scholarly journals Edge-Based Color Image Segmentation Using Particle Motion in a Vector Image Field Derived from Local Color Distance Images

2020 ◽  
Vol 6 (7) ◽  
pp. 72
Author(s):  
Wutthichai Phornphatcharaphong ◽  
Nawapak Eua-Anant

This paper presents an edge-based color image segmentation approach, derived from the method of particle motion in a vector image field, which could previously be applied only to monochrome images. Rather than using an edge vector field derived from a gradient vector field and a normal compressive vector field derived from a Laplacian-gradient vector field, two novel orthogonal vector fields were directly computed from a color image, one parallel and another orthogonal to the edges. These were then used in the model to force a particle to move along the object edges. The normal compressive vector field is created from the collection of the center-to-centroid vectors of local color distance images. The edge vector field is later derived from the normal compressive vector field so as to obtain a vector field analogous to a Hamiltonian gradient vector field. Using the PASCAL Visual Object Classes Challenge 2012 (VOC2012), the Berkeley Segmentation Data Set, and Benchmarks 500 (BSDS500), the benchmark score of the proposed method is provided in comparison to those of the traditional particle motion in a vector image field (PMVIF), Watershed, simple linear iterative clustering (SLIC), K-means, mean shift, and J-value segmentation (JSEG). The proposed method yields better Rand index (RI), global consistency error (GCE), normalized variation of information (NVI), boundary displacement error (BDE), Dice coefficients, faster computation time, and noise resistance.

Author(s):  
Wutthichai Phornphatcharaphong ◽  
Nawapak Eua-Anant

This paper presents an Edge-based color image segmentation derived from the method of Particle Motion in a Vector Image Fields (PMVIF) that could previously be applied only to monochrome images. Instead of using an edge vector field derived from a gradient vector field and a normal compressive vector field derived from a Laplacian-gradient vector field, two novel orthogonal vector fields, directly computed from a color image, one parallel and another orthogonal to the edges, were used in the model to force a particle to move along the object edges. The normal compressive vector field is derived from the center-to-centroid vectors of local color distance images. Next, the edge vector field is derived by taking the normal compressive vector field, multiplied by differences of auxiliary image pixels to obtain a vector field analogous to a Hamiltonian gradient vector field. Using the PASCAL Visual Object Classes Challenge 2012 (VOC2012) and the Berkeley Segmentation Data Set and Benchmarks 500 (BSDS500), the benchmark score of the proposed method is provided in comparison with those of the traditional PMVIF, Watershed, SLIC, K-means, Mean shift, and JSEG. The proposed method yields better RI, GCE, NVI, BDE, Dice coefficients, faster computation time, and noise resistance.


Author(s):  
Shin-ichi Ohta

AbstractWe investigate the structure of a Finsler manifold of nonnegative weighted Ricci curvature including a straight line, and extend the classical Cheeger–Gromoll–Lichnerowicz Splitting Theorem. Such a space admits a diffeomorphic, measure-preserving splitting in general. As for a special class of Berwald spaces, we can perform the isometric splitting in the sense that there is a one-parameter family of isometries generated from the gradient vector field of the Busemann function. A Betti number estimate is also given for Berwald spaces.


2007 ◽  
Vol 40 (4) ◽  
pp. 1255-1269 ◽  
Author(s):  
Wooi-Boon Goh ◽  
Kai-Yun Chan

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