In this paper, we explore the use of the diffusion geometry framework for the fusion of geometric and photometric information in local and global shape descriptors. Our construction is based on the definition of a diffusion process on the shape manifold embedded into a high-dimensional space where the embedding coordinates represent the photometric information. Experimental results show that su...

is book is a guide for researchers and practitioners to the new frontiers of 3D shape analysis and the complex mathematical tools most methods rely on. e target reader includes students, researchers and professionals with an undergraduate mathematics background, who wish to understand the mathematics behind shape analysis. e authors begin with a quick review of basic concepts in geometry, to...

In this paper a fully automated segmentation system for the femur in the knee in Magnetic Resonance Images and the brain in Single Photon Emission Computed Tomography images is presented. To do this several data sets were first segmented manually. The resulting structures were represented by unorganised point clouds. With level set methods surfaces were fitted to these point clouds. The iterate...

Conventional methods for shape analysis, based upon Procrustes and PCA, seem incapable of dealing with ‘non-landmark’ features, meaning measured positions not associated with well defined locations. This is due to an assumption of homogeneous errors, associated with an attempt to extract linear models with biologically meaningful descriptions. We propose a shape analysis system based upon the d...

Abstract: A system for real-time traffic sign detection is described in this paper. The vision-based traffic sign detection module developed in this work is intended for assisted driving of road vehicles by handling color images in RGB (Red, Green and Blue) format. In a first step a preattentive area of interest is determined based on the vertical projection of edge pixels. In a second step, a ...

To analyze given object shapes, it is necessary rst to model the shapes and then to analyze the models. This paper proposes a method of modeling and analyzing two-dimensional (2D) and three-dimensional (3D) shapes based on singularities. First, a function is dened on an object. The object is then modeled by the distribution of the singularities of the function. Finally, the extracted singular p...

In order to improve the effectiveness of shape based classification there is an ongoing interest in creating new shape descriptors or creating new measures for descriptors that are already defined and used in shape classification tasks. Convexity is one of the most widely used shape descriptors and also one of the most studied in the literature. There are already several defined convexity measu...

There have been various developments in shape analysis in the last decade. We describe here some relationships of shape analysis with directional statistics. For shape, rotations are to be integrated out or to be optimized over whilst they are the basis for directional statistics. However, various concepts are connected. In particular, certain distributions of directional statistics have emerge...

We introduce an (equi-)affine invariant geometric structure by which surfaces that go through squeeze and shear transformations can still be properly analyzed. The definition of an affine invariant metric enables us to evaluate a new form of geodesic distances and to construct an invariant Laplacian from which local and global diffusion geometry is constructed. Applications of the proposed fram...