Variational Approach for the Reconstruction of Damaged Optical Satellite Images Through Their Co-Registration with Synthetic Aperture Radar

In this paper the problem of reconstruction of damaged multi-band opticalimages is studied in the case where we have no information about brightness of suchimages in the damage region. Mostly motivated by the crop field monitoring problem,we propose a new variational approach for exact reconstruction of damaged multi-bandimages using results of their co-registration with Synthetic Aperture Radar (SAR) imagesof the same regions. We discuss the consistency of the proposed problem, give the schemefor its regularization, derive the corresponding optimality system, and describe in detailthe algorithm for the practical implementation of the reconstruction procedure.In this paper the problem of reconstruction of damaged multi-band opticalimages is studied in the case where we have no information about brightness of suchimages in the damage region. Mostly motivated by the crop field monitoring problem,we propose a new variational approach for exact reconstruction of damaged multi-bandimages using results of their co-registration with Synthetic Aperture Radar (SAR) imagesof the same regions. We discuss the consistency of the proposed problem, give the schemefor its regularization, derive the corresponding optimality system, and describe in detailthe algorithm for the practical implementation of the reconstruction procedure

Colour image segmentation by the vector-valued Allen-Cahn phase-field model: a multigrid solution

We propose a new method for the numerical solution of a PDE-driven model for colour image segmentation and give numerical examples of the results. The method combines the vector-valued Allen-Cahn phase field equation with initial data fitting terms. This method is known to be closely related to the Mumford-Shah problem and the level set segmentation by Chan and Vese. Our numerical solution is performed using a multigrid splitting of a finite element space, thereby producing an efficient and robust method for the segmentation of large images.Comment: 17 pages, 9 figure

A stochastic-variational model for soft Mumford-Shah segmentation

In contemporary image and vision analysis, stochastic approaches demonstrate great flexibility in representing and modeling complex phenomena, while variational-PDE methods gain enormous computational advantages over Monte-Carlo or other stochastic algorithms. In combination, the two can lead to much more powerful novel models and efficient algorithms. In the current work, we propose a stochastic-variational model for soft (or fuzzy) Mumford-Shah segmentation of mixture image patterns. Unlike the classical hard Mumford-Shah segmentation, the new model allows each pixel to belong to each image pattern with some probability. We show that soft segmentation leads to hard segmentation, and hence is more general. The modeling procedure, mathematical analysis, and computational implementation of the new model are explored in detail, and numerical examples of synthetic and natural images are presented.Comment: 22 page

Mathematical Modeling of Textures: Application to Color Image Decomposition with a Projected Gradient Algorithm

International audienceIn this paper, we are interested in color image processing, and in particular color image decomposition. The problem of image decomposition consists in splitting an original image f into two components u and v. u should contain the geometric information of the original image, while v should be made of the oscillating patterns of f, such as textures. We propose here a scheme based on a projected gradient algorithm to compute the solution of various decomposition models for color images or vector-valued images. We provide a direct convergence proof of the scheme, and we give some analysis on color texture modeling

Mathematical Approaches for Image Enhancement Problems

This thesis develops novel techniques that can solve some image enhancement problems using theoretically and technically proven and very useful mathematical tools to image processing such as wavelet transforms, partial differential equations, and variational models. Three subtopics are mainly covered. First, color image denoising framework is introduced to achieve high quality denoising results by considering correlations between color components while existing denoising approaches can be plugged in flexibly. Second, a new and efficient framework for image contrast and color enhancement in the compressed wavelet domain is proposed. The proposed approach is capable of enhancing both global and local contrast and brightness as well as preserving color consistency. The framework does not require inverse transform for image enhancement since linear scale factors are directly applied to both scaling and wavelet coefficients in the compressed domain, which results in high computational efficiency. Also contaminated noise in the image can be efficiently reduced by introducing wavelet shrinkage terms adaptively in different scales. The proposed method is able to enhance a wavelet-coded image computationally efficiently with high image quality and less noise or other artifact. The experimental results show that the proposed method produces encouraging results both visually and numerically compared to some existing approaches. Finally, image inpainting problem is discussed. Literature review, psychological analysis, and challenges on image inpainting problem and related topics are described. An inpainting algorithm using energy minimization and texture mapping is proposed. Mumford-Shah energy minimization model detects and preserves edges in the inpainting domain by detecting both the main structure and the detailed edges. This approach utilizes faster hierarchical level set method and guarantees convergence independent of initial conditions. The estimated segmentation results in the inpainting domain are stored in segmentation map, which is referred by a texture mapping algorithm for filling textured regions. We also propose an inpainting algorithm using wavelet transform that can expect better global structure estimation of the unknown region in addition to shape and texture properties since wavelet transforms have been used for various image analysis problems due to its nice multi-resolution properties and decoupling characteristics

A Perception-based Color Space for Illumination-invariant Image Processing

Motivated by perceptual principles, we derive a new color space in which the associated metric approximates perceived distances and color displacements capture relationships that are robust to spectral changes in illumination. The resulting color space can be used with existing image processing algorithms with little or no change to the methods.Engineering and Applied Science