We introduce techniques for the processing of motion and animations of non-rigid shapes. The idea is to regard animations of deformable objects as curves in shape space. Then, we use the geometric structure on shape space to transfer concepts from curve processing in Rn to the processing of motion of non-rigid shapes. Following this principle, we introduce a discrete geometric flow for curves i...

In order to analyze shapes of continuous curves in R3, we parameterize them by arclength and represent them as curves on a unit two-sphere. We identify the set denoting the closed curves, and study its differential geometry. To compute geodesics between any two such curves, we connect them with an arbitrary path, and then iteratively straighten this path using the gradient of an energy associat...

In this paper, a novel transformation connecting an arbitrary Planar Array to a virtual Uniform Linear Array (ULA) with a larger number of sensors is proposed. The array orientation, number of sensors and phase characteristics of the virtual array are a function of the array shape of the planar array. The two parameter manifold (azimuth,elevation) of a planar array of N sensors is a conoid surf...

We propose a Riemannian framework for shape analysis of annotated curves, curves that have certain attributes defined along them, in addition to their geometries. These attributes may be in form of vector-valued functions, discrete landmarks, or symbolic labels, and provide auxiliary information along the curves. The resulting shape analysis, that is comparing, matching, and deforming, is natur...