Topological analysis of scalar fields with outliers

Given a real-valued function $f$ defined over a manifold $M$ embedded in $\mathbb{R}^d$, we are interested in recovering structural information about $f$ from the sole information of its values on a finite sample $P$. Existing methods provide approximation to the persistence diagram of $f$ when geometric noise and functional noise are bounded. However, they fail in the presence of aberrant values, also called outliers, both in theory and practice. We propose a new algorithm that deals with outliers. We handle aberrant functional values with a method inspired from the k-nearest neighbors regression and the local median filtering, while the geometric outliers are handled using the distance to a measure. Combined with topological results on nested filtrations, our algorithm performs robust topological analysis of scalar fields in a wider range of noise models than handled by current methods. We provide theoretical guarantees and experimental results on the quality of our approximation of the sampled scalar field

Local And Semi-Global Feature-Correlative Techniques For Face Recognition

Face recognition is an interesting field of computer vision with many commercial and scientific applications. It is considered as a very hot topic and challenging problem at the moment. Many methods and techniques have been proposed and applied for this purpose, such as neural networks, PCA, Gabor filtering, etc. Each approach has its weaknesses as well as its points of strength. This paper introduces a highly efficient method for the recognition of human faces in digital images using a new feature extraction method that combines the global and local information in different views (poses) of facial images. Feature extraction techniques are applied on the images (faces) based on Zernike moments and structural similarity measure (SSIM) with local and semi-global blocks. Pre-processing is carried out whenever needed, and numbers of measurements are derived. More specifically, instead of the usual approach for applying statistics or structural methods only, the proposed methodology integrates higher-order representation patterns extracted by Zernike moments with a modified version of SSIM (M-SSIM). Individual measurements and metrics resulted from mixed SSIM and Zernike-based approaches give a powerful recognition tool with great results. Experiments reveal that correlative Zernike vectors give a better discriminant compared with using 2D correlation of the image itself. The recognition rate using ORL Database of Faces reaches 98.75%, while using FEI (Brazilian) Face Database we got 96.57%. The proposed approach is robust against rotation and noise

Seismic Fault Preserving Diffusion

This paper focuses on the denoising and enhancing of 3-D reflection seismic data. We propose a pre-processing step based on a non linear diffusion filtering leading to a better detection of seismic faults. The non linear diffusion approaches are based on the definition of a partial differential equation that allows us to simplify the images without blurring relevant details or discontinuities. Computing the structure tensor which provides information on the local orientation of the geological layers, we propose to drive the diffusion along these layers using a new approach called SFPD (Seismic Fault Preserving Diffusion). In SFPD, the eigenvalues of the tensor are fixed according to a confidence measure that takes into account the regularity of the local seismic structure. Results on both synthesized and real 3-D blocks show the efficiency of the proposed approach.Comment: 10 page

Automatic Document Image Binarization using Bayesian Optimization

Document image binarization is often a challenging task due to various forms of degradation. Although there exist several binarization techniques in literature, the binarized image is typically sensitive to control parameter settings of the employed technique. This paper presents an automatic document image binarization algorithm to segment the text from heavily degraded document images. The proposed technique uses a two band-pass filtering approach for background noise removal, and Bayesian optimization for automatic hyperparameter selection for optimal results. The effectiveness of the proposed binarization technique is empirically demonstrated on the Document Image Binarization Competition (DIBCO) and the Handwritten Document Image Binarization Competition (H-DIBCO) datasets