# Showing papers on "Illumination problem published in 2016"

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19 Feb 2016TL;DR: In this paper, the authors survey the recent advances in the area of illumination conjecture in discrete geometry, computational geometry, and geometric analysis, and describe two new approaches to make progress on the illumination problem.

Abstract: At a first glance, the problem of illuminating the boundary of a convex body by external light sources and the problem of covering a convex body by its smaller positive homothetic copies appear to be quite different. They are in fact two sides of the same coin and give rise to one of the important longstanding open problems in discrete geometry, namely, the Illumination Conjecture. In this paper, we survey the activity in the areas of discrete geometry, computational geometry and geometric analysis motivated by this conjecture. Special care is taken to include the recent advances that are not covered by the existing surveys. We also include some of our recent results related to these problems and describe two new approaches – one conventional and the other computer-assisted – to make progress on the illumination problem. Some open problems and conjectures are also presented.

34 citations

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TL;DR: In this article, the authors survey the recent advances in the area of illumination conjecture in discrete geometry, computational geometry, and geometric analysis, and describe two new approaches to make progress on the illumination problem.

Abstract: At a first glance, the problem of illuminating the boundary of a convex body by external light sources and the problem of covering a convex body by its smaller positive homothetic copies appear to be quite different. They are in fact two sides of the same coin and give rise to one of the important longstanding open problems in discrete geometry, namely, the Illumination Conjecture. In this paper, we survey the activity in the areas of discrete geometry, computational geometry and geometric analysis motivated by this conjecture. Special care is taken to include the recent advances that are not covered by the existing surveys. We also include some of our recent results related to these problems and describe two new approaches -- one conventional and the other computer-assisted -- to make progress on the illumination problem. Some open problems and conjectures are also presented.

20 citations

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TL;DR: In this article, it was shown that, arbitrarily close to the Euclidean ball, there is a centrally symmetric convex body of illumination number exponentially large in the dimension.

Abstract: The Illumination Problem may be phrased as the problem of covering a convex body in Euclidean $n$-space by a minimum number of translates of its interior. By a probabilistic argument, we show that, arbitrarily close to the Euclidean ball, there is a centrally symmetric convex body of illumination number exponentially large in the dimension.

10 citations

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TL;DR: In this article, the authors survey the recent advances in the area of illumination conjecture in discrete geometry, computational geometry, and geometric analysis, and describe two new approaches to make progress on the illumination problem.

Abstract: At a first glance, the problem of illuminating the boundary of a convex body by external light sources and the problem of covering a convex body by its smaller positive homothetic copies appear to be quite different. They are in fact two sides of the same coin and give rise to one of the important longstanding open problems in discrete geometry, namely, the Illumination Conjecture. In this paper, we survey the activity in the areas of discrete geometry, computational geometry and geometric analysis motivated by this conjecture. Special care is taken to include the recent advances that are not covered by the existing surveys. We also include some of our recent results related to these problems and describe two new approaches -- one conventional and the other computer-assisted -- to make progress on the illumination problem. Some open problems and conjectures are also presented.

5 citations

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TL;DR: This paper focuses on the statistical treatment of illumination artefacts on digital images in the presence of an additional random noise and derivation of a new estimator of R which is shown to be consistent under suitable identifiability and regularity conditions.

Abstract: This paper focuses on the statistical treatment of illumination artefacts on digital images in the presence of an additional random noise We assume that this artefact consists of "smooth" variations of the intensity of the signal of interest R Such an assumption is classically modelled using a function L which acts in a multiplicative way on R Our goal is to estimate R from observations of a random variable Y which obeys the regression model Y = R L + e Our main contribution lies in the derivation of a new estimator of R which is shown to be consistent under suitable identifiability and regularity conditions The accuracy of this new estimation procedure is studied from a theoretical point of view through the rate of convergence of the uniform risk Applications to real Scanning Electron Microscopy images are presented, as well as a qualitative study of the performances of our method with respect to other image processing techniques

5 citations

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14 May 2016

TL;DR: An enhancement algorithm based on segmenting non-uniform illumination image into two sub images and filtering separately is proposed and the experiment shows image enhancement effect of the proposed algorithm.

Abstract: To solve the non-uniform illumination problem of digital images, an enhancement algorithm based on segmenting non-uniform illumination image into two sub images and filtering separately is proposed. The method how to segment the non-uniform illumination image into two sub images and fix on the cut-off frequency of homomorphic filter is studied. The experiment shows image enhancement effect of the proposed algorithm in this paper.

2 citations

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01 Oct 2016TL;DR: A mixed reality system for aircraft design is developed based on the research results of all the work above which realize the illumination and shadow effects on the virtual aircraft.

Abstract: Consistent illumination is an important research target in the augmented reality system. In this paper, an efficient illumination method is implemented to solve the consistent illumination problem for mixed reality application. We design and implement an all-frequency environment rendering methods based on wavelet transform, and proposed an accelerated rendering method on GPU. The environment rendering method consists of two steps, one is precomputation and the other real-time rendering. An improved shadow algorithm based on shadow map is propose, which can solve least area where light source view frustum should surround according to the relationship of view frustum in eye space and terrain. In the end, we develop a mixed reality system for aircraft design based on the research results of all the work above which realize the illumination and shadow effects on the virtual aircraft. It can be used to assess how the weather impact on the operating.

1 citations