arXiv subjects

Mateu Sbert

Publications and source records attributed to Mateu Sbert.

6 recordsLinked to original sources

arXiv2021

A Bounded Measure for Estimating the Benefit of Visualization: Case Studies and Empirical Evaluation

Many visual representations, such as volume-rendered images and metro maps, feature a noticeable amount of information loss. At a glance, there seem to be numerous opportunities for viewers to misinterpret the data being visualized, hence undermining the benefits of these visual representations. In practice, there is little doubt that these visual representations are useful. The recently-proposed information-theoretic measure for analyzing the cost-benefit ratio of visualization processes can explain such usefulness experienced in practice, and postulate that the viewers' knowledge can reduce the potential distortion (e.g., misinterpretation) due to information loss. This suggests that viewers' knowledge can be estimated by comparing the potential distortion without any knowledge and the actual distortion with some knowledge. In this paper, we describe several case studies for collecting instances that can (i) support the evaluation of several candidate measures for estimating the potential distortion distortion in visualization, and (ii) demonstrate their applicability in practical scenarios. Because the theoretical discourse on choosing an appropriate bounded measure for estimating the potential distortion is yet conclusive, it is the real world data about visualization further informs the selection of a bounded measure, providing practical evidence to aid a theoretical conclusion. Meanwhile, once we can measure the potential distortion in a bounded manner, we can interpret the numerical values characterizing the benefit of visualization more intuitively.

cs.HC↗

arXiv2021

Is the Chen-Sbert Divergence a Metric?

Recently, Chen and Sbert proposed a general divergence measure. This report presents some interim findings about the question whether the divergence measure is a metric or not. It has been postulated that (i) the measure might be a metric when (0 < k <= 1), and (ii) the k-th root of the measure might be a metric when (k > 1). The report shows that for a 2-letter alphabet, postulation (i) can be proved. The possible pathway for obtaining a proof for (i) in n-letter cases is also discussed. The authors hope that the report may stimulate more scholarly effort to study the mathematical properties of this divergence measure.

cs.IT↗

arXiv2020

A Bounded Measure for Estimating the Benefit of Visualization

Information theory can be used to analyze the cost-benefit of visualization processes. However, the current measure of benefit contains an unbounded term that is neither easy to estimate nor intuitive to interpret. In this work, we propose to revise the existing cost-benefit measure by replacing the unbounded term with a bounded one. We examine a number of bounded measures that include the Jenson-Shannon divergence and a new divergence measure formulated as part of this work. We use visual analysis to support the multi-criteria comparison, narrowing the search down to those options with better mathematical properties. We apply those remaining options to two visualization case studies to instantiate their uses in practical scenarios, while the collected real world data further informs the selection of a bounded measure, which can be used to estimate the benefit of visualization.

cs.AI↗

arXiv2019

On the Upper Bound of the Kullback-Leibler Divergence and Cross Entropy

This archiving article consists of several short reports on the discussions between the two authors over the past two years at Oxford and Madrid, and their work carried out during that period on the upper bound of the Kullback-Leibler divergence and cross entropy. The work was motivated by the cost-benefit ratio proposed by Chen and Golan [1], and the less desirable property that the Kullback-Leibler (KL) divergence used in the measure is unbounded. The work subsequently (i) confirmed that the KL-divergence used in the cost-benefit ratio should exhibit a bounded property, (ii) proposed a new divergence measure, and (iii) compared this new divergence measure with a few other bounded measures.

cs.IT↗

arXiv2019

Generalizing the Balance Heuristic Estimator in Multiple Importance Sampling

In this paper, we propose a novel and generic family of multiple importance sampling estimators. We first revisit the celebrated balance heuristic estimator, a widely used Monte Carlo technique for the approximation of intractable integrals. Then, we establish a generalized framework for the combination of samples simulated from multiple proposals. We show that the novel framework contains the balance heuristic as a particular case. In addition, we study the optimal choice of the free parameters in such a way the variance of the resulting estimator is minimized. A theoretical variance study shows the optimal solution is always better than the balance heuristic estimator (except in degenerate cases where both are the same). As a side result of this analysis, we also provide new upper bounds for the balance heuristic estimator. Finally, we show the gap in the variance of both estimators by means of five numerical examples.

stat.CO↗

arXiv2019

Dense Haze: A benchmark for image dehazing with dense-haze and haze-free images

Single image dehazing is an ill-posed problem that has recently drawn important attention. Despite the significant increase in interest shown for dehazing over the past few years, the validation of the dehazing methods remains largely unsatisfactory, due to the lack of pairs of real hazy and corresponding haze-free reference images. To address this limitation, we introduce Dense-Haze - a novel dehazing dataset. Characterized by dense and homogeneous hazy scenes, Dense-Haze contains 33 pairs of real hazy and corresponding haze-free images of various outdoor scenes. The hazy scenes have been recorded by introducing real haze, generated by professional haze machines. The hazy and haze-free corresponding scenes contain the same visual content captured under the same illumination parameters. Dense-Haze dataset aims to push significantly the state-of-the-art in single-image dehazing by promoting robust methods for real and various hazy scenes. We also provide a comprehensive qualitative and quantitative evaluation of state-of-the-art single image dehazing techniques based on the Dense-Haze dataset. Not surprisingly, our study reveals that the existing dehazing techniques perform poorly for dense homogeneous hazy scenes and that there is still much room for improvement.

cs.CV↗