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Digital Straightness, Circularity, and Their Applications to Image Analysis

  • Chapter
Digital Geometry Algorithms

Part of the book series: Lecture Notes in Computational Vision and Biomechanics ((LNCVB,volume 2))

Abstract

This chapter contains some theoretical properties of digital straightness and digital circularity, which are helpful in designing algorithms related to image analysis. These properties are obtained mainly from word-theoretic and number-theoretic analysis. Existing techniques on straight line recognition, circular arc recognition, vectorization, etc. have been discussed along with their historical connections. Some salient points that discriminate digital geometry from real geometry have also been mentioned. Relevant experimental results have been given to demonstrate the elegance of digital-geometric techniques in performing desired tasks in the digital plane. Some open problems have been given at the end to point out the challenges and prospects of digital straightness and circularity in image analysis.

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Notes

  1. 1.

    In [79], Q is considered to be a digital disk if there exists a Euclidean/real circle such that Q comprises of all the digital points lying on or inside that real circle.

  2. 2.

    The notion of inexactness in our work corresponds to a range of radius (and positions), which has some conceptual resemblance with the existence of generalized circumcenter proposed recently in [121].

  3. 3.

    Here we use L((x,y),(x′,y′)) to denote the digital straight line segment joining the points (x,y) and (x′,y′).

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Authors and Affiliations

  1. Department of Computer Science and Engineering, Indian Institute of Technology, Kharagpur, India

    Partha Bhowmick

  2. Advanced Computing and Microelectronics Unit, Indian Statistical Institute, Kolkata, India

    Bhargab B. Bhattacharya

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  1. Partha Bhowmick
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Correspondence to Partha Bhowmick .

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  1. Buffalo State College, Department of Mathematics, State University of New York, Elmwood Avenue 1300, Buffalo, 14222, New York, USA

    Valentin E. Brimkov

  2. Department of Computer Science, State University of New York at Fredonia, Central Ave. 280, Fredonia, 14063, New York, USA

    Reneta P. Barneva

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Bhowmick, P., Bhattacharya, B.B. (2012). Digital Straightness, Circularity, and Their Applications to Image Analysis. In: Brimkov, V., Barneva, R. (eds) Digital Geometry Algorithms. Lecture Notes in Computational Vision and Biomechanics, vol 2. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4174-4_9

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