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

Deep Model-Based Super-Resolution with Non-uniform Blur

We propose a state-of-the-art method for super-resolution with non-uniform blur. Single-image super-resolution methods seek to restore a high-resolution image from blurred, subsampled, and noisy measurements. Despite their impressive performance, existing techniques usually assume a uniform blur kernel. Hence, these techniques do not generalize well to the more general case of non-uniform blur. Instead, in this paper, we address the more realistic and computationally challenging case of spatially-varying blur. To this end, we first propose a fast deep plug-and-play algorithm, based on linearized ADMM splitting techniques, which can solve the super-resolution problem with spatially-varying blur. Second, we unfold our iterative algorithm into a single network and train it end-to-end. In this way, we overcome the intricacy of manually tuning the parameters involved in the optimization scheme. Our algorithm presents remarkable performance and generalizes well after a single training to a large family of spatially-varying blur kernels, noise levels and scale factors

Dictionary optimization for representing sparse signals using Rank-One Atom Decomposition (ROAD)

Dictionary learning has attracted growing research interest during recent years. As it is a bilinear inverse problem, one typical way to address this problem is to iteratively alternate between two stages: sparse coding and dictionary update. The general principle of the alternating approach is to fix one variable and optimize the other one. Unfortunately, for the alternating method, an ill-conditioned dictionary in the training process may not only introduce numerical instability but also trap the overall training process towards a singular point. Moreover, it leads to difficulty in analyzing its convergence, and few dictionary learning algorithms have been proved to have global convergence. For the other bilinear inverse problems, such as short-and-sparse deconvolution (SaSD) and convolutional dictionary learning (CDL), the alternating method is still a popular choice. As these bilinear inverse problems are also ill-posed and complicated, they are tricky to handle. Additional inner iterative methods are usually required for both of the updating stages, which aggravates the difficulty of analyzing the convergence of the whole learning process. It is also challenging to determine the number of iterations for each stage, as over-tuning any stage will trap the whole process into a local minimum that is far from the ground truth. To mitigate the issues resulting from the alternating method, this thesis proposes a novel algorithm termed rank-one atom decomposition (ROAD), which intends to recast a bilinear inverse problem into an optimization problem with respect to a single variable, that is, a set of rank-one matrices. Therefore, the resulting algorithm is one stage, which minimizes the sparsity of the coefficients while keeping the data consistency constraint throughout the whole learning process. Inspired by recent advances in applying the alternating direction method of multipliers (ADMM) to nonconvex nonsmooth problems, an ADMM solver is adopted to address ROAD problems, and a lower bound of the penalty parameter is derived to guarantee a convergence in the augmented Lagrangian despite nonconvexity of the optimization formulation. Compared to two-stage dictionary learning methods, ROAD simplifies the learning process, eases the difficulty of analyzing convergence, and avoids the singular point issue. From a practical point of view, ROAD reduces the number of tuning parameters required in other benchmark algorithms. Numerical tests reveal that ROAD outperforms other benchmark algorithms in both synthetic data tests and single image super-resolution applications. In addition to dictionary learning, the ROAD formulation can also be extended to solve the SaSD and CDL problems. ROAD can still be employed to recast these problems into a one-variable optimization problem. Numerical tests illustrate that ROAD has better performance in estimating convolutional kernels compared to the latest SaSD and CDL algorithms.Open Acces

Robust Subspace Estimation Using Low-rank Optimization. Theory And Applications In Scene Reconstruction, Video Denoising, And Activity Recognition.

