further more, it is difficult for the conventional DFF reconstruction techniques to preserve depth edges and fine details while maintaining spatial consistency. In this dissertation, we address these problems and propose an DFF depth recovery framework which is robust over texture-less regions, and can reconstruct a depth image with clear edges and fine details. The depth recovery framework proposed in this dissertation is composed of two processes: depth reconstruction and depth refinement. To recovery an accurate 3D depth, We first formulate the depth reconstruction as a maximum a posterior (MAP) estimation problem with the inclusion of matting Laplacian prior. The nonlocal principle is adopted during the construction stage of the matting Laplacian matrix to preserve depth edges and fine details. Additionally, a depth variance based confidence measure with the combination of the reliability measure of focus measure is proposed to maintain the spatial smoothness, such that the smooth depth regions in initial depth could have high confidence value and the reconstructed depth could be more derived from the initial depth. As the nonlocal principle breaks the spatial consistency, the reconstructed depth image is spatially inconsistent. Meanwhile, it suffers from texture-copy artifacts. To smooth the noise and suppress the texture-copy artifacts introduced in the reconstructed depth image, we propose a closed-form edge-preserving depth refinement algorithm that formulates the depth refinement as a MAP estimation problem using Markov random fields (MRFs). With the incorporation of pre-estimated depth edges and mutual structure information into our energy function and the specially designed smoothness weight, the proposed refinement method can effectively suppress noise and texture-copy artifacts while preserving depth edges. Additionally, with the construction of undirected weighted graph representing the energy function, a closed-form solution is obtained by using the Laplacian matrix corresponding to the graph. The proposed framework presents a novel method of 3D depth recovery from a focal stack. The proposed algorithm shows the superiority in depth recovery over texture-less regions owing to the effective variance based confidence level computation and the matting Laplacian prior. Additionally, this proposed reconstruction method can obtain a depth image with clear edges and fine details due to the adoption of nonlocal principle in the construct]ion of matting Laplacian matrix. The proposed closed-form depth refinement approach shows that the ability in noise removal while preserving object structure with the usage of common edges. Additionally, it is able to effectively suppress texture-copy artifacts by utilizing mutual structure information. The proposed depth refinement provides a general idea for edge-preserving image smoothing, especially for depth related refinement such as stereo vision. Both quantitative and qualitative experimental results show the supremacy of the proposed method in terms of robustness in texture-less regions, accuracy, and ability to preserve object structure while maintaining spatial smoothness.Chapter 1 Introduction 1 1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4 Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Chapter 2 Related Works 9 2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2 Principle of depth-from-focus . . . . . . . . . . . . . . . . . . . . 9 2.2.1 Focus measure operators . . . . . . . . . . . . . . . . . . . 12 2.3 Depth-from-focus reconstruction . . . . . . . . . . . . . . . . . . 14 2.4 Edge-preserving image denoising . . . . . . . . . . . . . . . . . . 23 Chapter 3 Depth-from-Focus Reconstruction using Nonlocal Matting Laplacian Prior 38 3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.2 Image matting and matting Laplacian . . . . . . . . . . . . . . . 40 3.3 Depth-from-focus . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3.4 Depth reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.4.1 Problem statement . . . . . . . . . . . . . . . . . . . . . . 47 3.4.2 Likelihood model . . . . . . . . . . . . . . . . . . . . . . . 48 3.4.3 Nonlocal matting Laplacian prior model . . . . . . . . . . 50 3.5 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.5.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.5.2 Data configuration . . . . . . . . . . . . . . . . . . . . . . 55 3.5.3 Reconstruction results . . . . . . . . . . . . . . . . . . . . 56 3.5.4 Comparison between reconstruction using local and nonlocal matting Laplacian . . . . . . . . . . . . . . . . . . . 56 3.5.5 Spatial consistency analysis . . . . . . . . . . . . . . . . . 59 3.5.6 Parameter setting and analysis . . . . . . . . . . . . . . . 59 3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 Chapter 4 Closed-form MRF-based Depth Refinement 63 4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.2 Problem statement . . . . . . . . . . . . . . . . . . . . . . . . . . 65 4.3 Closed-form solution . . . . . . . . . . . . . . . . . . . . . . . . . 69 4.4 Edge preservation . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 4.5 Texture-copy artifacts suppression . . . . . . . . . . . . . . . . . 73 4.6 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . 76 4.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 Chapter 5 Evaluation 82 5.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 5.2 Evaluation metrics . . . . . . . . . . . . . . . . . . . . . . . . . . 83 5.3 Evaluation on synthetic datasets . . . . . . . . . . . . . . . . . . 84 5.4 Evaluation on real scene datasets . . . . . . . . . . . . . . . . . . 89 5.5 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 5.6 Computational performances . . . . . . . . . . . . . . . . . . . . 93 Chapter 6 Conclusion 96 Bibliography 99Docto

A graph-based mathematical morphology reader

This survey paper aims at providing a "literary" anthology of mathematical morphology on graphs. It describes in the English language many ideas stemming from a large number of different papers, hence providing a unified view of an active and diverse field of research

Visibility recovery on images acquired in attenuating media. Application to underwater, fog, and mammographic imaging

