We present a new method for morphing 2D and 3D objects. In particular we focus on the problem of smooth interpolation on a shape manifold. The proposed method takes advantage of two recent works on 2D and 3D shape analysis to compute elastic geodesics between any two arbitrary shapes and interpolations on a Riemannian manifold. Given a finite set of frames of the same (2D or 3D) object from a v...

This paper introduces the concept of discrete multidimensional size function, a mathematical tool studying the so-called size graphs. These graphs constitute an ingredient of Size Theory, a geometrical/topological approach to shape analysis and comparison. A global method for reducing size graphs is presented, together with a theorem stating that size graphs reduced in such a way preserve all t...

This paper describes the work that has been done during the first year of the 3-SHIRT project, which aims at developing innovative solutions in all the phases of content-based 3D shape retrieval, namely: shape analysis and segmentation, design of shape descriptors, shape indexing and matching, and evaluation.

In this paper, we propose a region-based blend shape approach to facial expression cloning that automatically extracts a set of coherently-moving regions of the source face model and their counterparts in the target face model without any extra input data except the source and target key face models and their correspondence. We represent a face mesh as a mass-spring network to define two measur...

Power quality is one of the areas that the power sector is worried about. Power quality is the measure of practical system resemblance to ideal system. Voltage quality can be defined as the maintenance of voltage waveform shape close to ideal shape with proper magnitude and frequency. Even a slight change in voltage of the system can cause serious damage to the power system. Sensitive loads can...

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...