Finding the Optimal Bit-Quad Patterns for Computing the Euler Number of 2D Binary Images Using Simulated Annealing

Gómez-Flores, Wilfrido; Sossa, Humberto; Arce, Fernando

doi:10.1007/978-3-030-77004-4_23

Cited by 2 publications

(2 citation statements)

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“…Furthermore, to obtain the Euler number, Gomez [21] and Sossa [22] presented alternative formulas by use of bit-quads. Similar to the C-BQ algorithm, there are pixels that are accessed repeatedly upon implementation, and the proposed algorithm can be improved by using the strategies of state transition and multi-row scanning.…”

Section: Strategy Of Multi-row Scanningmentioning

confidence: 99%

“…For example, taking advantages of the skeleton, the perimeter/contact perimeter and the special contour pixels of the image, we can compute the Euler number in different ways. (3) Algorithms that compute the Euler number by counting specific blocks/patterns in the image [17][18][19][20][21][22][23][24][25]. In these algorithms, specific patterns with 2 × 2 pixels and consecutive foreground pixel blocks in the same row in the image, called runs, can be employed for calculating the Euler number.…”

Section: Introductionmentioning

confidence: 99%

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A Review for the Euler Number Computing Problem

Yao,

He,

Kang

et al. 2023

Electronics

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In a binary image, the Euler number is a crucial topological feature that holds immense significance in image understanding and image analysis owing to its invariance under scaling, rotation, or any arbitrary rubber-sheet transformation of images. This paper focuses on the Euler number computing problem in a binary image. The state-of-the-art Euler number computing algorithms are reviewed, which obtain the Euler number through different techniques, such as definition, features of binary images, and special data structures representing forms of binary images, and we explain the main principles and strategies of the algorithms in detail. Afterwards, we present the experimental results to bring order of the prevailing Euler number computing algorithms in 8-connectivity cases. Then, we discuss both the parallel implementation and the hardware implementation of algorithms for calculating the Euler number and present the algorithm extension for 3D image Euler number computation. Lastly, we aim to outline forthcoming efforts concerning the computation of the Euler number.

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Section: Strategy Of Multi-row Scanningmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Review for the Euler Number Computing Problem

Yao,

He,

Kang

et al. 2023

Electronics

View full text Add to dashboard Cite

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Euler Characteristic Computation by Means of a Chain Code Applied to Binary Images

Gómez-Gómez,

Sánchez-Cruz

2024

Int. J. Patt. Recogn. Artif. Intell.

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This paper presents a new approach for calculating the Euler characteristic in 2D binary images. The problem is addressed using the Three OrThogonal symbol chain code (3OT code), using only one symbol for the calculation of the Euler characteristic. Using this code, it is possible to introduce new geometric concepts represented by the same symbol of the 3OT alphabet and to simplify the overall equation of the Euler characteristic. This process is supported by the proof of a set of theorems and their numerical validation, using a set of binary images with a variable number of holes. Thus, this research proves that the 3OT code can be used not only for image compression as reported in the literature, but also to simplify the expression of the Euler characteristic as well as for the analysis and simplification of the shape of contours.

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Finding the Optimal Bit-Quad Patterns for Computing the Euler Number of 2D Binary Images Using Simulated Annealing

Cited by 2 publications

References 8 publications

A Review for the Euler Number Computing Problem

A Review for the Euler Number Computing Problem

Euler Characteristic Computation by Means of a Chain Code Applied to Binary Images

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