On Nonrigid Shape Similarity and Correspondence

An important operation in geometry processing is finding the correspondences between pairs of shapes. The Gromov-Hausdorff distance, a measure of dissimilarity between metric spaces, has been found to be highly useful for nonrigid shape comparison. Here, we explore the applicability of related shape similarity measures to the problem of shape correspondence, adopting spectral type distances. We propose to evaluate the spectral kernel distance, the spectral embedding distance and the novel spectral quasi-conformal distance, comparing the manifolds from different viewpoints. By matching the shapes in the spectral domain, important attributes of surface structure are being aligned. For the purpose of testing our ideas, we introduce a fully automatic framework for finding intrinsic correspondence between two shapes. The proposed method achieves state-of-the-art results on the Princeton isometric shape matching protocol applied, as usual, to the TOSCA and SCAPE benchmarks

An Angiosperm species dataset reveals relationships between seed size and two-dimensional shape

Datasets containing information on seed size have been published and are currently available. Nevertheless, there is a lack in the literature of a dataset dedicated to seed shape. We present a preliminary version for a dataset on seed morphology based on a comparison of seed shape with geometric figures. Similarity of the outline of seed images with geometric models is considered as a basis to classify seeds according to the geometric figures they resemble (e.g., ellipse, oval, cardioid). This allows, first, the classification of plant species according to their geometric type of seed, and second, seed shape quantification. For each seed image, the percent of similarity of their outline with a geometric figure can be calculated as a J index. Similarity in absolute terms is considered only when the J index >90. This criterion is important to avoid ambiguity and increase discrimination. The dataset opens the possibility of studying the relationship between seed shape and other variables such as seed size, genome complexity, life form or adaptive responses

Liquid jet eruption from hollow relaxation

A cavity hollowed out on a free liquid surface is relaxing, forming an intense liquid jet. Using a model experiment where a short air pulse sculpts an initial large crater, we depict the different stages in the gravitational cavity collapse and in the jet formation. Prior eversion, all cavity profiles are found to exhibit a shape similarity. Following hollow relaxation, a universal scaling law establishing an unexpected relation between the jet eruption velocity, the initial cavity geometry and the liquid viscosity is evidenced experimentally. On further analysing the jet forms we demonstrate that the stretched liquid jet also presents shape similarity. Considering that the jet shape is a signature of the initial flow focusing, we elaborate a simple model capturing the key features of the erupting jet velocity scaling

Perceptual grouping abilities in individuals with Autism Spectrum Disorder: exploring patterns of ability in relation to grouping type and levels of development

This study further investigates findings of impairment in Gestalt, but not global processing in Autism Spectrum Disorder (ASD) [Brosnan, Scott, Fox, & Pye, 2004]. Nineteen males with ASD and nineteen typically developing (TD) males matched by nonverbal ability, took part in five Gestalt perceptual grouping tasks. Results showed that performance differed according to grouping type. The ASD group showed typical performance for grouping by proximity and by alignment, impairment on low difficulty trials for orientation and luminance similarity, and general impairment for grouping by shape similarity. Group differences were also observed developmentally; for the ASD group, with the exception of grouping by shape similarity, perceptual grouping performance was poorer at lower than higher levels of nonverbal ability. In contrast, no developmental progression was observed in the TD controls

Shape-Based Models for Interactive Segmentation of Medical Images

Accurate image segmentation is one of the key problems in computer vision. In domains such as radiation treatment planning, dosimetrists must manually trace the outlines of a few critical structures on large numbers of images. Considerable similarity can be seen in the shape of these regions, both between adjacent slices in a particular patient and across the spectrum of patients. Consequently we should be able to model this similarity and use it to assist in the process of segmentation. Previous work has demonstrated that a constraint-based 2D radial model can capture generic shape information for certain shape classes, and can reduce user interaction by a factor of three over purely manual segmentation. Additional simulation studies have shown that a probabilistic version of the model has the potential to further reduce user interaction. This paper describes an implementation of both models in a general-purpose imaging and graphics framework and compares the usefulness of the models on several shape classes