Abstract
We introduce a variational model for multi-phase image segmentation that uses a multiscale sparse representation frame (wavelets or other) in a modified diffuse interface context. The segmentation model we present differs from other state-of-the-art models in several ways. The diffusive nature of the method originates from the sparse representations and thus propagates information in a different manner comparing to any existing PDE models, allowing one to combine the advantages of non-local information processing with sharp edges in the output. The regularizing part of the model is based on the wavelet Ginzburg–Landau (WGL) functional, and the fidelity part consists of two terms: one ensures the mean square proximity of the output to the original image; the other takes care of preserving the main edge set. Multiple numerical experiments show that the model is robust to noise yet can preserve the edge information. This method outperforms the algorithms from other classes in cases of images with significant presence of noise or highly uneven illumination
Highlights
Image segmentation is a technique of partitioning an image domain into multiple regions such that each region is homogeneous with respect to some characteristic such as intensity, texture and/or color
Highlighting the previously-mentioned feature of the model, a more relaxed dependence on e as the diffuse interface parameter comparing to the classical PDE-based models, let us remark that in our numerical examples, a typical value of e is of order N −1/2 and is always greater than N4
It facilitates the wavelet-based diffusion that forms components of reasonable scale with a piecewise smooth boundary, yet the actual black to white transitions are far from blurry and have a width that is small enough to leave no artifacts after thresholding
Summary
Image segmentation is a technique of partitioning an image domain into multiple regions such that each region is homogeneous with respect to some characteristic such as intensity, texture and/or color. It is often used to locate objects or to find the respective boundary. It is an active research topic with numerous practical applications. Image segmentation can be very challenging for images with noise, low contrast and multi-scale, multi-directional details. Conducting multiphase segmentation, rather than binary “object vs background” segmentation in these cases adds complexity to the problem
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