In this dissertation, we discuss the problem of robust linear subspace estimation using low-rank optimization and propose three formulations of it. We demonstrate how these formulations can be used to solve fundamental computer vision problems, and provide superior performance in terms of accuracy and running time. Consider a set of observations extracted from images (such as pixel gray values, local features, trajectories . . . etc). If the assumption that these observations are drawn from a liner subspace (or can be linearly approximated) is valid, then the goal is to represent each observation as a linear combination of a compact basis, while maintaining a minimal reconstruction error. One of the earliest, yet most popular, approaches to achieve that is Principal Component Analysis (PCA). However, PCA can only handle Gaussian noise, and thus suffers when the observations are contaminated with gross and sparse outliers. To this end, in this dissertation, we focus on estimating the subspace robustly using low-rank optimization, where the sparse outliers are detected and separated through the `1 norm. The robust estimation has a two-fold advantage: First, the obtained basis better represents the actual subspace because it does not include contributions from the outliers. Second, the detected outliers are often of a specific interest in many applications, as we will show throughout this thesis. We demonstrate four different formulations and applications for low-rank optimization. First, we consider the problem of reconstructing an underwater sequence by removing the iii turbulence caused by the water waves. The main drawback of most previous attempts to tackle this problem is that they heavily depend on modelling the waves, which in fact is ill-posed since the actual behavior of the waves along with the imaging process are complicated and include several noise components; therefore, their results are not satisfactory. In contrast, we propose a novel approach which outperforms the state-of-the-art. The intuition behind our method is that in a sequence where the water is static, the frames would be linearly correlated. Therefore, in the presence of water waves, we may consider the frames as noisy observations drawn from a the subspace of linearly correlated frames. However, the noise introduced by the water waves is not sparse, and thus cannot directly be detected using low-rank optimization. Therefore, we propose a data-driven two-stage approach, where the first stage “sparsifies” the noise, and the second stage detects it. The first stage leverages the temporal mean of the sequence to overcome the structured turbulence of the waves through an iterative registration algorithm. The result of the first stage is a high quality mean and a better structured sequence; however, the sequence still contains unstructured sparse noise. Thus, we employ a second stage at which we extract the sparse errors from the sequence through rank minimization. Our method converges faster, and drastically outperforms state of the art on all testing sequences. Secondly, we consider a closely related situation where an independently moving object is also present in the turbulent video. More precisely, we consider video sequences acquired in a desert battlefields, where atmospheric turbulence is typically present, in addition to independently moving targets. Typical approaches for turbulence mitigation follow averaging or de-warping techniques. Although these methods can reduce the turbulence, they distort the independently moving objects which can often be of great interest. Therefore, we address the iv problem of simultaneous turbulence mitigation and moving object detection. We propose a novel three-term low-rank matrix decomposition approach in which we decompose the turbulence sequence into three components: the background, the turbulence, and the object. We simplify this extremely difficult problem into a minimization of nuclear norm, Frobenius norm, and `1 norm. Our method is based on two observations: First, the turbulence causes dense and Gaussian noise, and therefore can be captured by Frobenius norm, while the moving objects are sparse and thus can be captured by `1 norm. Second, since the object’s motion is linear and intrinsically different than the Gaussian-like turbulence, a Gaussian-based turbulence model can be employed to enforce an additional constraint on the search space of the minimization. We demonstrate the robustness of our approach on challenging sequences which are significantly distorted with atmospheric turbulence and include extremely tiny moving objects. In addition to robustly detecting the subspace of the frames of a sequence, we consider using trajectories as observations in the low-rank optimization framework. In particular, in videos acquired by moving cameras, we track all the pixels in the video and use that to estimate the camera motion subspace. This is particularly useful in activity recognition, which typically requires standard preprocessing steps such as motion compensation, moving object detection, and object tracking. The errors from the motion compensation step propagate to the object detection stage, resulting in miss-detections, which further complicates the tracking stage, resulting in cluttered and incorrect tracks. In contrast, we propose a novel approach which does not follow the standard steps, and accordingly avoids the aforementioned diffi- culties. Our approach is based on Lagrangian particle trajectories which are a set of dense trajectories obtained by advecting optical flow over time, thus capturing the ensemble motions v of a scene. This is done in frames of unaligned video, and no object detection is required. In order to handle the moving camera, we decompose the trajectories into their camera-induced and object-induced components. Having obtained the relevant object motion trajectories, we compute a compact set of chaotic invariant features, which captures the characteristics of the trajectories. Consequently, a SVM is employed to learn and recognize the human actions using the computed motion features. We performed intensive experiments on multiple benchmark datasets, and obtained promising results. Finally, we consider a more challenging problem referred to as complex event recognition, where the activities of interest are complex and unconstrained. This problem typically pose significant challenges because it involves videos of highly variable content, noise, length, frame size . . . etc. In this extremely challenging task, high-level features have recently shown a promising direction as in [53, 129], where core low-level events referred to as concepts are annotated and modelled using a portion of the training data, then each event is described using its content of these concepts. However, because of the complex nature of the videos, both the concept models and the corresponding high-level features are significantly noisy. In order to address this problem, we propose a novel low-rank formulation, which combines the precisely annotated videos used to train the concepts, with the rich high-level features. Our approach finds a new representation for each event, which is not only low-rank, but also constrained to adhere to the concept annotation, thus suppressing the noise, and maintaining a consistent occurrence of the concepts in each event. Extensive experiments on large scale real world dataset TRECVID Multimedia Event Detection 2011 and 2012 demonstrate that our approach consistently improves the discriminativity of the high-level features by a significant margin

