Rate-Distortion Efficient Piecewise Planar 3D Scene Representation from 2-D Images

Cataloged from PDF version of article.In any practical application of the 2-D-to-3-D conversion that involves storage and transmission, representation effi- ciency has an undisputable importance that is not reflected in the attention the topic received. In order to address this problem, a novel algorithm, which yields efficient 3-D representations in the rate distortion sense, is proposed. The algorithm utilizes two views of a scene to build a mesh-based representation incrementally, via adding new vertices, while minimizing a distortion measure. The experimental results indicate that, in scenes that can be approximated by planes, the proposed algorithm is superior to the dense depth map and, in some practical situations, to the block motion vector-based representations in the rate-distortion sense

A Review of Bandlet Methods for Geometrical Image Representation

International audienceThis article reviews bandlet approaches to geometric image repre- sentations. Orthogonal bandlets using an adaptive segmentation and a local geometric flow well suited to capture the anisotropic regularity of edge struc- tures. They are constructed with a “bandletization” which is a local orthogonal transformation applied to wavelet coeffi cients. The approximation in these bandlet bases exhibits an asymptotically optimal decay for images that are regular outside a set of regular edges. These bandlets can be used to perform image compression and noise removal. More flexible orthogonal bandlets with less vanishing moments are constructed with orthogonal grouplets that group wavelet coeffi cients alon a multiscale association field. Applying a translation invariant grouplet transform over a translation invariant wavelet frame leads to state of the art results for image denoising and super-resolution

Acquisition, compression and rendering of depth and texture for multi-view video

Three-dimensional (3D) video and imaging technologies is an emerging trend in the development of digital video systems, as we presently witness the appearance of 3D displays, coding systems, and 3D camera setups. Three-dimensional multi-view video is typically obtained from a set of synchronized cameras, which are capturing the same scene from different viewpoints. This technique especially enables applications such as freeviewpoint video or 3D-TV. Free-viewpoint video applications provide the feature to interactively select and render a virtual viewpoint of the scene. A 3D experience such as for example in 3D-TV is obtained if the data representation and display enable to distinguish the relief of the scene, i.e., the depth within the scene. With 3D-TV, the depth of the scene can be perceived using a multi-view display that renders simultaneously several views of the same scene. To render these multiple views on a remote display, an efficient transmission, and thus compression of the multi-view video is necessary. However, a major problem when dealing with multiview video is the intrinsically large amount of data to be compressed, decompressed and rendered. We aim at an efficient and flexible multi-view video system, and explore three different aspects. First, we develop an algorithm for acquiring a depth signal from a multi-view setup. Second, we present efficient 3D rendering algorithms for a multi-view signal. Third, we propose coding techniques for 3D multi-view signals, based on the use of an explicit depth signal. This motivates that the thesis is divided in three parts. The first part (Chapter 3) addresses the problem of 3D multi-view video acquisition. Multi-view video acquisition refers to the task of estimating and recording a 3D geometric description of the scene. A 3D description of the scene can be represented by a so-called depth image, which can be estimated by triangulation of the corresponding pixels in the multiple views. Initially, we focus on the problem of depth estimation using two views, and present the basic geometric model that enables the triangulation of corresponding pixels across the views. Next, we review two calculation/optimization strategies for determining corresponding pixels: a local and a one-dimensional optimization strategy. Second, to generalize from the two-view case, we introduce a simple geometric model for estimating the depth using multiple views simultaneously. Based on this geometric model, we propose a new multi-view depth-estimation technique, employing a one-dimensional optimization strategy that (1) reduces the noise level in the estimated depth images and (2) enforces consistent depth images across the views. The second part (Chapter 4) details the problem of multi-view image rendering. Multi-view image rendering refers to the process of generating synthetic images using multiple views. Two different rendering techniques are initially explored: a 3D image warping and a mesh-based rendering technique. Each of these methods has its limitations and suffers from either high computational complexity or low image rendering quality. As a consequence, we present two image-based rendering algorithms that improves the balance on the aforementioned issues. First, we derive an alternative formulation of the relief texture algorithm which was extented to the geometry of multiple views. The proposed technique features two advantages: it avoids rendering artifacts ("holes") in the synthetic image and it is suitable for execution on a standard Graphics Processor Unit (GPU). Second, we propose an inverse mapping rendering technique that allows a simple and accurate re-sampling of synthetic pixels. Experimental comparisons with 3D image warping show an improvement of rendering quality of 3.8 dB for the relief texture mapping and 3.0 dB for the inverse mapping rendering technique. The third part concentrates on the compression problem of multi-view texture and depth video (Chapters 5–7). In Chapter 5, we extend the standard H.264/MPEG-4 AVC video compression algorithm for handling the compression of multi-view video. As opposed to the Multi-view Video Coding (MVC) standard that encodes only the multi-view texture data, the proposed encoder peforms the compression of both the texture and the depth multi-view sequences. The proposed extension is based on exploiting the correlation between the multiple camera views. To this end, two different approaches for predictive coding of views have been investigated: a block-based disparity-compensated prediction technique and a View Synthesis Prediction (VSP) scheme. Whereas VSP relies on an accurate depth image, the block-based disparity-compensated prediction scheme can be performed without any geometry information. Our encoder adaptively selects the most appropriate prediction scheme using a rate-distortion criterion for an optimal prediction-mode selection. We present experimental results for several texture and depth multi-view sequences, yielding a quality improvement of up to 0.6 dB for the texture and 3.2 dB for the depth, when compared to solely performing H.264/MPEG-4AVC disparitycompensated prediction. Additionally, we discuss the trade-off between the random-access to a user-selected view and the coding efficiency. Experimental results illustrating and quantifying this trade-off are provided. In Chapter 6, we focus on the compression of a depth signal. We present a novel depth image coding algorithm which concentrates on the special characteristics of depth images: smooth regions delineated by sharp edges. The algorithm models these smooth regions using parameterized piecewiselinear functions and sharp edges by a straight line, so that it is more efficient than a conventional transform-based encoder. To optimize the quality of the coding system for a given bit rate, a special global rate-distortion optimization balances the rate against the accuracy of the signal representation. For typical bit rates, i.e., between 0.01 and 0.25 bit/pixel, experiments have revealed that the coder outperforms a standard JPEG-2000 encoder by 0.6-3.0 dB. Preliminary results were published in the Proceedings of 26th Symposium on Information Theory in the Benelux. In Chapter 7, we propose a novel joint depth-texture bit-allocation algorithm for the joint compression of texture and depth images. The described algorithm combines the depth and texture Rate-Distortion (R-D) curves, to obtain a single R-D surface that allows the optimization of the joint bit-allocation in relation to the obtained rendering quality. Experimental results show an estimated gain of 1 dB compared to a compression performed without joint bit-allocation optimization. Besides this, our joint R-D model can be readily integrated into an multi-view H.264/MPEG-4 AVC coder because it yields the optimal compression setting with a limited computation effort

