Journal of Sensors

Volume 2018, Article ID 6269214, 17 pages

https://doi.org/10.1155/2018/6269214

## An Efficient Multi-Scale Local Binary Fitting-Based Level Set Method for Inhomogeneous Image Segmentation

School of Aeronautics and Astronautics, University of Electronic Science and Technology of China, Chengdu 611731, China

Correspondence should be addressed to Dengwei Wang; moc.621@iewgnedw

Received 28 February 2018; Revised 23 June 2018; Accepted 28 June 2018; Published 5 August 2018

Academic Editor: Giovanni Diraco

Copyright © 2018 Dengwei Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

An efficient level set model based on multiscale local binary fitting (MLBF) is proposed for image segmentation. By introducing multiscale idea into the LBF model, the proposed MLBF model can effectively and efficiently segment images with intensity inhomogeneity. In addition, by adding a reaction diffusion term into the level set evolution (LSE) equation, the regularization of the level set function (LSF) can be achieved, thus completely eliminating the time-consuming reinitialization process. In the implementation phase, in order to greatly improve the efficiency of the numerical solution of the level set segmentation model, we introduce three strategies: The first is the additive operator splitting (AOS) solver which is used for breaking the restrictions on time step; the second is the salient target detection mechanism which is used to achieve full automatic initialization of the LSE process; the third is the sparse filed method (SFM) which is used to restrict the groups of pixels that need to be updated in a small strip region. Under the combined effect of these three strategies, the proposed model achieves very high execution efficiency in the following aspects: contour location accuracy, speed of evolution convergence, robustness against initial contour position, and robustness against noise interference.

#### 1. Introduction

In the process of researching and applying images, people tend to be interested only in certain parts of the image, often referred to as target or foreground; they generally correspond to specific regions of the image that have unique properties. In order to identify and analyze the target, these areas need to be separated and extracted, and then it is possible to make further use of the target, such as feature extraction and measurement. Image segmentation is the technique and process of segmenting an image into distinct regions and extracting interesting objects. Image segmentation is the key step from image processing to image analysis, and it is also a basic computer vision technology. Image segmentation has been paid great attention for many years; so far, a lot of image segmentation algorithms [1–5] have been proposed. In particular, the active contour models [6–7] have been widely used because they are able to provide smooth and closed boundary contours as segmentation results. The level set method [8] is an implicit representation of active contours. Compared to explicit active contour models [6, 9] which utilize parametric equations to represent evolving contours, level set methods represent the evolving contours as the zero level set of a higher-dimensional function, thus making them numerically stable and easily able to handle topological changes. Without loss of generality, we can classify the level set-based active contour models into two categories: the edge-based models [7, 9–11] and the region-based models [12–16]. The edge-based model uses the gradient information of the image to construct the driving force required for the evolution process. Such models are not only sensitive to noise interference but also difficult to detect weak target boundaries. In addition, the final output is heavily dependent on the initial position of the contour. The region-based model constructs the driving force needed for the evolution process based on the regional statistical information of the image. Compared with the edge-based methods, such methods have the following advantages: (1) They do not rely on the gradient information of the image, so they can segment the weak edges, and (2) because the region information adopted is global, it is usually robust to noise. One of the most successful region-based models is the Chan-Vese (CV) model [12], which has been widely used in binary phase segmentation with the assumption that each image region is statistically homogeneous. However, the homogeneity assumption cannot precisely describe the intensity distribution of region with intensity inhomogeneity. Thus, it often fails to segment the images with intensity inhomogeneity.

In order to overcome the segmentation difficulty caused by the intensity inhomogeneity, the researchers have proposed some local region-based segmentation models: they are the local binary fitting (LBF) model [17], the local Gaussian distribution fitting (LGDF) model [18], the local image fitting (LIF) model [19], and so on. These methods generally believe that the images with intensity inhomogeneity satisfy the assumption of homogeneity within a very small local region; that is, within a sufficiently small local image region, we can assume that the intensity of the image is approximately statistically uniform. Thus, by fitting the given image in the sense of local region rather than global region, they can segment the images with slight inhomogeneity.

In practical implementation, they generally use a statistical function with a fixed scale to measure the characteristic parameters of the local region centered at the current sampling point. However, the degree of inhomogeneity between different local regions is usually inconsistent; that is to say, the nonlinear phenomenon of inhomogeneity is very common. Therefore, the practice of fixing the scale for all local regions does not apply to the images with severe inhomogeneity. In view of the universality of the aforementioned issues, to improve the segmentation performance of severe inhomogeneous images, we need to introduce multiscale idea into our model framework.

In this paper, we propose a level set model based on MLBF by introducing the idea of multiscale modeling into the original LBF model and apply it to the practice of inhomogeneous image segmentation. Firstly, an implicit scheme called AOS [20] is utilized to break the time-step limitation of traditional explicit schemes. Under this numerical implementation strategy, the iterative process can take a larger time step, so the evolution curve can quickly converge to the real target contour. Secondly, an automatic initialization strategy driven by a salient target detection mechanism is adopted. By performing a CV [12] model-based segmentation operation on the output of the salient object detection algorithm, we can get the initial curve required for the evolution process. This process is completely automated and does not require any form of human involvement. Thirdly, a level set function update strategy called SFM [21] is used to minimize the number of pixels of the level set function that need to be updated in each iteration. Under the SFM framework, the object to be updated for each iteration is only one-pixel width; thus, the SFM is an extreme narrowband [22, 23] strategy. Obviously, this strategy can further accelerate the evolution of the level set function. Fourthly, to further control the smoothness of the evolving curve and avoid the oversegmentation phenomenon, the regularization term is included in the energy functional. Finally, the multiscale segmentation is performed by minimizing the new formed level set energy functional.

The remainder of this paper is organized as follows. Section 2 is a brief description of the background. Section 3 presents the proposed model. Section 4 gives the three implementation strategies adopted in this paper. Section 5 validates the proposed model by extensive experiments and discussions on a lot of images. Last, conclusions are drawn in Section 6.

#### 2. Background

##### 2.1. Level Set Method

The level set methods implicitly represent the planar closed curve C by the zero level set of a Lipschitz function , such that if the point is inside *C*, if is outside *C*, and if is on *C*.

The variable in the expression indicates that the level set function changes with time, and its evolutionary process can be expressed by the following equation: where “” represents the gradient operator, is the speed function of the evolutionary process, and is the LSF.

The variational LSF considers LSE as a problem of minimization of certain energy functional , that is,

By using different energy terms to express the information components related to the evolutionary process, the active contours will be freely changed for different application purposes. Thus, the variational level set methods are convenient for developing new segmentation models and have received great attention in recent years.

The core idea of the level set method is as follows: when dealing with the evolution of the plane contour, the level set method does not directly track the position of the active contour, but updates the LSF through the evolution equation shown in (1) and then achieves the purpose of updating the active contour hidden in the LSF [8]. The biggest advantage of this curve evolution style is that the LSF remains a valid function even if the topological change (splitting or merging) occurs in the closed curve which is hidden in the LSF. Figure 1 shows an example of the LSE; the first row represents the three states in the LSE process, and the second is the zero level set curve corresponding to the first row. From this diagram, we can find that the topological structure changes of the evolving curve can be well handled (the topological change here is splitting type) by using the level set expression.