Optimisation for image processing

The main purpose of optimisation in image processing is to compensate for missing, corrupted image data, or to find good correspondences between input images. We note that image data essentially has infinite dimensionality that needs to be discretised at certain levels of resolution. Most image processing methods find a suboptimal solution, given the characteristics of the problem. While the general optimisation literature is vast, there does not seem to be an accepted universal method for all image problems. In this thesis, we consider three interrelated optimisation approaches to exploit problem structures of various relaxations to three common image processing problems: 1. The first approach to the image registration problem is based on the nonlinear programming model. Image registration is an ill-posed problem and suffers from many undesired local optima. In order to remove these unwanted solutions, certain regularisers or constraints are needed. In this thesis, prior knowledge of rigid structures of the images is included in the problem using linear and bilinear constraints. The aim is to match two images while maintaining the rigid structure of certain parts of the images. A sequential quadratic programming algorithm is used, employing dimensional reduction, to solve the resulting discretised constrained optimisation problem. We show that pre-processing of the constraints can reduce problem dimensionality. Experimental results demonstrate better performance of our proposed algorithm compare to the current methods. 2. The second approach is based on discrete Markov Random Fields (MRF). MRF has been successfully used in machine learning, artificial intelligence, image processing, including the image registration problem. In the discrete MRF model, the domain of the image problem is fixed (relaxed) to a certain range. Therefore, the optimal solution to the relaxed problem could be found in the predefined domain. The original discrete MRF is NP hard and relaxations are needed to obtain a suboptimal solution in polynomial time. One popular approach is the linear programming (LP) relaxation. However, the LP relaxation of MRF (LP-MRF) is excessively high dimensional and contains sophisticated constraints. Therefore, even one iteration of a standard LP solver (e.g. interior-point algorithm), may take too long to terminate. Dual decomposition technique has been used to formulate a convex-nondifferentiable dual LP-MRF that has geometrical advantages. This has led to the development of first order methods that take into account the MRF structure. The methods considered in this thesis for solving the dual LP-MRF are the projected subgradient and mirror descent using nonlinear weighted distance functions. An analysis of the convergence properties of the method is provided, along with improved convergence rate estimates. The experiments on synthetic data and an image segmentation problem show promising results. 3. The third approach employs a hierarchy of problem's models for computing the search directions. The first two approaches are specialised methods for image problems at a certain level of discretisation. As input images are infinite-dimensional, all computational methods require their discretisation at some levels. Clearly, high resolution images carry more information but they lead to very large scale and ill-posed optimisation problems. By contrast, although low level discretisation suffers from the loss of information, it benefits from low computational cost. In addition, a coarser representation of a fine image problem could be treated as a relaxation to the problem, i.e. the coarse problem is less ill-conditioned. Therefore, propagating a solution of a good coarse approximation to the fine problem could potentially improve the fine level. With the aim of utilising low level information within the high level process, we propose a multilevel optimisation method to solve the convex composite optimisation problem. This problem consists of the minimisation of the sum of a smooth convex function and a simple non-smooth convex function. The method iterates between fine and coarse levels of discretisation in the sense that the search direction is computed using information from either the gradient or a solution of the coarse model. We show that the proposed algorithm is a contraction on the optimal solution and demonstrate excellent performance on experiments with image restoration problems.Open Acces