Dictionary Learning-based Inpainting on Triangular Meshes

The problem of inpainting consists of filling missing or damaged regions in images and videos in such a way that the filling pattern does not produce artifacts that deviate from the original data. In addition to restoring the missing data, the inpainting technique can also be used to remove undesired objects. In this work, we address the problem of inpainting on surfaces through a new method based on dictionary learning and sparse coding. Our method learns the dictionary through the subdivision of the mesh into patches and rebuilds the mesh via a method of reconstruction inspired by the Non-local Means method on the computed sparse codes. One of the advantages of our method is that it is capable of filling the missing regions and simultaneously removes noise and enhances important features of the mesh. Moreover, the inpainting result is globally coherent as the representation based on the dictionaries captures all the geometric information in the transformed domain. We present two variations of the method: a direct one, in which the model is reconstructed and restored directly from the representation in the transformed domain and a second one, adaptive, in which the missing regions are recreated iteratively through the successive propagation of the sparse code computed in the hole boundaries, which guides the local reconstructions. The second method produces better results for large regions because the sparse codes of the patches are adapted according to the sparse codes of the boundary patches. Finally, we present and analyze experimental results that demonstrate the performance of our method compared to the literature

A Panorama on Multiscale Geometric Representations, Intertwining Spatial, Directional and Frequency Selectivity

The richness of natural images makes the quest for optimal representations in image processing and computer vision challenging. The latter observation has not prevented the design of image representations, which trade off between efficiency and complexity, while achieving accurate rendering of smooth regions as well as reproducing faithful contours and textures. The most recent ones, proposed in the past decade, share an hybrid heritage highlighting the multiscale and oriented nature of edges and patterns in images. This paper presents a panorama of the aforementioned literature on decompositions in multiscale, multi-orientation bases or dictionaries. They typically exhibit redundancy to improve sparsity in the transformed domain and sometimes its invariance with respect to simple geometric deformations (translation, rotation). Oriented multiscale dictionaries extend traditional wavelet processing and may offer rotation invariance. Highly redundant dictionaries require specific algorithms to simplify the search for an efficient (sparse) representation. We also discuss the extension of multiscale geometric decompositions to non-Euclidean domains such as the sphere or arbitrary meshed surfaces. The etymology of panorama suggests an overview, based on a choice of partially overlapping "pictures". We hope that this paper will contribute to the appreciation and apprehension of a stream of current research directions in image understanding.Comment: 65 pages, 33 figures, 303 reference

Radial Basis Functions: Biomedical Applications and Parallelization

Radial basis function (RBF) is a real-valued function whose values depend only on the distances between an interpolation point and a set of user-specified points called centers. RBF interpolation is one of the primary methods to reconstruct functions from multi-dimensional scattered data. Its abilities to generalize arbitrary space dimensions and to provide spectral accuracy have made it particularly popular in different application areas, including but not limited to: finding numerical solutions of partial differential equations (PDEs), image processing, computer vision and graphics, deep learning and neural networks, etc. The present thesis discusses three applications of RBF interpolation in biomedical engineering areas: (1) Calcium dynamics modeling, in which we numerically solve a set of PDEs by using meshless numerical methods and RBF-based interpolation techniques; (2) Image restoration and transformation, where an image is restored from its triangular mesh representation or transformed under translation, rotation, and scaling, etc. from its original form; (3) Porous structure design, in which the RBF interpolation used to reconstruct a 3D volume containing porous structures from a set of regularly or randomly placed points inside a user-provided surface shape. All these three applications have been investigated and their effectiveness has been supported with numerous experimental results. In particular, we innovatively utilize anisotropic distance metrics to define the distance in RBF interpolation and apply them to the aforementioned second and third applications, which show significant improvement in preserving image features or capturing connected porous structures over the isotropic distance-based RBF method. Beside the algorithm designs and their applications in biomedical areas, we also explore several common parallelization techniques (including OpenMP and CUDA-based GPU programming) to accelerate the performance of the present algorithms. In particular, we analyze how parallel programming can help RBF interpolation to speed up the meshless PDE solver as well as image processing. While RBF has been widely used in various science and engineering fields, the current thesis is expected to trigger some more interest from computational scientists or students into this fast-growing area and specifically apply these techniques to biomedical problems such as the ones investigated in the present work