Integrated shape-sensitive functional metrics

Shape metrics, warping and statistics

We propose to use approximations of shape metrics, such as the Hausdorff distance, to define similarity measures between shapes. Our approximations being continuous and differentiable, they provide an obvious way to warp a shape onto another by solving a Partial Differential Equation (PDE), in effect a curve flow, obtained from their first order variation. This first order variation defines a n...

Shape Sensitive Geometric Complexity

Shape Sensitive Geometri Permutations

Growth and shape: measurements and metrics.

Magwene (2001) presented an interesting analysis of growth in turtles, making the case that information about process should be incorporated in ontogenetic studies. More speciŽcally, descriptions of shape and size are insufŽcient for understanding process and, one must dig deeper and consider explicitly the mechanisms and processes responsible for thepatterns detected in size and shape data. In...

Statistical shape analysis using non-Euclidean metrics

The contribution of this paper is the adaptation of data driven methods for non-Euclidean metric decomposition of tangent space shape coordinates. The basic idea is to extend principal component analysis (PCA) to take into account the noise variance at different landmarks and at different shapes. We show examples where these non-Euclidean metric methods allow for easier interpretation by decomp...