A Simple and Correct Even-Odd Algorithm for the Point-in-Polygon Problem for Complex Polygons

Galetzka, Michael; Glauner, Patrick

doi:10.5220/0006040801750178

Cited by 21 publications

(8 citation statements)

References 3 publications

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“…Note that we use a method proposed in [12] to judge whether a point is inside a polygon, and this method is also known as the crossing number algorithm or the evenodd rule algorithm [5]. The comparison between previous method and our algorithm is shown in Figure 3, our method shows satisfactory performance for computing polygonal area in practice.…”

Section: Shared Monte-carlo Methodsmentioning

confidence: 84%

Deep Matching Prior Network: Toward Tighter Multi-oriented Text Detection

Liu

Jin

2017

2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)

313

171

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Detecting incidental scene text is a challenging task because of multi-orientation, perspective distortion, and variation of text size, color and scale. Retrospective research has only focused on using rectangular bounding box or horizontal sliding window to localize text, which may result in redundant background noise, unnecessary overlap or even information loss. To address these issues, we propose a new Convolutional Neural Networks (CNNs) based method, named Deep Matching Prior Network (DMPNet), to detect text with tighter quadrangle. First, we use quadrilateral sliding windows in several specific intermediate convolutional layers to roughly recall the text with higher overlapping area and then a shared Monte-Carlo method is proposed for fast and accurate computing of the polygonal areas. After that, we designed a sequential protocol for relative regression which can exactly predict text with compact quadrangle. Moreover, a auxiliary smooth Ln loss is also proposed for further regressing the position of text, which has better overall performance than L2 loss and smooth L1 loss in terms of robustness and stability. The effectiveness of our approach is evaluated on a public word-level, multioriented scene text database, ICDAR 2015 Robust Reading Competition Challenge 4 "Incidental scene text localization". The performance of our method is evaluated by using F-measure and found to be 70.64%, outperforming the existing state-of-the-art method with F-measure 63.76%.

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Section: Shared Monte-carlo Methodsmentioning

confidence: 84%

Deep Matching Prior Network: Toward Tighter Multi-oriented Text Detection

Liu

Jin

2017

2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)

313

171

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“…The winding number version, however, provides the correct answer also for non-simple polygons or particular cases, whereas the ray casting algorithm, as it has been presented, fails. Nevertheless, a more recent review of the ray casting [96] method has also smoothed out this difference, making the two versions practically equivalent.…”

Section: Winding Number Version -mentioning

confidence: 99%

sEMG-based Control Strategy for a Hand Exoskeleton System

Secciani

2022

Springer Theses

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“…In many studies, this type of algorithm is called the ray-crossing [2], crossings-count [4], odd-even [3], odd parity [3], or even-odd [2,10] algorithm because the structures and principles of the different algorithms are all slightly different. However, virtually all of these algorithms evolved from the ray-intersection algorithm, which works by shooting a ray − → PQ in any direction (see Figure 5; in general, this is done parallel to the x-axis) from the test point P to infinity and counts the number of intersections between the ray − → PQ and all edges of input polygon.…”

Section: Ray-intersection Algorithmmentioning

confidence: 99%

Optimal Reliable Point-in-Polygon Test and Differential Coding Boolean Operations on Polygons

et al. 2018

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This paper provides a full theoretical and experimental analysis of a serial algorithm for the point-in-polygon test, which requires less running time than previous algorithms and can handle all degenerate cases. The serial algorithm can quickly determine whether a point is inside or outside a polygon and accurately determine the contours of input polygon. It describes all degenerate cases and simultaneously provides a corresponding solution to each degenerate case to ensure the stability and reliability. This also creates the prerequisites and basis for our novel boolean operations algorithm that inherits all the benefits of the serial algorithm. Using geometric probability and straight-line equation, it optimizes our two algorithms that avoid the division operation and do not need to compute any intersection points. Our algorithms are applicable to any polygon that may be self-intersecting or with holes nested to any level of depth. They do not have to sort the vertices clockwise or counterclockwise beforehand. Consequently, they process all edges one by one in any order for input polygons. This allows a parallel implementation of each algorithm to be made very easily. We also prove several theorems guaranteeing the correctness of algorithms. To speed up the operations, we assign each vector a number code and derive two iterative formulas using differential calculus. However, the experimental results as well as the theoretical proof show that our serial algorithm for the point-in-polygon test is optimal and the time complexities of all algorithms are linear. Our methods can be extended to three-dimensional space, in particular, they can be applied to 3D printing to improve its performance.

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A Simple and Correct Even-Odd Algorithm for the Point-in-Polygon Problem for Complex Polygons

Cited by 21 publications

References 3 publications

Deep Matching Prior Network: Toward Tighter Multi-oriented Text Detection

Deep Matching Prior Network: Toward Tighter Multi-oriented Text Detection

sEMG-based Control Strategy for a Hand Exoskeleton System

Optimal Reliable Point-in-Polygon Test and Differential Coding Boolean Operations on Polygons

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