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Efficient segmentation based on Eikonal and diffusion equations

Alvino, C. V., Unal, G.B., Slabaugh, G.G., Peny, B. and Fang, T. (2007). Efficient segmentation based on Eikonal and diffusion equations. International Journal of Computer Mathematics, 84(9), pp. 1309-1324. doi: 10.1080/00207160701324249

Abstract

Segmentation of regions of interest in an image has important applications in medical image analysis, particularly in computer aided diagnosis. Segmentation can enable further quantitative analysis of anatomical structures. We present efficient image segmentation schemes based on the solution of distinct partial differential equations (PDEs). For each known image region, a PDE is solved, the solution of which locally represents the weighted distance from a region known to have a certain segmentation label. To achieve this goal, we propose the use of two separate PDEs, the Eikonal equation and a diffusion equation. In each method, the segmentation labels are obtained by a competition criterion between the solutions to the PDEs corresponding to each region. We discuss how each method applies the concept of information propagation from the labelled image regions to the unknown image regions. Experimental results are presented on magnetic resonance, computed tomography, and ultrasound images and for both two-region and multi-region segmentation problems. These results demonstrate the high level of efficiency as well as the accuracy of the proposed methods.

Publication Type: Article
Additional Information: This is an Accepted Manuscript of an article published by Taylor & Francis in International Journal of Computer Mathematics on 13/9/2007, available online: http://wwww.tandfonline.com/10.1080/00207160701324249
Publisher Keywords: Computer vision, Image processing, Pattern recognition, Variational methods; Segmentation
Subjects: Q Science > QA Mathematics
Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Departments: School of Mathematics, Computer Science & Engineering > Computer Science
URI: http://openaccess.city.ac.uk/id/eprint/4410
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