Disjunctive Normal Parametric Level Set With Application to Image Segmentation

Abstract

Level set methods are widely used for image segmentation because of their convenient shape representation for numerical computations and capability to handle topological changes. However, in spite of the numerous works in the literature, the use of level set methods in image segmentation still has several drawbacks. These shortcomings include formation of irregularities of the signed distance function, sensitivity to initialization, lack of locality, and expensive computational cost, which increases dramatically as the number of objects to be simultaneously segmented grows. In this paper, we propose a novel parametric level set method called disjunctive normal level set (DNLS), and apply it to both two-phase (single object) and multiphase (multiobject) image segmentations. DNLS is a differentiable model formed by the union of polytopes, which themselves are created by intersections of half-spaces. We formulate the segmentation algorithm in a Bayesian framework and use a variational approach to minimize the energy with respect to the parameters of the model. The proposed DNLS can be considered as an open framework that allows the use of different appearance models and shape priors. Compared with the conventional level sets available in the literature, the proposed DNLS has the following major advantages: it requires significantly less computational time and memory, it naturally keeps the level set function regular during the evolution, it is more suitable for multiphase and local region-based image segmentations, and it is less sensitive to noise and initialization. The experimental results show the potential of the proposed method.

Research on improved level set image segmentation method

“…In Eq (15), δ(ϕ) is the Dirac function and H(−ϕ) is the Heaviside function in Eq (16), and g is the edge guide function.…”

“…The concept of balancing the thrust and image contour strength of the DRLSE model for contour segmentation was used to redefine the contour convergence / divergence forces to make it more feasible for complex boundaries [ 15 ]. Mesadi Fitsum et al proposed a new parametric level set method, the Disjunctive Normal Level Set (DNLS), and applied it to two-phase (single-object) and multiphase (multi-object) image segmentation formulated segmentation algorithms in a Bayesian framework and used variational methods to minimize the energy relative to the model parameters [ 16 ]. Jiang Xiaoliang proposed a level set image segmentation algorithm with a local cross-entropy measure of fuzzy C-means and its simplified model.…”

Image Segmentation with Pseudo-marginal MCMC Sampling and Nonparametric Shape Priors

“…Kim et al [21] and Cremers et al [8] incorporate nonparametric density estimation based shape priors into the segmentation process using level sets. Therefore, these methods and their variants can learn "multimodal" shape densities, which can be encountered in problems involving shape densities containing multiple classes of shapes [14], [6], [31], [28], [9], [23], [11], [24]. These methods minimize an energy function and find a solution at a local optimum.…”