Coded aperture imaging

This thesis studies the coded aperture camera, a device consisting of a conventional camera with a modified aperture mask, that enables the recovery of both depth map and all-in-focus image from a single 2D input image. Key contributions of this work are the modeling of the statistics of natural images and the design of efficient blur identification methods in a Bayesian framework. Two cases are distinguished: 1) when the aperture can be decomposed in a small set of identical holes, and 2) when the aperture has a more general configuration. In the first case, the formulation of the problem incorporates priors about the statistical variation of the texture to avoid ambiguities in the solution. This allows to bypass the recovery of the sharp image and concentrate only on estimating depth. In the second case, the depth reconstruction is addressed via convolutions with a bank of linear filters. Key advantages over competing methods are the higher numerical stability and the ability to deal with large blur. The all-in-focus image can then be recovered by using a deconvolution step with the estimated depth map. Furthermore, for the purpose of depth estimation alone, the proposed algorithm does not require information about the mask in use. The comparison with existing algorithms in the literature shows that the proposed methods achieve state-of-the-art performance. This solution is also extended for the first time to images affected by both defocus and motion blur and, finally, to video sequences with moving and deformable objects

Overcomplete Dictionary and Deep Learning Approaches to Image and Video Analysis

Extracting useful information while ignoring others (e.g. noise, occlusion, lighting) is an essential and challenging data analyzing step for many computer vision tasks such as facial recognition, scene reconstruction, event detection, image restoration, etc. Data analyzing of those tasks can be formulated as a form of matrix decomposition or factorization to separate useful and/or fill in missing information based on sparsity and/or low-rankness of the data. There has been an increasing number of non-convex approaches including conventional matrix norm optimizing and emerging deep learning models. However, it is hard to optimize the ideal l0-norm or learn the deep models directly and efficiently. Motivated from this challenging process, this thesis proposes two sets of approaches: conventional and deep learning based. For conventional approaches, this thesis proposes a novel online non-convex lp-norm based Robust PCA (OLP-RPCA) approach for matrix decomposition, where 0 < p < 1. OLP-RPCA is developed from the offline version LP-RPCA. A robust face recognition framework is also developed from Robust PCA and sparse coding approaches. More importantly, OLP-RPCA method can achieve real-time performance on large-scale data without parallelizing or implementing on a graphics processing unit. We mathematically and empirically show that our OLP-RPCA algorithm is linear in both the sample dimension and the number of samples. The proposed OLP-RPCA and LP-RPCA approaches are evaluated in various applications including Gaussian/non-Gaussian image denoising, face modeling, real-time background subtraction and video inpainting and compared against numerous state-of-the-art methods to demonstrate the robustness of the algorithms. In addition, this thesis proposes a novel Robust lp-norm Singular Value Decomposition (RP-SVD) method for analyzing two-way functional data. The proposed RP-SVD is formulated as an lp-norm based penalized loss minimization problem. The proposed RP-SVD method is evaluated in four applications, i.e. noise and outlier removal, estimation of missing values, structure from motion reconstruction and facial image reconstruction. For deep learning based approaches, this thesis explores the idea of matrix decomposition via Robust Deep Boltzmann Machines (RDBM), an alternative form of Robust Boltzmann Machines, which aiming at dealing with noise and occlusion for face-related applications, particularly. This thesis proposes an extension to texture modeling in the Deep Appearance Models (DAMs) by using RDBM to enhance its robustness against noise and occlusion. The extended model can cope with occlusion and extreme poses when modeling human faces in 2D image reconstruction. This thesis also introduces new fitting algorithms with occlusion awareness through the mask obtained from the RDBM reconstruction. The proposed approach is evaluated in various applications by using challenging face datasets, i.e. Labeled Face Parts in the Wild (LFPW), Helen, EURECOM and AR databases, to demonstrate its robustness and capabilities