Author manuscript, published in "CompIMAGE, Buffalo-Niagara: États-Unis (2010)" Curvature Estimation for Discrete Curves Based on Auto-adaptive Masks of Convolution

Abstract. We propose a method that we call auto-adaptive convolution which extends the classical notion of convolution in pictures analysis to function analysis on a discrete set. We define an averaging kernel which takes into account the local geometry of a discrete shape and adapts itself to the curvature. Its defining property is to be local and to follow a normal law on discrete lines of any slope. We used it together with classical differentiation masks to estimate first and second derivatives and give a curvature estimator of discrete functions.

Functional Maps for Brain Classification on Spectral Domain

In this paper we exploit the Functional maps approach for brain classification. The functional representation of brain shapes, or their subparts, enables us to improve the detection of morphological abnormalities associated with the analyzed disease. The proposed method is based on the spectral shape paradigm that is largely used for generic geometric processing but still few exploited in the medical context. The key aspect of the Functional maps framework is that it moves the estimation of correspondences from the shape space to the functional space enhancing the potential of spectral analysis. Moreover, we propose a new kernel, called the Functional maps kernel (FM-kernel) for the Support Vector Machine (SVM) classification that is specifically designed to work on the functional space. The obtained results for bipolar disorder detection on the putamen regions are promising in comparison with other spectral-based approaches

3D point of interest detection via spectral irregularity diffusion

This paper presents a method for detecting points of interest on 3D meshes. It comprises two major stages. In the first, we capture saliency in the spectral domain by detecting spectral irregularities of a mesh. Such saliency corresponds to the interesting portions of surface in the spatial domain. In the second stage, to transfer saliency information from the spectral domain to the spatial domain, we rely on spectral irregularity diffusion (SID) based on heat diffusion. SID captures not only the information about neighbourhoods of a given point in a multiscale manner, but also cues related to the global structure of a shape. It thus preserves information about both local and global saliency. We finally extract points of interest by looking for global and local maxima of the saliency map. We demonstrate the advantages of our proposed method using both visual and quantitative comparisons based on a publicly available benchmark