Geometrical-based algorithm for variational segmentation and smoothing of vector-valued images

An optimisation method based on a nonlinear functional is considered for segmentation and smoothing of vector-valued images. An edge-based approach is proposed to initially segment the image using geometrical properties such as metric tensor of the linearly smoothed image. The nonlinear functional is then minimised for each segmented region to yield the smoothed image. The functional is characterised with a unique solution in contrast with the Mumford–Shah functional for vector-valued images. An operator for edge detection is introduced as a result of this unique solution. This operator is analytically calculated and its detection performance and localisation are then compared with those of the DroGoperator. The implementations are applied on colour images as examples of vector-valued images, and the results demonstrate robust performance in noisy environments

Variational methods and its applications to computer vision

Many computer vision applications such as image segmentation can be formulated in a ''variational'' way as energy minimization problems. Unfortunately, the computational task of minimizing these energies is usually difficult as it generally involves non convex functions in a space with thousands of dimensions and often the associated combinatorial problems are NP-hard to solve. Furthermore, they are ill-posed inverse problems and therefore are extremely sensitive to perturbations (e.g. noise). For this reason in order to compute a physically reliable approximation from given noisy data, it is necessary to incorporate into the mathematical model appropriate regularizations that require complex computations. The main aim of this work is to describe variational segmentation methods that are particularly effective for curvilinear structures. Due to their complex geometry, classical regularization techniques cannot be adopted because they lead to the loss of most of low contrasted details. In contrast, the proposed method not only better preserves curvilinear structures, but also reconnects some parts that may have been disconnected by noise. Moreover, it can be easily extensible to graphs and successfully applied to different types of data such as medical imagery (i.e. vessels, hearth coronaries etc), material samples (i.e. concrete) and satellite signals (i.e. streets, rivers etc.). In particular, we will show results and performances about an implementation targeting new generation of High Performance Computing (HPC) architectures where different types of coprocessors cooperate. The involved dataset consists of approximately 200 images of cracks, captured in three different tunnels by a robotic machine designed for the European ROBO-SPECT project.Open Acces

Joint methods in imaging based on diffuse image representations

This thesis deals with the application and the analysis of different variants of the Mumford-Shah model in the context of image processing. In this kind of models, a given function is approximated in a piecewise smooth or piecewise constant manner. Especially the numerical treatment of the discontinuities requires additional models that are also outlined in this work. The main part of this thesis is concerned with four different topics. Simultaneous edge detection and registration of two images: The image edges are detected with the Ambrosio-Tortorelli model, an approximation of the Mumford-Shah model that approximates the discontinuity set with a phase field, and the registration is based on these edges. The registration obtained by this model is fully symmetric in the sense that the same matching is obtained if the roles of the two input images are swapped. Detection of grain boundaries from atomic scale images of metals or metal alloys: This is an image processing problem from materials science where atomic scale images are obtained either experimentally for instance by transmission electron microscopy or by numerical simulation tools. Grains are homogenous material regions whose atomic lattice orientation differs from their surroundings. Based on a Mumford-Shah type functional, the grain boundaries are modeled as the discontinuity set of the lattice orientation. In addition to the grain boundaries, the model incorporates the extraction of a global elastic deformation of the atomic lattice. Numerically, the discontinuity set is modeled by a level set function following the approach by Chan and Vese. Joint motion estimation and restoration of motion-blurred video: A variational model for joint object detection, motion estimation and deblurring of consecutive video frames is proposed. For this purpose, a new motion blur model is developed that accurately describes the blur also close to the boundary of a moving object. Here, the video is assumed to consist of an object moving in front of a static background. The segmentation into object and background is handled by a Mumford-Shah type aspect of the proposed model. Convexification of the binary Mumford-Shah segmentation model: After considering the application of Mumford-Shah type models to tackle specific image processing problems in the previous topics, the Mumford-Shah model itself is studied more closely. Inspired by the work of Nikolova, Esedoglu and Chan, a method is developed that allows global minimization of the binary Mumford-Shah segmentation model by solving a convex, unconstrained optimization problem. In an outlook, segmentation of flowfields into piecewise affine regions using this convexification method is briefly discussed

A region growing method for detecting interfaces in X-ray view cell images

X-ray transmission videography is used to observe the thermodynamic phase behavior of heavy oil mixtures of industrial interest that are opaque to visible light. The knowledge of the volumes of various phases provide important information for enhancing oil refining technology. Phase boundaries are usually marked by visual examination based upon which the volumes and densities of the phases are computed. Typically, phase behavior is computed at various temperatures and pressures to generate the phase diagram. This paper presents an image processing algorithm, which automates the task of detecting phase boundaries in the generated images. The interface and region models are first obtained from the image generation process. Using these models, a new method for interface detection based on the Mumford-Shah model is presented. Results are presented to show that the algorithm detects the phase boundaries to subpixel accurac

Fully automated breast boundary and pectoral muscle segmentation in mammograms

Breast and pectoral muscle segmentation is an essential pre-processing step for the subsequent processes in Computer Aided Diagnosis (CAD) systems. Estimating the breast and pectoral boundaries is a difficult task especially in mammograms due to artifacts, homogeneity between the pectoral and breast regions, and low contrast along the skin-air boundary. In this paper, a breast boundary and pectoral muscle segmentation method in mammograms is proposed. For breast boundary estimation, we determine the initial breast boundary via thresholding and employ Active Contour Models without edges to search for the actual boundary. A post-processing technique is proposed to correct the overestimated boundary caused by artifacts. The pectoral muscle boundary is estimated using Canny edge detection and a pre-processing technique is proposed to remove noisy edges. Subsequently, we identify five edge features to find the edge that has the highest probability of being the initial pectoral contour and search for the actual boundary via contour growing. The segmentation results for the proposed method are compared with manual segmentations using 322, 208 and 100 mammograms from the Mammographic Image Analysis Society (MIAS), INBreast and Breast Cancer Digital Repository (BCDR) databases, respectively. Experimental results show that the breast boundary and pectoral muscle estimation methods achieved dice similarity coefficients of 98.8% and 97.8% (MIAS), 98.9% and 89.6% (INBreast) and 99.2% and 91.9% (BCDR), respectively