Parallel computation of the Euler number via Connectivity Graph

Chiavetta, Franco; Gesù, Vito Di

doi:10.1016/0167-8655(93)90148-7

Cited by 33 publications

(35 citation statements)

References 6 publications

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“…In refs. [10][11][12], some fast algorithms to calculate the Euler Number had been researched. Other methods of Euler Number computing were discussed in refs.…”

Section: Introductionmentioning

confidence: 99%

A proof of image Euler Number formula

et al. 2006

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Euler Number is one of the most important characteristics in topology. In twodimension digital images, the Euler characteristic is locally computable. The form of Euler Number formula is different under 4-connected and 8-connected conditions. Based on the definition of the Foreground Segment and Neighbor Number, a formula of the Euler Number computing is proposed and is proved in this paper. It is a new idea to locally compute Euler Number of 2D image.

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“…In refs. [10][11][12], some fast algorithms to calculate the Euler Number had been researched. Other methods of Euler Number computing were discussed in refs.…”

Section: Introductionmentioning

confidence: 99%

A proof of image Euler Number formula

et al. 2006

View full text Add to dashboard Cite

show abstract

“…Further, the number of leaf nodes may vary widely for different image samples. The best known parallel algorithm has been proposed in [17] that uses the connectivity graph (CG) derived from the cylindrical algebraic decomposition of the Euclidean plane. The authors describe a parallel implementation of their algorithm on a linear array network topology that uses the CG as the image data structure and performs a parallel searching of the sub graphs in CG.…”

Section: Comparisons With Other Methodsmentioning

confidence: 99%

“…This property allows us to split the image into smaller subimages, and calculate the overall Euler number by combining the Euler numbers of the smaller subimages. An essential feature common to most of these methods is the addition and subtraction of the Euler numbers or some other parameters of the subimages [3,11,[16][17][18]21]. Thus for fast computation of Euler number, the design of the adder is most vital.…”

Section: Hardware Implementationmentioning

confidence: 99%

“…Chen and Yen [3] developed a parallel localized algorithm using square graphs to calculate the Euler number of a given binary image on a square grid. Chiavetta and Gesú [17] used connectivity graph representation of a binary image and developed an algorithm for computing the Euler number. The connectivity graph was derived from the discrete version of the cylindrical algebraic decomposition of the digital plane.…”

Section: Introductionmentioning

confidence: 99%

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A pipeline architecture for computing the Euler number of a binary image

Bishnu

Bhattacharya

Kundu

et al. 2005

Journal of Systems Architecture

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Euler number of a binary image is a fundamental topological feature that remains invariant under translation, rotation, scaling, and rubber-sheet transformation of the image. In this work, a run-based method for computing Euler number is formulated and a new hardware implementation is described. Analysis of time complexity and performance measure is provided to demonstrate the efficiency of the method. The sequential version of the proposed algorithm requires significantly fewer number of pixel accesses compared to the existing methods and tools based on bit-quad counting or quad-tree, both for the worst case and the average case. A pipelined architecture is designed with a single adder tree to implement the algorithm on-chip by exploiting its inherent parallelism. The architecture uses O(N) 2-input gates and requires O(N log N) time to compute the Euler number of an N · N image. The same hardware, with minor modification, can be used to handle arbitrarily large pixel matrices. A standard cell based VLSI implementation of the architecture is also reported. As Euler number is a widely used parameter, the proposed design can be readily used to save computation time in many image processing applications.

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“…For example, there are parallel algorithm for bit-plane computers [7], * graphbased algorithm [8], hardware algorithm [9], and algorithms for images with special formats [10], [11]. For the ordinary computer architecture and pixel-based format images, the algorithm proposed by Gray [12], which was adopted by the famous commercial image processing tools MATLAB [13], is one of the most efficient algorithms.…”

Section: Introductionmentioning

confidence: 99%

An Efficient Strategy for Bit-Quad-Based Euler Number Computing Algorithm

Yao

Yang

et al. 2014

IEICE Trans. Inf. & Syst.

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SUMMARYThe Euler number of a binary image is an important topological property for pattern recognition, and can be calculated by counting certain bit-quads in the image. This paper proposes an efficient strategy for improving the bit-quad-based Euler number computing algorithm. By use of the information obtained when processing the previous bit quad, the number of times that pixels must be checked in processing a bit quad decreases from 4 to 2. Experiments demonstrate that an algorithm with our strategy significantly outperforms conventional Euler number computing algorithms.

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Parallel computation of the Euler number via Connectivity Graph

Cited by 33 publications

References 6 publications

A proof of image Euler Number formula

A proof of image Euler Number formula

A pipeline architecture for computing the Euler number of a binary image

An Efficient Strategy for Bit-Quad-Based Euler Number Computing Algorithm

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