A crucial problem in shape deformation analysis is to determine a deformation of a given shape into another one, which is optimal for a certain cost. It has a number of applications in particular in medical imaging. In this article we provide a new general approach to shape deformation analysis, within the framework of optimal control theory, in which a deformation is represented as the flow of...

In this paper‎, ‎we model and solve the problem of optimal shaping and placing to put sensors for a 3-D wave equation with constant damping in a bounded open connected subset‎ ‎of 3-dimensional space‎. ‎The place of sensor is modeled by a subdomain‎ ‎of this region of a given measure‎. ‎By using an approach based on the embedding process‎, ‎first‎, ‎the system is formulated in variational form;...

Preface When I finished high school (gymnasium), I said I would never again do anything concerned with natural sciences or technology, it was just too boring. I kept my word for seven years, during which I worked as a cinema projectionist and got a B.A. (fil.kand.) in philosophy. I loved it. Then I realized I had to get a job, and since philosophers were not in high demand at the time, I sat do...

In this paper, we consider the rate-distortion optimal encoding of shape information using a skeleton decomposition and the minmum maximum (MINMAX) distortion criterion. For bit budget constrained video communication applications, whose goal is to achieve as low as possible but almost constant distortion, the MINMAX criterion is the natural choice. We propose a 4D DAG (directed acyclic graph) s...

This paper presents a new method for 2-D and 3-D shape retrieval based on geodesic signatures. These signatures are high dimensional statistical distributions computed by extracting several features from the set of geodesic distance maps to each point. The resulting high dimensional distributions are matched to perform retrieval using a fast approximate Wasserstein metric. This allows to propos...

Statistical shape models are used widely as a basis for segmenting and interpreting images. A major drawback of the approach is the need, during training, to establish a dense correspondence across a training set of segmented shapes. We show that model construction can be treated as an optimisation problem, automating the process and guaranteeing the effectiveness of the resulting models. This ...

Within the framework of classical linear regression model optimal design criteria of stochastic nature are considered. The particular attention is paid to the shape criterion. Also its limit behaviour is established which generalizes that of the distance stochastic optimality criterion. Examples of the limit maximin criterion are considered and optimal designs for the line fit model are found.