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...

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 ...

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...

Shape is one of the most important visual attributes used to characterize objects, playing a important role in pattern recognition. There are various approaches to extract relevant information of a shape. An approach widely used in shape analysis is the complexity, and Fractal Dimension and Multi-Scale Fractal Dimension are both well-known methodologies to estimate it. This papers presents a co...

Digital representation of three dimensional curves is considered. Two dimensional representation schemes are rst reviewed, then methods applicable to curves in three and higher dimensional spaces are described. Desirable properties of curve representation schemes are identiied and used as a basis for qualitative and quantitative comparison of the various methods that have been suggested. Conclu...

The present work shows a novel fractal dimension method for shape analysis. The proposed technique extracts descriptors from a shape by applying a multi-scale approach to the calculus of the fractal dimension. The fractal dimension is estimated by applying the curvature scale-space technique to the original shape. By applying a multi-scale transform to the calculus, we obtain a set of descripto...

This paper presents some basics for the analysis of point clouds using the geometrically intuitive mathematical framework of conformal geometric algebra. In this framework it is easy to compute with osculating circles for the description of local curvature. Also methods for the fitting of spheres as well as bounding spheres are presented. In a nutshell, this paper provides a starting point for ...

The 2D Fourier Descriptor is an elegant and powerful technique for 2D shape analysis. This paper intends to extend such technique to 3D. Though conceptually natural, such an extension is not trivial in that two critical problems, the spherical parametrization and invariants construction, must be solved. By using a newly developed surface parametrization method–the discrete conformal mapping (DC...