A Modified Distortion Measurement Algorithm for Shape Coding

Efficient encoding of object boundaries has become increasingly prominent in areas such as content-based storage and retrieval, studio and television post-production facilities, mobile communications and other real-time multimedia applications. The way distortion between the actual and approximated shapes is measured however, has a major impact upon the quality of the shape coding algorithms. In existing shape coding methods, the distortion measure do not generate an actual distortion value, so this paper proposes a new distortion measure, called a modified distortion measure for shape coding (DMSC) which incorporates an actual perceptual distance. The performance of the Operational Rate Distortion optimal algorithm [1] incorporating DMSC has been empirically evaluated upon a number of different natural and synthetic arbitrary shapes. Both qualitative and quantitative results confirm the superior results in comparison with the ORD lgorithm for all test shapes, without any increase in computational complexity

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

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

Sliding-window designs for vertex-based shape coding

Traditionally the sliding window, (SW) has been employed in vertex-based operational rate distortion (ORD) optimal shape coding algorithms to ensure consistent distortion (quality) measurement and improve computational efficiency. It also regulates the memory requirements for an encoder design enabling regular, symmetrical hardware implementations. This paper presents a series of new enhancements to existing techniques for determining the best SW-length within a rate-distortion (RD) framework, and analyses the nexus between SW-length and storage for ORD hardware realisations. In addition, it presents an efficient bit-allocation strategy for managing multiple shapes together with a generalised adaptive SW scheme which integrates localised curvature information (cornerity) on contour points with a bi-directional spatial distance, to afford a superior and more pragmatic SW design compared with existing adaptive SW solutions which are based on only cornerity values. Experimental results consistently corroborate the effectiveness of these new strategies