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...

Size Theory has proven to be a useful geometrical/topological approach to shape analysis and comparison. Originally introduced by considering 1-dimensional properties of shapes, described by means of real-valued functions, it has been subsequently generalized to take into account multidimensional properties coded by functions valued in Rk. In the context of Size Theory, this generalization has ...

A method of shape generation using shape grammars which take shape as primitive and have shape-specific rules is presented. A formalism for the complete, generative specification of a class of non-representational, geometric paintings or sculptures is defined which has shape grammars as its structural component. Paintings are material representations of two-dimensional shapes gen~rated by shape...

Correct and efficient segmentation of Uyghur words into characters is crucial to the successful recognition. However, little work has been done in this area. There are many connected characters in cursive Uyghur handwriting, which makes the segmentation and recognition of Uyghur words very difficult. To enable large vocabulary Uyghur word recognition using character models, we propose a charact...

This report documents the program and the results of Dagstuhl Seminar 11142 Innovations for Shape Analysis: Models and Algorithms, taking place April 3-8 in 2011. The focus of the seminar was to discuss modern and emerging topics in shape analysis by researchers from different scientific communities, as there is no conference specifically devoted to this field. Seminar 03.–08. April, 2011 – www...