李春明的LBF局部二值拟合能量驱动的隐式活跃轮廓模型

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Chunming Li的LBF（Local Binary Fitting）水平集模型是一篇重要的研究论文，关注于图像分割领域的改进方法。在图像处理中，准确地分割具有强度不均匀性的图像对于许多应用至关重要，如医学影像分析、目标检测等。传统的区域基主动轮廓模型，如分段常数模型，虽然在全局上处理图像结构有一定效果，但往往忽视了局部区域的图像信息，这限制了它们在处理复杂场景时的精确性。该论文的创新之处在于提出了一个基于区域的主动轮廓模型，特别强调利用局部图像信息。作者提出了一种名为"Local Binary Fitting Energy"（LBF能量函数），其核心是引入了一个带核函数，这个核函数能够有效地提取和融合局部图像特征。通过这种方式，LBF模型能够在处理强度不均匀的图像时，更加精确地反映局部细节，从而克服了传统分段常数模型的局限性。 LBF模型的优势在于它能够动态地调整轮廓形状，使其更好地适应图像中的边缘和纹理变化，特别是在图像的局部区域。这得益于其能量函数的设计，它不仅考虑了轮廓与物体边界的一致性，还充分考虑了邻域内的像素对比度信息。相比于其他主要的区域基模型，如PDE（偏微分方程）模型或者GrabCut等，LBF模型展示了更强的适应性和准确性。为了验证模型的有效性，论文进行了详细的实验比较，包括与PDE模型、GrabCut以及其他经典方法的性能对比，结果显示LBF模型在处理具有强度不均匀性的图像时，无论是分割精度还是速度上，都表现出显著的优势。因此，Chunming Li的LBF水平集模型为图像分割领域提供了一种实用且有效的技术手段，极大地推动了该领域的研究进展。

Implicit Active Contours Driven by Local Binary Fitting Energy

Chunming Li

, Chiu-Yen Kao

, John C. Gore

, and Zhaohua Ding

Institute of Imaging Science

Department of Mathematics

Vanderbilt University The Ohio State University

Nashville, TN 37232-2310, USA Columbus, OH 43210-1174, USA

{chunming.li,john.gore,zhaohua.ding}@vanderbilt.edu kao@math.ohio-state.edu

Abstract

Local image information is crucial for accurate segmen-

tation of images with intensity inhomogeneity. However, im-

age information in local region is not embedded in popular

region-based active contour models, such as the piecewise

constant models. In this paper, we propose a region-based

active contour model that is able to utilize image informa-

tion in local regions. The major contribution of this paper is

the introduction of a local binary ﬁtting energy with a kernel

function, which enables the extraction of accurate local im-

age information. Therefore, our model can be used to seg-

ment images with intensity inhomogeneity, which overcomes

the limitation of piecewise constant models. Comparisons

with other major region-based models, such as the piece-

wise smooth model, show the advantages of our method in

terms of computational efﬁciency and accuracy. In addi-

tion, the proposed method has promising application to im-

age denoising.

1. Introduction

Active contour models have been one of the most suc-

cessful methods for image segmentation [1, 3–7, 12]. The

existing active contour models can be categorized into two

classes: edge-based models [1, 4–6] and region-based mod-

els [2,9,10]. These two types of models both have their pros

and cons, and the choice of them in applications depends on

different characteristics of images.

Edge-based models utilize image gradient to stop the

evolving contours on the object boundaries. Typical edge-

based active contour models have an edge-based stopping

term and a balloon force term to control the motion of the

contour. The edge-based stopping term serves to stop the

contour on the desired object boundary. The balloon force

term is introduced to shrink or expand the active contour

so that the initial contour can be placed far away from the

desired object boundary. However, appropriate choice of

balloon force is sometimes difﬁcult. If the balloon force

is not large enough, the evolving contour may not able to

pass some narrow parts of the object. If the balloon force is

too large, the active contour is likely to pass through weak

object boundary.

Region-based active contour models have the following

advantages over edge-based models. First, region-based

models do not utilize the image gradient and therefore have

better performance for the image with weak object bound-

aries. Second, they are signiﬁcantly less sensitive to the

location of initial contours. One of the most popular region-

based active contour models is Chan-Vese model [2]. This

model has been successful for images with two regions,

each having a distinct mean of pixel intensity. In [11], Vese

and Chan extended their earlier work in [2] by using a mul-

tiphase level set formulation, in which multiple regions can

be represented by multiple level set functions. These mod-

els are called piecewise constant (PC) models, since they

assume that an image consists of statistically homogeneous

regions. However, the regions of interest in images are often

not statistically homogeneous, and therefore the PC models

are not applicable to those types of images.

To handle more general scenario, Vese and Chan [11]

and Tsai et al. [10] proposed two similar region-based ac-

tive contour models, aiming at minimization of Mumford-

Shah functional [8]. In [11], Vese and Chan proposed a

piecewise smooth (PS) model, which overcomes the limita-

tion of their original work [2]. But these methods are com-

putationally inefﬁcient. The technique proposed by Tsai et

al. [10] can address the segmentation of images with in-

tensity inhomogeneity. However, the computation in their

method is also expensive. As proposed in [10], one way to

reduce the computational cost is to use a contour near the

object boundaries as the initial contour. In their method,

such initial contour is obtained by a preliminary segmenta-

tion using other active contour models, such as Chan and

Vese’s PC model. However, for images with intensity inho-

mogeneity, PC model can result in a contour that is still far

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