Convergence of the "relativistic" heat equation to the heat equation as c → ∞

We prove that the entropy solutions of the so-called relativistic heat equation converge to solutions of the heat equation as the speed of light c tends to ∞ for any initial condition u0 ≥ 0 in L1 (RN ) ∩ L∞(RN )

The M-components of level sets of continuous functions in WBV

We prove that the topographic map structure of upper semicontinuous functions, defined in terms of classical connected components of its level sets, and of functions of bounded variation (or a generalization, the WBV functions), defined in terms of M-connected components of its level sets, coincides when the function is a continuous function in WBV. Both function spaces are frequently used as models for images. Thus, if the domain [omega] of the image is Jordan domain, a rectangle, for instance, and the image u [member of] C([omega]) [intersection] WBV([omega]) (being constant near [delta omega]), we prove that for almost all levels [lambda] of u, the classical connected components of positive measure of[u [greater than or equal] [lambda]] coincide with the M-components of [u [greater than or equal] [lambda]]. Thus the notion of M-component can be seen as a relaxation of the classical notion of connected component when going from C([omega]) to WBV([omega])

Variational Principles and Perceptual Color Correction of Digital Images

Variational principles appear in a vast number of scientific disciplines. They often provide a 'view from above' which permits to better comprehend and analyse problems. In this paper we show how variational techniques can be used to modelise perceptual color correction of digital images. We will show that the basic human visual phenomenology defines a unique class of functionals whose minimization gives rise to color enhancement. This framework provides a unified home for noticeable models of perceptual color correction, as e.g. Retinex. This record was migrated from the OpenDepot repository service in June, 2017 before shutting down

Introduction to the Special Issue on Partial Differential Equations and Geometry-Driven Diffusion in Image Processing and Analysis

©1998 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or distribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.DOI: 10.1109/TIP.1998.66117

Teaching discourse markers to EFL Primary Education students

Treball final de Màster en Ensenyament i Adquisició de la Llengua Anglesa en Contextos Multilingües. Codi: SAY031. Curs acadèmic 2013-2014Students of English as a foreign language in primary schools usually have problems with their communicative competence. The activities they do in the English classroom do not allow them to gain fluency in their speech and are more directed to improve grammar and vocabulary, focusing more on the written channel. As a consequence, their speech is very schematic and students have several problems to establish coherent and fluent conversations among them using the English language. The following teaching proposal pretends to demonstrate if the acquisition and use of discourse markers helps student to acquire fluency and coherence in their speech and their ability for understanding information raises. It also pretends to help students to develop communicative competence and improve their English language knowledge

A contrario selection of optimal partitions for image segmentation

We present a novel segmentation algorithm based on a hierarchical representation of images. The main contribution of this work is to explore the capa- bilities of the a contrario reasoning when applied to the segmentation problem, and to overcome the limitations of current algorithms within that framework. This ex- ploratory approach has three main goals. Our first goal is to extend the search space of greedy merging algorithms to the set of all partitions spanned by a certain hierarchy, and to cast the segmentation as a selection problem within this space. In this way we increase the number of tested partitions and thus we potentially improve the segmentation results. In addition, this space is considerably smaller than the space of all possible partitions, thus we still keep the complexity controlled. Our second goal aims to improve the locality of region merging algorithms, which usually merge pairs of neighboring regions. In this work, we overcome this limitation by introducing a validation procedure for complete partitions, rather than for pairs of regions. The third goal is to perform an exhaustive exper- imental evaluation methodology in order to provide reproducible results. Finally, we embed the selection process on a statistical a contrario framework which allows us to have only one free parameter related to the desired scale

Image inpainting

Trabajo presentado en la 27th Annual Conference on Computer Graphics and Interactive TechniquesInpainting, the technique of modifying an image in an undetectable form, is as ancient as art itself. The goals and applications of inpainting are numerous, from the restoration of damaged paintings and photographs to the removal/replacement of selected objects. In this paper, we introduce a novel algorithm for digital inpainting of still images that attempts to replicate the basic techniques used by professional restorators. After the user selects the regions to be restored, the algorithm automatically fills-in these regions with information surrounding them. The fill-in is done in such a way that isophote lines arriving at the regions’ boundaries are completed inside. In contrast with previous approaches, the technique here introduced does not require the user to specify where the novel information comes from. This is automatically done (and in a fast way), thereby allowing to simultaneously fill-in numerous regions containing completely different structures and surrounding backgrounds. In addition, no limitations are imposed on the topology of the region to be inpainted. Applications of this technique include the restoration of old photographs and damaged film; removal of superimposed text like dates, subtitles, or publicity; and the removal of entire objects from the image like microphones or wires in special effects

A Contrast Invariant Approach to Motion Estimation. In:

Summary. We consider a contrast invariant approach to motion estimation which uses the direction of the gradient fields. The approach is region-based and assumes an affine motion model for each region. We propose to check if the estimated motion parameters fit properly the apparent motion of the region by a motion significance analysis. Moreover, we propose a motion field improvement which consider those regions that are not properly estimated according to the significance analysis and reassign them a motion model of a properly estimated neighboring region

Detección y Agrupación de Logos

In this paper we develop an algorithm for logo detection and grouping in images. For logo detection, the “Scale-Invariant Feature Transform” (SIFT) descriptor is used, which is one of the most studied and used in pattern recognition in the fields of image analysis and computer vision. We have developed a geometric algorithm for grouping and counting the detected logos. This algorithm is based on the so-called “Geometric Hashing” algorithm. Finally, we perform some tests in order to analyze the robustness of the algorithm.En el presente trabajo se desarrolla un algoritmo para la detección y agrupación de logos en imágenes. Para la detección de logos se usa el descriptor “Scale-Invariant Feature Transform” (SIFT) que es uno de los más estudiado y usado en la detección de patrones en los campos de análisis de imágenes y visión por computadora (computer vision). Luego, se desarrolla un algoritmo geométrico para la agrupación y el conteo de los logos detectados. Este algoritmo se basa en el algoritmo llamado “Geometric Hashing”. Finalmente, se realizan pruebas para analizar la robustez del algoritmo

Line search multilevel optimization as computational methods for dense optical flow

We evaluate the performance of different optimization techniques developed in the context of optical flowcomputation with different variational models. In particular, based on truncated Newton methods (TN) that have been an effective approach for large-scale unconstrained optimization, we develop the use of efficient multilevel schemes for computing the optical flow. More precisely, we evaluate the performance of a standard unidirectional multilevel algorithm - called multiresolution optimization (MR/OPT), to a bidrectional multilevel algorithm - called full multigrid optimization (FMG/OPT). The FMG/OPT algorithm treats the coarse grid correction as an optimization search direction and eventually scales it using a line search. Experimental results on different image sequences using four models of optical flow computation show that the FMG/OPT algorithm outperforms both the TN and MR/OPT algorithms in terms of the computational work and the quality of the optical flow estimation