Topic

# Illumination problem

About: Illumination problem is a research topic. Over the lifetime, 93 publications have been published within this topic receiving 5859 citations.

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TL;DR: Different solutions to the classical illumination problems as known from computational geometry literature under this light attenuation model are presented, based on convex optimization, discretization and linear programming, as well as a purely combinatorial approximation algorithm.

Abstract: Consider the following illumination problem: given a stage represented by a line segment L and a set of light sources represented by a set of points S in the plane, assign powers to the light sources such that every point on the stage receives a sufficient amount – e.g. one unit – of light while minimizing the overall power consumption. Under the assumption that the amount of light arriving from a fixed light source decreases rapidly with the distance from the light source, this becomes an interesting optimization problem. We propose to reconsider the classical illumination problems as known from computational geometry literature under this light attenuation model. This paper examines the simple problem introduced above and presents different solutions, based on convex optimization, discretization and linear programming, as well as a purely combinatorial approximation algorithm. Some experimental results are also provided.

4 citations

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01 Aug 2021TL;DR: In this paper, an underwater image enhancement algorithm based on the Retinex theory and the Alternating Direction Method of Multipliers (ADMM) was proposed to solve the image blurring and distortion problem caused by underwater non-uniform and low illumination.

Abstract: In order to solve the image blurring and distortion problem caused by underwater non-uniform and low illumination, this paper proposes an underwater image enhancement algorithm based on the Retinex theory and the Alternating Direction Method of Multipliers (ADMM). Firstly, the L component of the original image in the Lab space is extracted as the initial illumination map, and an Augmented Lagrange Multiplier (ALM) framework is constructed based on the ADMM to optimize the initial illumination map in order to obtain an accurate illumination image. In addition, the illumination map is further corrected in the luminance region with the Gamma Correction. Secondly, combined with the color constancy characteristics in the Retinex theory, the reflected image of the object is obtained. Finally, the bilateral filter is picked to suppress the underwater noise and obtain a more detailed enhanced image. The experimental results show that the underwater image enhancement algorithm can effectively solve the non-uniform illumination problem caused by natural light or artificial light source and improve the underwater image quality, thus having a better performance than other algorithms.

4 citations

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21 Dec 2018

TL;DR: Zhang et al. as mentioned in this paper provided a construction method for non-negative feature extraction and face recognition application, which comprises the following steps: characterizing loss degree by cosine measure, characterising loss degree after matrix decomposition, determining loss degree between matrices, and obtaining an update iteration formula: the objective function is transformed to form the optimization problem, and the updated iterative formula of the algorithm is obtained by constructing auxiliary function.

Abstract: The invention provides a construction method for non-negative feature extraction and face recognition application, which comprises the following steps: characterizing loss degree by cosine measure; characterizing loss degree after matrix decomposition by cosine measure between matrices; and determining loss degree by cosine measure between matrices. A method for constructing an objective functioncomprises that step of characterizing a loss degree by a cosine measure to form an objective function; obtaining an update iteration formula: the objective function is transformed to form the optimization problem to be solved, and the updated iterative formula of the algorithm is obtained by constructing auxiliary function. The invention has the advantages that: 1. the illumination problem encountered in the face recognition process is solved; 2. the convergence of the algorithm proposed by the invention is not only proved in theory by using auxiliary function, but also verified in experiment,and our algorithm has higher convergence; 3. compared with the related algorithm in the face database with illumination influence, the result shows that the algorithm of the invention has certain superiority.

4 citations

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26 Jan 2011

TL;DR: In this paper, a method for obtaining human face illumination invariant images based on multiscale anisotropic diffusion, belonging to the field of image processing technologies, was proposed.

Abstract: The invention relates to a method for obtaining human face illumination invariant images based on multiscale anisotropic diffusion, belonging to the field of image processing technologies. The invention is based on a Lambertian convex surface model for decomposing the human face image to a small-scale feature image and a large-scale feature image. The small-scale feature image can be regarded as the ideal human face illumination invariant feature image. The core is characterized in that new descriptors with inconsistent intervals are introduced for strengthening edge retention capability of an anisotropic diffusion algorithm to low frequency domain images so as to greatly weaken image halo effect of the algorithm; meanwhile, a new transfer coefficient is provided, and noised caused by edge sharpening is reduced; and an anisotropic diffusion constraint is introduced, and the method is more suitable for treating the illumination problem of the human body image. Experiments show that the invention can obtain good treatment effect even in extremely poor lighting conditions and can effectively improve robustness of face recognition or face certification to changes in lighting conditions.

4 citations

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TL;DR: In this paper, 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.

4 citations