Using Intersection Graphs for Smartphone-Based Document Localization

Arlazarov, Vladimir V.; Zhukovsky, Alexander; Krivtsov, Valeriy E.; Postnikov, Vassili V.

doi:10.3103/s0147688217050021

Cited by 2 publications

(2 citation statements)

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“…In this article, we introduce an interval catch digraph (ICD) family, provide the distribution of its domination number for random vertices, and employ the domination number in testing uniformity of one-dimensional data. Interval graphs and digraphs have applications in many fields such as chronological ordering of artifacts in archeology, modeling traffic lights in transportation, food web models in ecology, document localization, classification of RNA structures and so on (see Roberts (1976), Drachenberg (1994), Arlazarov et al (2017), and Quadrini et al (2017)). ICDs were introduced as a special type of interval digraphs and found applications in various fields (see Prisner (1989Prisner ( , 1994 for a characterization and detailed discussion of ICDs).…”

Section: Introductionmentioning

confidence: 99%

Domination number of an interval catch digraph family and its use for testing uniformity

Ceyhan

2020

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We consider a special type of interval catch digraph (ICD) family for one-dimensional data in a randomized setting and propose its use for testing uniformity. These ICDs are defined with an expansion and a centrality parameter, hence we will refer to this ICD as parameterized ICD (PICD). We derive the exact (and asymptotic) distribution of the domination number of this PICD family when its vertices are from a uniform (and non-uniform) distribution in one dimension for the entire range of the parameters; thereby determine the parameters for which the asymptotic distribution is non-degenerate. We observe jumps (from degeneracy to non-degeneracy or from a non-degenerate distribution to another) in the asymptotic distribution of the domination number at certain parameter combinations. We use the domination number for testing uniformity of data in real line, prove its consistency against certain alternatives, and compare it with two commonly used tests and three recently proposed tests in literature and also arc density of this ICD and of another ICD family in terms of size and power. Based on our extensive Monte Carlo simulations, we demonstrate that domination number of our PICD has higher power for certain types of deviations from uniformity compared to other tests.

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Section: Introductionmentioning

confidence: 99%

Domination number of an interval catch digraph family and its use for testing uniformity

Ceyhan

2020

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“…Curves detection can be also useful for a document localization in the image. The papers [25,26] consider cases when the document image has the shape of a quadrangle or is very close to it, that is, the document boundaries in the image are straight lines. If the document has been bent, the document boundaries are curves and the proposed algorithms will fail.…”

Section: Introductionmentioning

confidence: 99%

A method of detecting end-to-end curves of limited curvature

Panfilova¹,

Aliev²,

Kunina

et al. 2020

Twelfth International Conference on Machine Vision (ICMV 2019)

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In this paper we consider a method for detecting end-to-end curves of limited curvature like the k-link polylines with bending angle between adjacent segments in a given range. The approximation accuracy is achieved by maximization of the quality function in the image matrix. The method is based on a dynamic programming scheme constructed over Fast Hough Transform calculation results for image bands. The proposed method asymptotic complexity is O(h⋅(w+h/k)⋅log(h/k)), where h and w are the image size, and k is the approximating polyline links number, which is an analogue of the complexity of the fast Fourier transform or the fast Hough transform. We also show the results of the proposed method on synthetic and real data.

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Using Intersection Graphs for Smartphone-Based Document Localization

Cited by 2 publications

References 5 publications

Domination number of an interval catch digraph family and its use for testing uniformity

Domination number of an interval catch digraph family and its use for testing uniformity

A method of detecting end-to-end curves of limited curvature

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