136 p.When acquired in attenuating media, digital images of ten suffer from a particularly complex degradation that reduces their visual quality, hindering their suitability for further computational applications, or simply decreasing the visual pleasan tness for the user. In these cases, mathematical image processing reveals it self as an ideal tool to recover some of the information lost during the degradation process. In this dissertation,we deal with three of such practical scenarios in which this problematic is specially relevant, namely, underwater image enhancement, fogremoval and mammographic image processing. In the case of digital mammograms,X-ray beams traverse human tissue, and electronic detectorscapture them as they reach the other side. However, the superposition on a bidimensional image of three-dimensional structures produces low contraste dimages in which structures of interest suffer from a diminished visibility, obstructing diagnosis tasks. Regarding fog removal, the loss of contrast is produced by the atmospheric conditions, and white colour takes over the scene uniformly as distance increases, also reducing visibility.For underwater images, there is an added difficulty, since colour is not lost uniformly; instead, red colours decay the fastest, and green and blue colours typically dominate the acquired images. To address all these challenges,in this dissertation we develop new methodologies that rely on: a)physical models of the observed degradation, and b) the calculus of variations.Equipped with this powerful machinery, we design novel theoreticaland computational tools, including image-dependent functional energies that capture the particularities of each degradation model. These energie sare composed of different integral terms that are simultaneous lyminimized by means of efficient numerical schemes, producing a clean,visually-pleasant and use ful output image, with better contrast and increased visibility. In every considered application, we provide comprehensive qualitative (visual) and quantitative experimental results to validateour methods, confirming that the developed techniques out perform other existing approaches in the literature

Robust density modelling using the student's t-distribution for human action recognition

The extraction of human features from videos is often inaccurate and prone to outliers. Such outliers can severely affect density modelling when the Gaussian distribution is used as the model since it is highly sensitive to outliers. The Gaussian distribution is also often used as base component of graphical models for recognising human actions in the videos (hidden Markov model and others) and the presence of outliers can significantly affect the recognition accuracy. In contrast, the Student's t-distribution is more robust to outliers and can be exploited to improve the recognition rate in the presence of abnormal data. In this paper, we present an HMM which uses mixtures of t-distributions as observation probabilities and show how experiments over two well-known datasets (Weizmann, MuHAVi) reported a remarkable improvement in classification accuracy. © 2011 IEEE

Understanding and advancing PDE-based image compression

This thesis is dedicated to image compression with partial differential equations (PDEs). PDE-based codecs store only a small amount of image points and propagate their information into the unknown image areas during the decompression step. For certain classes of images, PDE-based compression can already outperform the current quasi-standard, JPEG2000. However, the reasons for this success are not yet fully understood, and PDE-based compression is still in a proof-of-concept stage. With a probabilistic justification for anisotropic diffusion, we contribute to a deeper insight into design principles for PDE-based codecs. Moreover, by analysing the interaction between efficient storage methods and image reconstruction with diffusion, we can rank PDEs according to their practical value in compression. Based on these observations, we advance PDE-based compression towards practical viability: First, we present a new hybrid codec that combines PDE- and patch-based interpolation to deal with highly textured images. Furthermore, a new video player demonstrates the real-time capacities of PDE-based image interpolation and a new region of interest coding algorithm represents important image areas with high accuracy. Finally, we propose a new framework for diffusion-based image colourisation that we use to build an efficient codec for colour images. Experiments on real world image databases show that our new method is qualitatively competitive to current state-of-the-art codecs.Diese Dissertation ist der Bildkompression mit partiellen Differentialgleichungen (PDEs, partial differential equations) gewidmet. PDE-Codecs speichern nur einen geringen Anteil aller Bildpunkte und transportieren deren Information in fehlende Bildregionen. In einigen Fällen kann PDE-basierte Kompression den aktuellen Quasi-Standard, JPEG2000, bereits schlagen. Allerdings sind die Gründe für diesen Erfolg noch nicht vollständig erforscht, und PDE-basierte Kompression befindet sich derzeit noch im Anfangsstadium. Wir tragen durch eine probabilistische Rechtfertigung anisotroper Diffusion zu einem tieferen Verständnis PDE-basierten Codec-Designs bei. Eine Analyse der Interaktion zwischen effizienten Speicherverfahren und Bildrekonstruktion erlaubt es uns, PDEs nach ihrem Nutzen für die Kompression zu beurteilen. Anhand dieser Einsichten entwickeln wir PDE-basierte Kompression hinsichtlich ihrer praktischen Nutzbarkeit weiter: Wir stellen einen Hybrid-Codec für hochtexturierte Bilder vor, der umgebungsbasierte Interpolation mit PDEs kombiniert. Ein neuer Video-Dekodierer demonstriert die Echtzeitfähigkeit PDE-basierter Interpolation und eine Region-of-Interest-Methode erlaubt es, wichtige Bildbereiche mit hoher Genauigkeit zu speichern. Schlussendlich stellen wir ein neues diffusionsbasiertes Kolorierungsverfahren vor, welches uns effiziente Kompression von Farbbildern ermöglicht. Experimente auf Realwelt-Bilddatenbanken zeigen die Konkurrenzfähigkeit dieses Verfahrens auf