Largest inscribed rectangles in convex polygons

Knauer, Christian; Schlipf, Lena; Schmidt, Jens M.; Tiwary, Hans Raj

doi:10.1016/j.jda.2012.01.002

Cited by 24 publications

(14 citation statements)

References 5 publications

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“…Finding the largest convex region inside of a non-convex polygon was originally proposed and dubbed the “potato peeling problem” by Goodman [ 13 ] and the “convex skull problem” by Woo [ 14 ] and was later solved in polynomial time by Chang and Yap [ 15 ]. Other works have found solutions or approximate solutions to sub-problems such as the largest inscribed rectangle [ 31 , 32 ], longest line segment, or largest ellipse [ 33 ] contained within a non-convex polygon.…”

Section: Methodsmentioning

confidence: 99%

Optimal Camera Pose and Placement Configuration for Maximum Field-of-View Video Stitching

Watras

Kim

Liu

et al. 2018

Sensors

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An optimal camera placement problem is investigated. The objective is to maximize the area of the field of view (FoV) of a stitched video obtained by stitching video streams from an array of cameras. The positions and poses of these cameras are restricted to a given set of selections. The camera array is designed to be placed inside the abdomen to support minimally invasive laparoscopic surgery. Hence, a few non-traditional requirements/constraints are imposed: Adjacent views are required to overlap to support image registration for seamless video stitching. The resulting effective FoV should be a contiguous region without any holes and should be a convex polygon. With these requirements, traditional camera placement algorithms cannot be directly applied to solve this problem. In this work, we show the complexity of this problem grows exponentially as a function of the problem size, and then present a greedy polynomial time heuristic solution that approximates well to the globally optimal solution. We present a new approach to directly evaluate the combined coverage area (area of FoV) as the union of a set of quadrilaterals. We also propose a graph-based approach to ensure the stitching requirement (overlap between adjacent views) is satisfied. We present a method to find a convex polygon with maximum area from a given polygon. Several design examples show that the proposed algorithm can achieve larger FoV area while using much less computing time.

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Section: Methodsmentioning

confidence: 99%

Optimal Camera Pose and Placement Configuration for Maximum Field-of-View Video Stitching

Watras

Kim

Liu

et al. 2018

Sensors

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“…After superpixel segmentation [20] on the Ychannel, the superpixel (SP) with the largest area and largest average luma value (∈ L target ) is selected as the target SP, SP target . The ER is then defined as the largest inscribed region within SP target [21]. Fig.…”

Section: A Embedding Region Selectionmentioning

confidence: 99%

“…The ER C region is binarized such that pixel values larger than 198 are set to 0 and pixel values within the L target range are set to 1. Then, the largest inscribed region [29] within this binarized region is selected as the ER location. 4) Once the ER location is found, the watermark embedding process described in Section III-B is performed.…”

Section: B Scene-based Watermarkingmentioning

confidence: 99%

Scene-based Imperceptible-visible Watermarking for HDR Video Content

Perez-Daniel

García-Ugalde

Sánchez

2019

2019 7th International Workshop on Biometrics and Forensics (IWBF)

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“…If the effective phase space area is approximated with a convex polygon, the problem of finding this largest area inscribed rectangle is computationally treatable, although it is far from simple [19]. For this purpose, we developed a customized algorithm, based on a convolution iterative process, comprising the following sequence:…”

Section: Sampling the Effective Object Phase Spacementioning

confidence: 99%

Efficient characterization of phase space mapping in axially symmetric optical systems

Barbero¹,

Portilla²

2017

J. Opt.

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The phase space mapping, between an object and image plane, characterizes an optical system within geometrical optics framework. We propose a novel idea to characterize the phase mapping in axially symmetric optical systems for arbitrary object locations not restricted to a specific object plane. The idea is based on decomposing the phase mapping into a set a bivariate equations corresponding to different values of the radial coordinate at an specific object surface (most likely the entrance pupil). These equations are then approximated through bivariate Chebyshev interpolation at Chebyshev nodes, which guarantees uniform convergence. Additionally we propose the use of a new concept (effective object phase space), defined as the set of points of the phase space at the first optical element (typically the entrance pupil) that are effectively mapped onto a set of points included at the image surface. The effective object phase space provides a way to avoid tracing rays that do not reach the image surface, by means of an inclusion test.

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Largest inscribed rectangles in convex polygons

Cited by 24 publications

References 5 publications

Optimal Camera Pose and Placement Configuration for Maximum Field-of-View Video Stitching

Optimal Camera Pose and Placement Configuration for Maximum Field-of-View Video Stitching

Scene-based Imperceptible-visible Watermarking for HDR Video Content

Efficient characterization of phase space mapping in axially symmetric optical systems

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