Various geometric operators have been playing an important role in surface processing. For example, many shape analysis algorithms have been developed based on eigenfunctions of the Laplace–Beltrami operator (LBO), which is defined based on the first fundamental form of the surface. In this paper, we introduce two new geometric operators based on the second fundamental form of the surface, name...

We introduce a shape categorisation method for architectural drawings that takes shape characteristics derived from those drawings as features. We propose a feature-based shape analysis procedure and a formal model of shape categorisation based upon the measurement of featural similarity of shapes. Shape categorisation is demonstrated in experiments on architectural drawings.

Abstract. This paper is concerned with a shape sensitivity analysis of a viscous incompressible fluid driven by Stokes equations with nonhomogeneous boundary condition. The structure of shape gradient with respect to the shape of the variable domain for a given cost function is established by using the differentiability of a minimax formulation involving a Lagrangian functional combining with f...

The study of the Laplace operator and its corresponding eigenvalue problem is crucial to understand the foundations of 3D shape analysis. For that reason the most important mathematical properties of the Laplace operator in Euclidean spaces, its eigenvalues and eigenfunctions are summarized and explained in this report. The basic definitions and concepts of infinite dimensional function spaces,...

The computation of curvature quantities over discrete geometry is often required when processing geometry composed of meshes. Curvature information is often important for the purpose of shape analysis, feature recognition and geometry segmentation. In this paper we present a method for accurate estimation of curvature on discrete geometry especially those composed of meshes. We utilise a method...

In discrete geometry, the Distance Transformation and the Medial Axis Extraction are classical tools for shape analysis. In this paper, we present a Hierarchical Discrete Medial Axis, based on a pyramidal representation of the object, in order to efficiently create a sphere-tree, which has many applications in collision detection or image synthesis.

This paper proposes a framework for dealing with several problems related to the analysis of shapes. Two related such problems are the definition of the relevant set of shapes and that of defining a metric on it. Following a recent research monograph by Delfour and Zolésio [11], we consider the characteristic functions of the subsets of R2 and their distance functions. The L2 norm of the differ...

A general approach for developing distribution free tests for general linear models based on simplicial depth is applied to multiple regression. The tests are based on the asymptotic distribution of the simplicial regression depth, which depends only on the distribution law of the vector product of regressor variables. Based on this formula, the spectral decomposition and thus the asymptotic di...

In this paper, we explore the use of the diffusion geometry framework for the fusion of geometric and photometric information in local heat kernel signature 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 s...

In the context of structural optimization via a level-set method we propose a framework to handle geometric constraints related to a notion of local thickness. The local thickness is calculated using the signed distance function to the shape. We formulate global constraints using integral functionals and compute their shape derivatives. We discuss different strategies and possible approximation...