Abstract
A new image segmentation based on fast implementation of the Chan-Vese model is proposed. This approach differs from previous methods in that we do not need to solve the Euler-Lagrange equation of the underlying variational problem. First, through experiments, we observe that for the smooth image segmentation, Chan-Vese model (CVM) can be simplified. Utilizing the Gaussian low pass filter, we pretreat the original image and regularize the level curves. Then, we calculate the energy directly on discrete gray level sets, find the minimizer of the energy, and obtain the segmentation results. We analyze the algorithm and prove that under discrete gray level sets, the global minimum of the energy is same as the one obtained by the previous methods. Another advantage of this method is that the reinitialization is not needed. Since there are at most 255 discrete gray level sets, the algorithm improves the computational speed dramatically. And the complexity of the algorithm isO(N), whereNis the number of pixels in the image. So even for the large images, it is also very efficient. We apply our segmentation algorithm to synthetic and real world images to emphasize the performances of our model compared with other segmentation models.
Highlights
Images are the proper 2D projections of the 3D world containing various objects
To successfully reconstruct the 3D world, at least approximately, the first crucial step is to identify the regions in images that correspond to individual objects
In [14, 15, 18], the authors develop fast algorithms based on calculating the variational energy of the Chan-Vese model directly without the length term, that is, solving partial differential equations (PDEs)
Summary
Images are the proper 2D projections of the 3D world containing various objects. To successfully reconstruct the 3D world, at least approximately, the first crucial step is to identify the regions in images that correspond to individual objects. In [14, 15, 18], the authors develop fast algorithms based on calculating the variational energy of the Chan-Vese model directly without the length term, that is, solving PDEs. In [14], the authors develop a fast method for image segmentation without solving the Euler-Lagrange equation of the underlying variational problem proposed by Chan and Vese [4]. In [14], the authors develop a fast method for image segmentation without solving the Euler-Lagrange equation of the underlying variational problem proposed by Chan and Vese [4] Instead, they calculate the energy directly and check if the energy is decreased when they change a point inside the level-set to outside or vice versa.
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