New Dynamic Enhancements to the Vertex-Based Rate-Distortion Optimal Shape Coding Framework

Existing vertex-based operational rate-distortion (ORD) optimal shape coding algorithms use a vertex band around the shape boundary as the source of candidate control points (CP) usually in combination with a tolerance band (TB) and sliding window (SW) arrangement, as their distortion measuring technique. These algorithms however, employ a fixed vertex-band width irrespective of the shape and admissible distortion (AD), so the full bit-rate reduction potential is not fulfilled. Moreover, despite the causal impact of the SW-length upon both the bit-rate and computational-speed, there is no formal mechanism for determining the most suitable SW-length. This paper introduces the concept of a variable width admissible CP band and new adaptive SW-length selection strategy to address these issues. The presented quantitative and qualitative results analysis endorses the superior performance achieved by integrating these enhancements into the existing vertex-based ORD optimal algorithms

Dynamic Bezier curves for variable rate-distortion

Bezier curves (BC) are important tools in a wide range of diverse and challenging applications, from computer-aided design to generic object shape descriptors. A major constraint of the classical BC is that only global information concerning control points (CP) is considered, consequently there may be a sizeable gap between the BC and its control polygon (CtrlPoly), leading to a large distortion in shape representation. While BC variants like degree elevation, composite BC and refinement and subdivision narrow this gap, they increase the number of CP and thereby both the required bit-rate and computational complexity. In addition, while quasi-Bezier curves (QBC) close the gap without increasing the number of CP, they reduce the underlying distortion by only a fixed amount. This paper presents a novel contribution to BC theory, with the introduction of a dynamic Bezier curve (DBC) model, which embeds variable localised CP information into the inherently global Bezier framework, by strategically moving BC points towards the CtrlPoly. A shifting parameter (SP) is defined that enables curves lying within the region between the BC and CtrlPoly to be generated, with no commensurate increase in CP. DBC provides a flexible rate-distortion (RD) criterion for shape coding applications, with a theoretical model for determining the optimal SP value for any admissible distortion being formulated. Crucially DBC retains core properties of the classical BC, including the convex hull and affine invariance, and can be seamlessly integrated into both the vertex-based shape coding and shape descriptor frameworks to improve their RD performance. DBC has been empirically tested upon a number of natural and synthetically shaped objects, with qualitative and quantitative results confirming its consistently superior shape approximation performance, compared with the classical BC, QBC and other established BC-based shape descriptor techniques

Quasi-Bezier curves integrating localised information

Bezier curves (BC) have become fundamental tools in many challenging and varied applications, ranging from computer-aided geometric design to generic object shape descriptors. A major limitation of the classical Bezier curve, however, is that only global information about its control points (CP) is considered, so there can often be a large gap between the curve and its control polygon, leading to large distortion in shape representation. While strategies such as degree elevation, composite BC, refinement and subdivision reduce this gap, they also increase the number of CP and hence bit-rate, and computational complexity. This paper presents novel contributions to BC theory, with the introduction of quasi-Bezier curves (QBC), which seamlessly integrate localised CP information into the inherent global Bezier framework, with no increase in either the number of CP or order of computational complexity. QBC crucially retains the core properties of the classical BC, such as geometric continuity and affine invariance, and can be embedded into the vertex-based shape coding and shape descriptor framework to enhance rate-distortion performance. The performance of QBC has been empirically tested upon a number of natural and synthetically shaped objects, with both qualitative and quantitative results confirming its consistently superior approximation performance in comparison with both the classical BC and other established BC-based shape descriptor methods

Geometric distortion measurement for shape coding: a contemporary review

Geometric distortion measurement and the associated metrics involved are integral to the rate-distortion (RD) shape coding framework, with importantly the efficacy of the metrics being strongly influenced by the underlying measurement strategy. This has been the catalyst for many different techniques with this paper presenting a comprehensive review of geometric distortion measurement, the diverse metrics applied and their impact on shape coding. The respective performance of these measuring strategies is analysed from both a RD and complexity perspective, with a recent distortion measurement technique based on arc-length-parameterisation being comparatively evaluated. Some contemporary research challenges are also investigated, including schemes to effectively quantify shape deformation

Fast Distortion Measurement Using Chord-Length Parameterisation within the Vertex-Based Rate-Distortion Optimal Shape Coding Framework

