On the focusing of thermal images

In this paper we present a new thermographic image database, suitable for the analysis of automatic focusing measures. This database contains the images of 10 scenes, each of which is represented once for each of 96 different focus positions. Using this database, we evaluate the usefulness of five focus measures with the goal of determining the optimal focus position. Experimental results reveal that the accurate automatic detection of optimal focus position can be achieved with a low computational burden. We also present an acquisition tool for obtaining thermal images. To the best of our knowledge, this is the first study on the automatic focusing of thermal images.     

Modified versions of the Bayesian Information Criterion for sparse Generalized Linear Models

The classical model selection criteria, such as the Bayesian Information Criterion (BIC) or Akaike information criterion (AIC), have a strong tendency to overestimate the number of regressors when the search is performed over a large number of potential explanatory variables. To handle the problem of the overestimation, several modifications of the BIC have been proposed. These versions rely on supplementing the original BIC with some prior distributions on the class of possible models. Three such modifications are presented and compared in the context of sparse Generalized Linear Models (GLMs). The related choices of priors are discussed and the conditions for the asymptotic equivalence of these criteria are provided. The performance of the modified versions of the BIC is illustrated with an extensive simulation study and a real data analysis. Also, simplified versions of the modified BIC, based on least squares regression, are investigated.     

Homotopy-based surface reconstruction with application to?acoustic signals

This work introduces a new algorithm for surface reconstruction in ℝ³ from spatially arranged one-dimensional cross sections embedded in ℝ³. This is generally the case with acoustic signals that pierce an object non-destructively. Continuous deformations (homotopies) that smoothly reconstruct information between any pair of successive cross sections are derived. The zero level set of the resulting homotopy field generates the desired surface. Four types of homotopies are suggested that are well suited to generate a smooth surface. We also provide derivation of necessary higher order homotopies that can generate a C ² surface. An algorithm to generate surface from acoustic sonar signals is presented with results. Reconstruction accuracies of the homotopies are compared by means of simulations performed on basic geometric primitives.     

Subgraphs of 4-Regular Planar Graphs

We shall present an algorithm for determining whether or not a given planar graph H can ever be a subgraph of a 4-regular planar graph. The algorithm has running time O(|H|^2.5) and can be used to find an explicit 4-regular planar graph G⊃H if such a graph exists. It shall not matter whether we specify that H and G must be simple graphs or allow them to be multigraphs.     

A GPU framework for parallel segmentation of volumetric images using discrete deformable models

Despite the ability of current GPU processors to treat heavy parallel computation tasks, its use for solving medical image segmentation problems is still not fully exploited and remains challenging. A lot of difficulties may arise related to, for example, the different image modalities, noise and artifacts of source images, or the shape and appearance variability of the structures to segment. Motivated by practical problems of image segmentation in the medical field, we present in this paper a GPU framework based on explicit discrete deformable models, implemented over the NVidia CUDA architecture, aimed for the segmentation of volumetric images. The framework supports the segmentation in parallel of different volumetric structures as well as interaction during the segmentation process and real-time visualization of the intermediate results. Promising results in terms of accuracy and speed on a real segmentation experiment have demonstrated the usability of the system.     

Illustrating volume data sets and layered models with importance-aware composition

Non-photorealistic (illustrative) rendering augments typical rendering models to selectively emphasize or de-emphasize specific structures of rendered objects. Illustrative techniques may affect not only the rendering style of specific portions of an object but also their visibility, ensuring that less important regions do not occlude more important ones. Cutaway views completely remove occluding, unimportant structures—possibly also removing valuable context information—while existing solutions for smooth reduction of occlusion based on importance lack precise visibility control, simplicity and generality. We introduce a new front-to-back fragment composition equation that directly takes into account a measure of sample importance and allows smooth and precise importance-based visibility control. We demonstrate the generality of our composition equation with several illustrative effects, which were obtained by using a set of importance measures calculated on the fly or defined by the user. The presented composition method is suitable for direct volume rendering as well as rendering of layered 3D models. We discuss both cases and show examples, though focusing mainly on illustration of volumetric data.     

Linear-Time Recognition of Helly Circular-Arc Models and Graphs

A circular-arc model ℳ is a circle C together with a collection A\mathcal{A} of arcs of C. If A\mathcal{A} satisfies the Helly Property then ℳ is a Helly circular-arc model. A (Helly) circular-arc graph is the intersection graph of a (Helly) circular-arc model. Circular-arc graphs and their subclasses have been the object of a great deal of attention in the literature. Linear-time recognition algorithms have been described both for the general class and for some of its subclasses. However, for Helly circular-arc graphs, the best recognition algorithm is that by Gavril, whose complexity is O(n ³). In this article, we describe different characterizations for Helly circular-arc graphs, including a characterization by forbidden induced subgraphs for the class. The characterizations lead to a linear-time recognition algorithm for recognizing graphs of this class. The algorithm also produces certificates for a negative answer, by exhibiting a forbidden subgraph of it, within this same bound.     

Product selection for promotion planning

This paper addresses a very important question—how to select the right products to promote in order to maximize promotional benefit. We set up a framework to incorporate promotion decisions into the data-mining process, formulate the profit maximization problem as an optimization problem, and propose a heuristic search solution to discover the right products to promote. Moreover, we are able to get access to real supermarket data and apply our solution to help achieve higher profits. Our experimental results on both synthetic data and real supermarket data demonstrate that our framework and method are highly effective and can potentially bring huge profit gains to a marketing campaign.     

Theories of initial segments of standard models of arithmetics and their complete extensions

We investigate families of finite initial segments of standard models for various arithmetics. We give an axiomatization of the theory of sentences true in almost all finite models with addition. We also characterize its complete extensions and relate its infinite models to models of Presburger arithmetic.We also estimate the complexity of complete extensions of the arithmetic with addition and multiplication.     

Parameterized complexity of coloring problems: Treewidth versus vertex cover

We compare the fixed parameter complexity of various variants of coloring problems (including List Coloring, Precoloring Extension, Equitable Coloring, L(p,1)-Labeling and Channel Assignment) when parameterized by treewidth and by vertex cover number. In most (but not all) cases we conclude that parametrization by the vertex cover number provides a significant drop in the complexity of the problems.