In this paper, we discuss a geometrical model of a space of deformable images or shapes, in which infinitesimal variations are combinations of elastic deformations (warping) and of photometric variations. Geodesics in this space are related to velocity-based image warping methods, which have proved to yield efficient and robust estimations of diffeomorphisms in the case of large deformation. Here, we provide a rigorous and general construction of this infinite dimensional “shape manifold ” on which we place a Riemannian metric. We then obtain the geodesic equations, for which we show the existence and uniqueness of solutions for all times. We finally use this to provide a geometrically founded linear approximation of the deformations of shapes in the neighborhood of a given template.

A multi-scale methodology for the study of the non-local geometry of eddy structures in turbulence is developed. Starting from a given three-dimensional field, this consists of three main steps: extraction, characterization and classification of structures. The extraction step is done in two stages

The local geometry, energy stabilization, and pseudolocal t 1u vibration mode of the Cu + impurity in the alkali halide crystals have been investigated with the ab initio Perturbed Ion (aiPI) cluster-inthe -lattice methodology. The electronic structure of different clusters, containing up

We present a novel rendering primitive that combines the modeling brevity of points with the rasterization efficiency of polygons. The surface is represented by a sampled collection of Differential Points (DP), each with embedded curvature information that captures the local differential geometry

for image retrieval systems. Step one of the review is image processing for retrieval sorted by color, texture, and local geometry. Features for retrieval are discussed next, sorted by: accumulative and global features, salient points, object and shape features, signs, and structural combinations thereof

We construct several new classes of isospectral manifolds with different local geometries. After reviewing a theorem by Carolyn Gordon on isospectral torus bundles and presenting certain useful specialized versions (Chapter 1) we apply these tools to construct the first examples of isospectral

Abstract. This paper studies local geometry of hypersurfaces of finite multitype. Catlin’s definition of multitype is applied to a general smooth hypersurface in C n+1. We prove biholomorphic equivalence of models in dimension three and describe all biholomorphisms between such models. A finite

The limitations of commonly used separable extensions of one-dimensional transforms, such as the Fourier and wavelet transforms, in capturing the geometry of image edges are well known. In this paper, we pursue a “true” two-dimensional transform that can capture the intrinsic geometrical structure

. ” Geometric structure is defined in terms of the concepts torsion and curvature of differential geometry. Local chain “chirality ” is the torsional handedness of four consecutive Ca positions and is positive for right-handed helices and negative for ideal twisted @-sheets. Curved pieces are defined as “bends

. Significant change of scale (3.5×), illumi-nation conditions, out-of-plane rotation, occlusion, locally anisotropic scale change and 3D translation of the viewpoint are all present in the test prob-lems. Good estimates of epipolar geometry (average distance from corre-sponding points to the epipolar line