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

Optimal Separable Algorithms to Compute the Reverse Euclidean Distance Transformation and Discrete Medial Axis in Arbitrary Dimension

In binary images, the distance transformation (DT) and the geometrical skeleton extraction are classic tools for shape analysis. In this paper, we present time optimal algorithms to solve the reverse Euclidean distance transformation and the reversible medial axis extraction problems for $d$-dimensional images. We also present a $d$-dimensional medial axis filtering process that allows us to control the quality of the reconstructed shape

Farey Sequences and the Planar Euclidean Medial Axis Test Mask

Abstract. The Euclidean test mask T (r) is the minimum neighbourhood sufficient to detect the Euclidean Medial Axis of any discrete shape whose inner radius does not exceed r. We establish a link between T (r) and the well-known Farey sequences, which allows us to propose two new algorithms. The first one computes T (r) in time O(r 4 ) and space O(r 2 ). The second one computes for any vector − → v the smallest r for which − → v ∈ T (r), in time O(r 3 ) and constant space

Features extraction based on the Discrete Hartley Transform for closed contour

In this paper the authors propose a new closed contour descriptor that could be seen as a Feature Extractor of closed contours based on the Discrete Hartley Transform (DHT), its main characteristic is that uses only half of the coefficients required by Elliptical Fourier Descriptors (EFD) to obtain a contour approximation with similar error measure. The proposed closed contour descriptor provides an excellent capability of information compression useful for a great number of AI applications. Moreover it can provide scale, position and rotation invariance, and last but not least it has the advantage that both the parameterization and the reconstructed shape from the compressed set can be computed very efficiently by the fast Discrete Hartley Transform (DHT) algorithm. This Feature Extractor could be useful when the application claims for reversible features and when the user needs and easy measure of the quality for a given level of compression, scalable from low to very high quality