Abstract
Abstract In this paper we propose a new scheme for image segmentation composed of two stages: in the first phase, we smooth the original image by some filters associated with noise types, such as Gaussian filters for Gaussian white noise and so on. Indeed, we propose a novel diffusion equations scheme derived from a non-convex functional for Gaussian noise removal in this paper. In the second phase, we apply a variational method for segmentation in the smoothed image domain obtained in the first phase, where we directly calculate the minimizer on the discrete gray level sets. In contrast to other image segmentation methods, there is no need for us to re-initialize parameters, which deduces the complexity of our algorithm to O ( N ) (N is the number of pixels) and provides significant efficiency improvement when dealing with large-scale images. The obtained numerical results of segmentation on synthetic images and real world images both clearly outperform the main alternative methods especially for images contaminated by noise.
Highlights
Images are the proper -D projections of the -D world containing various objects
A well-established class of methods consists of active contour models, which have been widely used in image segmentation with promising results
Chan and Vese [ ] developed an active contour without edge model to deal with image segmentation by using the level-set framework introduced by Osher and Sethian [ ], which is similar to the segmentation method independently proposed by Tsai et al [ ]
Summary
Images are the proper -D projections of the -D world containing various objects. To reconstruct the -D world perfectly, at least approximately, the first crucial step is to identify the regions in images that correspond to individual objects. Chan and Vese [ ] developed an active contour without edge model to deal with image segmentation by using the level-set framework introduced by Osher and Sethian [ ], which is similar to the segmentation method independently proposed by Tsai et al [ ]. These active contour methods based on level-set framework have some drawbacks Most of these methods have initialization problems: different initial curves produce different segmentations because of the non-convexity of Chan-Vese models [ ]. In [ ], the authors proposed a fast method for image segmentation without solving the EulerLagrange equation of the underlying variational problem proposed by Chan and Vese, they calculated the energy directly and checked if the energy is decreased when they change a point inside the level set to outside or vice versa.
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