Organizations: Department of Mathematics, University of California, Irvine, 340 Rowland Hall, Irvine, CA 92697-3875, USA · Université Paris Cité, CNRS, Sorbonne Université, Laboratoire Jacques-Louis Lions (LJLL), F-75006 Paris, France · & Octav Mayer Institute of Mathematics, Romanian Academy, Iaşi Branch, 700506 Iaşi, Romania.
Robust to intensity inhomogeneity, the local Chan--Vese (LCV) model extends the classical Chan--Vese (CV) image segmentation method by incorporating local statistical information around each pixel. Originally, the LCV model was solved using a finite difference scheme, following the approach used for the CV model. As an alternative to the finite difference scheme, a more efficient algorithm based on the Merriman-Bence-Osher (MBO) scheme was later developed for the CV model. In this paper, we derive a similar MBO-based algorithm to solve the LCV model and propose an efficient implementation. The algorithm is developed for both two-phase and multiphase segmentation, and an extension to color images is also discussed. To demonstrate the effectiveness of the proposed approach, we apply it to a variety of grayscale and color images, including medical and microscopy images.
In this paper, we propose a novel locally statistical active contour model (LACM) based on Aubert-Aujol (AA) denoising model and variational level set method, which can be used for SAR images segmentation with intensity inhomogeneity. Then we transform the proposed model into a global optimization model by using convex relaxation technique. Firstly, we apply the Split Bregman technique to transform the global optimization model into two alternating optimization processes of Shrink operator and Laplace operator, which is called SB_LACM model. Moreover, we propose two fast models to solve the global optimization model , which are more efficient than the SB_LACM model. The first model is: we add the proximal function to transform the global optimization model to a general ROF model[29], which can be solved by a fast denoising algorithm proposed by R.-Q.Jia, and H.Zhao; [29] was submitted on 29-Aug-2013, and our early edition was ever submitted to TGRS on 12-Jun-2012, Venkatakrishnan et al. [30] proposed their PnP algorithm on 29-May-2013, so Venkatakrishnan and we proposed the PnP algorithm almost simultaneously. Thus we obtain a fast segmentation algorithm with global optimization solver that does not involve partial differential equations or difference equation, and only need simple difference computation. The second model is: we use a different splitting approach than one model to transform the global optimization model into a differentiable term and a general ROF model term, which can be solved by the same technique as the first model.
Despite great advances, finding accurate segmentation remains a challenging task, especially in scenarios with cluttered backgrounds, complex intensity variations and topology appearance. Minimal path models have exhibited their strong ability in addressing image segmentation tasks. However, the performance of minimal paths-based segmentation approaches is heavily influenced by model initialization, hence limiting their application scope in practice. In this work, we propose a novel mask proposal voting framework that overcomes the major drawback of classical approaches, allowing robust segmentation even in complicated scenarios. Firstly, we introduce an efficient method for constructing adaptive domain cuts as a constraint for initializing the region-based min-cut evolution, by which diverse and reliable mask proposal candidates can be generated, substantially increasing the possibility of accurately covering the objective region by these proposals. Secondly, we propose a new mask voting scheme to build a voting score map encoding the final segmentation information. In contrast to classical path voting methods, our model allows incorporating priors to assign different importance to each individual mask. As a consequence, the proposed segmentation model is capable of accurately delineating object boundaries under complex scenarios, and is insensitive to initialization. Experiments demonstrate that our method consistently outperforms state-of-the-art minimal path-based approaches in both accuracy and robustness.
In this paper, we propose a novel locally statistical variational active contour model based on I-divergence-TV denoising model, which hybrides geodesic active contour (GAC) model with active contours without edges (ACWE) model, and can be used to segment images corrupted by multiplicative gamma noise. By adding a diffusion term into the level set evolution (LSE) equation of the proposed model, we construct a reaction-diffusion (RD) equation, which can gradually regularize the level set function (LSF) to be piecewise constant in each segment domain and gain the stable solution. We further transform the proposed model into a general ROF model by adding a proximity term ,and it can be solved by a fast denoising algorithm proposed by Jia-Zhao or soved by BM3D and NLM denoising algorithm, which also provide a unified solution framework for formally generalized-ROF-like subproblems arising in multivariate splitting algorithms.