Abstract: An efficient snake formulation should conform to the idea of picking the smoothest curve among all the shapes approximating an object of interest. In current geodesic snakes, the regularizing curvature also affects the convergence stage, hindering the latter at concave regions. In the present work, we make use of characteristic functions to define a novel geodesic formulation that decouples regularity and convergence. This term decoupling endows the snake with higher adaptability to non-convex shapes. Convergence is ensured by splitting the definition of the external force into an attractive vector field and a repulsive one. In our paper, we propose to use likelihood maps as approximation of characteristic functions of object appearance. The better efficiency and accuracy of our decoupled scheme are illustrated in the particular case of feature space-based segmentation.

Abstract: Medical imaging feeds research in many computer vision and image processing fields: image filtering, segmentation, shape recovery, registration, retrieval and pattern matching. Because of their low contrast changes and large variety of artifacts and noise, medical imaging processing techniques relying on an analysis of the geometry of image level sets rather than on intensity values result in more robust treatment. From the starting point of treatment of intravascular images, this PhD thesis ad- dresses the design of differential image operators based on geometric principles for a robust shape modelling and restoration. Among all fields applying shape recovery, we approach filtering and segmentation of image objects. For a successful use in real images, the segmentation process should go through three stages: noise removing, shape modelling and shape recovery. This PhD addresses all three topics, but for the sake of algorithms as automated as possible, techniques for image processing will be designed to satisfy three main principles: a) convergence of the iterative schemes to non-trivial states avoiding image degeneration to a constant image and representing smooth models of the originals; b) smooth asymptotic behav- ior ensuring stabilization of the iterative process; c) fixed parameter values ensuring equal (domain free) performance of the algorithms whatever initial images/shapes. Our geometric approach to the generic equations that model the different processes approached enables defining techniques satisfying all the former requirements. First, we introduce a new curvature-based geometric flow for image filtering achieving a good compromise between noise removing and resemblance to original images. Sec- ond, we describe a new family of diffusion operators that restrict their scope to image level curves and serve to restore smooth closed models from unconnected sets of points. Finally, we design a regularization of snake (distance) maps that ensures its smooth convergence towards any closed shape. Experiments show that performance of the techniques proposed overpasses that of state-of-the-art algorithms.

Abstract: In this article, we present a sequence of activities in the form of a project in order to promote
learning on design and analysis of algorithms. The project is based on the resolution of a real problem, the salesperson problem, and it is theoretically grounded on the fundamentals of mathematical modelling. In order to support the students’ work, a multimedia tool, called Graph-based Problem Explorer (GbPExplorer), has been designed and refined to promote the development of computer literacy in engineering and science university students. This tool incorporates several modules to allow coding different algorithmic techniques solving the salesman problem. Based on an educational design research along five years, we observe that working with GbPExplorer during the project provides students with the possibility of representing the situation to be studied in the form of graphs and analyze them from a computational point of view.

Abstract: This paper proposes a guidance in the process of choosing and using the parameters of elasticity of a snake in order to obtain a precise segmentation. A new two step procedure is defined based on upper and lower bounds on the parameters. Formulas, by which these bounds can be calculated for real images where parts of the contour may be missing, are presented. Experiments on segmentation of bone structures in X-ray images have verified the usefulness of the new procedure.

Abstract: In this paper we present a technique to interpret hand line drawings as objects in a three-dimensional space. The object domain considered is based on planar surfaces with straight edges, concretely, on ansextension of Origami world to hidden lines. The line drawing represents the object under orthographic projection and it is sensed using a scanner. Our method is structured in two modules: feature extraction and feature interpretation. In the first one, image processing techniques are applied under certain tolerance margins to detect lines and junctions on the hand line drawing. Feature interpretation module is founded on line labelling techniques using a labelled junction dictionary. A labelling algorithm is here proposed. It uses relaxation techniques to reduce the number of incompatible labels with the junction dictionary so that the convergence of solutions can be accelerated. We formulate some labelling hypotheses tending to eliminate elements in two sets of labelled interpretations. That is, those which are compatible with the dictionary but do not correspond to three-dimensional objects and those which represent objects not very probable to be specified by means of a line drawing. New entities arise on the line drawing as a result of the extension of Origami world. These are defined to enunciate the assumptions of our method as well as to clarify the algorithms proposed. This technique is framed in a project aimed to implement a system to create 3D objects to improve man-machine interaction in CAD systems.