Computing the Euler characteristic and related additive functionals of digital objects from their bintree representation

Bieri, Hanspeter

doi:10.1016/0734-189x(87)90059-4

Cited by 26 publications

(13 citation statements)

References 15 publications

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“…Many algorithms have been proposed for calculating the Euler number of a binary image [13][14][15][16][17]. A famous one is proposed by Pratt [18] and is used in the famous commercial image processing tools MATLAB [19].…”

Section: Introductionmentioning

confidence: 99%

An improvement on the Euler number computing algorithm used in MATLAB

Yao

Yang

et al. 2013

2013 IEEE International Conference of IEEE Region 10 (TENCON 2013)

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Computation of the Euler number of a binary image is often necessary in image matching, image database retrieval, image analysis, pattern recognition, and computer vision. This paper proposes an improvement on the Euler number computing algorithm used in the famous image processing tool MATLAB. By use of the information obtained during processing the previous pixel, the number of times of checking the neighbor pixels for processing a pixel decrease from 4 to 2. Our method is very simple in principle, and easily implemented. The experimental results demonstrated that our method outperforms significantly conventional Euler number computing algorithms.

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Section: Introductionmentioning

confidence: 99%

An improvement on the Euler number computing algorithm used in MATLAB

Yao

Yang

et al. 2013

2013 IEEE International Conference of IEEE Region 10 (TENCON 2013)

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“…Dyer [8] presents the computation of the Euler number of an image from its quadtree. Bieri [9] defines the computation of the Euler characteristic of digital objects from their bintree representation. Chiavetta and Di Gesu [10] present a method of parallel computation of the Euler number via a connectivity graph.…”

Section: Introductionmentioning

confidence: 99%

Computation of the Euler number using the contact perimeter

Bribiesca

2010

Computers & Mathematics with Applications

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a b s t r a c tWe present the computation of the Euler number of shapes using the contact perimeter. The contact perimeter was initially defined in [E. Bribiesca, Measuring 2D shape compactness using the contact perimeter, Comput. Math. Appl. 33 (1997) 1-9]. In this reference the contact perimeter was used to define a measure of compactness for 2D shapes. Now, in this paper we use the contact perimeter to compute the Euler number of unit-width objects composed of different side-connected cells and face-connected polyhedrons in two and three dimensions, respectively. Finally, we present some applications of this computation in knot and graph theory.

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“…More in detail, if Tps is the number of terminal points of the n skeletons from n objects in the image, and TEps is the number of three-edge points of these n skeletons, then Several methods have been proposed to obtain the Euler number of a binary image. Refer for example to [2], [3], [4], [5], [6], [7], [8], [9] and [14]. In particular in [3], the Euler of a binary image is computed from its quadtree, while in [7], this feature is computed from the connectivity graph of the image.…”

Section: Introductionmentioning

confidence: 99%