Existing vertex-based operational rate-distortion (ORD) optimal shape coding algorithms can use a number of different distortion measurement techniques, including the shortest absolute distance (SAD), the distortion band (DB), the tolerance band (TB), and the accurate distortion measurement technique for shape coding (ADMSC). From a computational time perspective, an N-point contour requires O(N2 ) time for DB and TB for both polygon and B-spline-based encoding, while SAD and ADMSC incur O(N) time for polygonal encoding but O(N2 ) for B-spline based encoding, thereby rendering the ORD optimal algorithms computationally inefficient. This letter presents a novel distortion measurement strategy based on chord-length parameterization (DMCLP) of a boundary that incurs order O(N) complexity for both polygon and B-spline-based encoding while preserving a comparable rate-distortion performance to the original ORD optimal shape coding algorithm

Variable Width Admissible Control Point Band for Vertex Based Operational-Rate-Distortion Optimal Shape Coding Algorithms

Existing vertex-based operational-rate-distortion (ORD) optimal shape coding algorithms use a fixed width admissible control point band (FCB) around the shape boundary as the search space for possible control points. The width of the band however, is fixed and arbitrarily chosen independent of the admissible distortion and shape contour, so it fails to fully exploit the admissible control point band to reduce the bit-rate. This paper proposes a variable width admissible control point band (VCB) where the width associated to each boundary point is dynamically determined from the admissible peak distortion and shape information. In addition, the paper uses an accurate distortion measurement method to overcome a key limitation of existing distortion and tolerance band based methods. Experimental results reveal that both the qualitative and quantitative performance of the existing ORD algorithms are improved by seamlessly integrating the VCB and accurate distortion measuring approac

Measurements, Models, Systems and Design

531 s.

Sparse image approximation with application to flexible image coding

Natural images are often modeled through piecewise-smooth regions. Region edges, which correspond to the contours of the objects, become, in this model, the main information of the signal. Contours have the property of being smooth functions along the direction of the edge, and irregularities on the perpendicular direction. Modeling edges with the minimum possible number of terms is of key importance for numerous applications, such as image coding, segmentation or denoising. Standard separable basis fail to provide sparse enough representation of contours, due to the fact that this kind of basis do not see the regularity of edges. In order to be able to detect this regularity, a new method based on (possibly redundant) sets of basis functions able to capture the geometry of images is needed. This thesis presents, in a first stage, a study about the features that basis functions should have in order to provide sparse representations of a piecewise-smooth image. This study emphasizes the need for edge-adapted basis functions, capable to accurately capture local orientation and anisotropic scaling of image structures. The need of different anisotropy degrees and orientations in the basis function set leads to the use of redundant dictionaries. However, redundant dictionaries have the inconvenience of giving no unique sparse image decompositions, and from all the possible decompositions of a signal in a redundant dictionary, just the sparsest is needed. There are several algorithms that allow to find sparse decompositions over redundant dictionaries, but most of these algorithms do not always guarantee that the optimal approximation has been recovered. To cope with this problem, a mathematical study about the properties of sparse approximations is performed. From this, a test to check whether a given sparse approximation is the sparsest is provided. The second part of this thesis presents a novel image approximation scheme, based on the use of a redundant dictionary. This scheme allows to have a good approximation of an image with a number of terms much smaller than the dimension of the signal. This novel approximation scheme is based on a dictionary formed by a combination of anisotropically refined and rotated wavelet-like mother functions and Gaussians. An efficient Full Search Matching Pursuit algorithm to perform the image decomposition in such a dictionary is designed. Finally, a geometric image coding scheme based on the image approximated over the anisotropic and rotated dictionary of basis functions is designed. The coding performances of this dictionary are studied. Coefficient quantization appears to be of crucial importance in the design of a Matching Pursuit based coding scheme. Thus, a quantization scheme for the MP coefficients has been designed, based on the theoretical energy upper bound of the MP algorithm and the empirical observations of the coefficient distribution and evolution. Thanks to this quantization, our image coder provides low to medium bit-rate image approximations, while it allows for on the fly resolution switching and several other affine image transformations to be performed directly in the transformed domain

Data compression and harmonic analysis

In this paper we review some recent interactions between harmonic analysis and data compression. The story goes back of course to Shannon’