Distance Regularized Level Set Evolution and Its Application to Image Segmentation

Abstract

Abstract-Level set methods have been widely used in image processing and computer vision. In conventional level set formulations, the level set function typically develops irregularities during its evolution, which may cause numerical errors and eventually destroy the stability of the evolution. Therefore, a numerical remedy, called reinitialization, is typically applied to periodically replace the degraded level set function with a signed distance function. However, the practice of reinitialization not only raises serious problems as when and how it should be performed, but also affects numerical accuracy in an undesirable way. This paper proposes a new variational level set formulation in which the regularity of the level set function is intrinsically maintained during the level set evolution. The level set evolution is derived as the gradient flow that minimizes an energy functional with a distance regularization term and an external energy that drives the motion of the zero level set toward desired locations. The distance regularization term is defined with a potential function such that the derived level set evolution has a unique forward-and-backward (FAB) diffusion effect, which is able to maintain a desired shape of the level set function, particularly a signed distance profile near the zero level set. This yields a new type of level set evolution called distance regularized level set evolution (DRLSE). The distance regularization effect eliminates the need for reinitialization and thereby avoids its induced numerical errors. In contrast to complicated implementations of conventional level set formulations, a simpler and more efficient finite difference scheme can be used to implement the DRLSE formulation. DRLSE also allows the use of more general and efficient initialization of the level set function. In its numerical implementation, relatively large time steps can be used in the finite difference scheme to reduce the number of iterations, while ensuring sufficient numerical accuracy. To demonstrate the effectiveness of the DRLSE formulation, we apply it to an edge-based active contour model for image segmentation, and provide a simple narrowband implementation to greatly reduce computational cost.Index Terms-Forward and backward diffusion, image segmentation, level set method, narrowband, reinitialization.

An interactive system of stereoscopic video conversion

“…Given an foreground object and the depth map of a key frame, we first directly warp the object contours to the non-key-frames according to the object motion, and use the warped curve as initialization of the object location, and then evolve the warped contour to the object boundary at the non-key-frames using an adapted Level set method based on [3]. We introduce the details in the following.…”

“…Eimg(φ) is the adapted term of the external energy in [3]. It depends upon the image data and depth map:…”

“…The energy functional ∆κ(φ) is a new added term to the original formulation proposed in [3]. Assuming that pixels on an object share similar depths, it is proposed to estimate accurate contours of foreground objects according to the gradient field of a depth map in addition to the intensity map.…”

Fast Region-based Active Contour Model Driven by Local Signed Pressure Force

“…The fundamental idea of ACM is to evolve a curve under some constraints from a given image to reach the boundaries of the desired objects, by minimizing energy functional. According to the energy, ACM are classified into two main categories: edge-based models [1][2][3][4] and region-based models [5][6][7][8].…”

An Automatic Mobile Cell Counting System for the Analysis of Biological Image

“…Other approaches used active contours [8] and level set method [9] for cell segmentation. Since the active contours method requires initialization of the boundary for each cell, it is difficult to make the process full automation.…”