Medial Axis LUT Computation for Chamfer Norms Using H-Polytopes

International audienceChamfer distances are discrete distances based on the propagation of local distances, or weights defined in a mask. The medial axis, i.e. the centers of the maximal disks (disks which are not contained in any other disk), is a powerful tool for shape representation and analysis. The extraction of maximal disks is performed in the general case with comparison tests involving look-up tables representing the covering relation of disks in a local neighborhood. Although look-up table values can be computed efficiently, the computation of the look-up table neighborhood tend to be very time-consuming. By using polytope descriptions of the chamfer disks, the necessary operations to extract the look-up tables are greatly reduced

Distance Transform Computation for Digital Distance Functions

International audienceIn image processing, the distancetransform (DT), in which each object grid point is assigned the distance to the closest background grid point, is a powerful and often used tool. In this paper, distancefunctions defined as minimal cost-paths are used and a number of algorithms that can be used to compute the DT are presented. We give proofs of the correctness of the algorithms

Medial Axis Lookup Table and Test Neighborhood Computation for 3D Chamfer Norms

International audienceChamfer distances are discrete distances based on the propagation of local distances, or weights defined in a mask. The medial axis, i.e. the centers of the maximal disks (disks which are not contained in any other disk), is a powerful tool for shape representation and analysis. The extraction of maximal disks is performed in the general case with comparison tests involving look-up tables representing the covering relation of disks in a local neighborhood. Although look-up table values can be computed efficiently, the computation of the look-up table neighborhood tend to be very time-consuming. By using polytope descriptions of the chamfer disks, the necessary operations to extract the look-up tables are greatly reduced

Fast Mojette Transform for Discrete Tomography

A new algorithm for reconstructing a two dimensional object from a set of one dimensional projected views is presented that is both computationally exact and experimentally practical. The algorithm has a computational complexity of O(n log2 n) with n = N^2 for an NxN image, is robust in the presence of noise and produces no artefacts in the reconstruction process, as is the case with conventional tomographic methods. The reconstruction process is approximation free because the object is assumed to be discrete and utilizes fully discrete Radon transforms. Noise in the projection data can be suppressed further by introducing redundancy in the reconstruction. The number of projections required for exact reconstruction and the response to noise can be controlled without comprising the digital nature of the algorithm. The digital projections are those of the Mojette Transform, a form of discrete linogram. A simple analytical mapping is developed that compacts these projections exactly into symmetric periodic slices within the Discrete Fourier Transform. A new digital angle set is constructed that allows the periodic slices to completely fill all of the objects Discrete Fourier space. Techniques are proposed to acquire these digital projections experimentally to enable fast and robust two dimensional reconstructions.Comment: 22 pages, 13 figures, Submitted to Elsevier Signal Processin

Single-scan skeletonization driven by a neighborhood-sequence distance

International audienceShape description is an important step in image analysis. Skeletonization methods are widely used in image analysis as they are a powerful tool to describe a shape. Indeed, a skeleton is a one point wide line centered in the shape which keeps the shape's topology. Commonly, at least two scans of the image are needed for the skeleton computation in the state of art methods of skeletonization. In this work, a single scan is used considering information propagation in order to compute the skeleton. This paper presents also a new single-scan skeletonization using different distances likes d4, d8 and dns

Fast recursive grayscale morphology operators: from the algorithm to the pipeline architecture

International audienceThis paper presents a new algorithm for an efficient computation of morphological operations for gray images and its specific hardware. The method is based on a new recursive morphological decomposition method of 8-convex structuring elements by only causal two-pixel structuring elements (2PSE). Whatever the element size, erosion or/and dilation can then be performed during a unique raster-like image scan involving a fixed reduced analysis neighborhood. The resulting process offers low computation complexity combined with easy description of the element form. The dedicated hardware is generic and fully regular, built from elementary interconnected stages. It has been synthesized into an FPGA and achieves high frequency performances for any shape and size of structuring element

Geometry Compression of 3D Static Point Clouds based on TSPLVQ

International audienceIn this paper, we address the challenging problem of the 3D point cloud compression required to ensure efficient transmission and storage. We introduce a new hierarchical geometry representation based on adaptive Tree-Structured Point-Lattice Vector Quantization (TSPLVQ). This representation enables hierarchically structured 3D content that improves the compression performance for static point cloud. The novelty of the proposed scheme lies in adaptive selection of the optimal quantization scheme of the geometric information, that better leverage the intrinsic correlations in point cloud. Based on its adaptive and multiscale structure, two quantization schemes are dedicated to project recursively the 3D point clouds into a series of embedded truncated cubic lattices. At each step of the process, the optimal quantization scheme is selected according to a rate-distortion cost in order to achieve the best trade-off between coding rate and geometry distortion, such that the compression flexibility and performance can be greatly improved. Experimental results show the interest of the proposed multi-scale method for lossy compression of geometry

Projections et distances discrètes

Le travail se situe dans le domaine de la géométrie discrète. La tomographie discrète sera abordée sous l'angle de ses liens avec la théorie de l'information, illustrés par l'application de la transformation Mojette et de la "Finite Radon Transform" au codage redondant d'information pour la transmission et le stockage distribué. Les distances discrètes seront exposées selon les points de vue théorique (avec une nouvelle classe de distances construites par des chemins à poids variables) et algorithmique (transformation en distance, axe médian, granulométrie) en particulier par des méthodes en un balayage d'image (en "streaming"). Le lien avec les séquences d'entiers non-décroissantes et l'inverse de Lambek-Moser sera mis en avant

Extraction of bone structure with a single-scan skeletonization driven by distance

International audienceShape description is an important step in image analysis. Skeletonization methods are widely used in image analysis since they are a powerful tool to describe a shape. This paper presents a new single-scan skeletonization using different diskrete distances. The application of this method is the extraction of caracteristics from µCT images in order to estimate the bone state