变分高斯混合模型在图像分割算法中的应用

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"基于变分高斯混合模型的图像分割算法 (2014年)" 是一篇工程技术类论文，主要探讨了一种利用变分推断方法改进的高斯混合模型在图像分割中的应用。该算法通过贝叶斯混合高斯模型对图像特征建模，并解决了模型参数学习的问题。在传统的高斯混合模型中，参数估计通常依赖于采样法，这种方法计算量大且无法自动优化混合个数。论文提出的变分推断算法则有效地解决了这些问题。变分推断是一种确定性的近似方法，它通过迭代过程减小近似概率分布与目标分布之间的Kullback-Leibler(KL)散度，从而找到最优解。这一方法能根据图像数据自动确定合适的成分数量，解决了模型选择问题。特别地，如果对应分布属于指数族分布，变分推断算法将收敛至全局最优解。为了防止模型参数出现奇异情况，论文进一步将标准的高斯混合模型扩展到完整的贝叶斯框架中，将模型参数视为随机变量处理。这样可以提高模型的稳定性和适应性。论文的结构如下：第一部分简要介绍了高斯混合模型，并将其扩展到全贝叶斯模型；第二部分详细分析了变分推断的数学原理，包括如何寻找最优解；接下来的章节可能涉及算法的具体实现、实验设计以及与其他经典图像分割算法的比较。实验结果显示，该方法在Berkeley的自然图像集上得到的分割精度较高，性能表现优秀，证明了其在图像分割领域的有效性和优势。该研究对于理解和改进图像处理中的混合模型和变分推断技术具有重要的理论和实践价值。

第27卷第1期, 2014年1月宁波大学学报（理工版）首届中国高校优秀科技期刊奖

Vol.27 No.1, Jan. 2014 JOURNAL OF NINGBO UNIVERSITY ( NSEE ) 浙江省优秀科技期刊一等奖

Image Segmentation via Variational Mixture of Gaussions

ZHANG Yuan-yuan, ZHONG Yi-wei

( Faculty of Information Science and Technology, Ningbo University, Ningbo 315211, China )

Abstract: Gaussian mixture model (GMM) has been effectively used in image segmentation. In this case,

the features of an image are described by a mixture model with

K different components. However, how to

choose the number of mixture components

and estimate model parameters are still short of solutions.

Current algorithms such as maximum likelihood and sampling methods are known for their own limitations.

So we present an alternative algorithm based on Bayesian variational method and apply it in image

segmentation. This method works at less computational cost than sampling methods, and can also naturally

handle the model selection problem. In the model’s iterative process, the algorithm can automatically

determine the number of mixture components in view of the data collected. By comparing our method

against other classical segmentation methods on natural images acquired from Berkeley Segmentation Data

Set, it suggests that our method provides better performance on image segmentation.

Key words: image segmentation; variational inference; Gaussian mixture models; expectation-maximization

CLC number: TP391.41 Document code: A Article ID: 1001-5132（2014）01-0023-06

Image segmentation is an important problem in

computer vision which is aim to partition an image into

disjoint regions, after that the pixels in the same region

have similar visual characteristics. Recently, Gaussian

mixture model is such a useful mathematical model used

for unsupervised image segmentation

[1-3]

. This method

models the image with mixture of Gaussians, and the

segmentation is a process of assigning each pixel to the

component which it most likely belongs to. In such case,

image segmentation is converting to an inference

problem that optimizes model parameters to fit the data.

A common technique used to inference is Expectation-

Maximization (EM) algorithm which is an iterative

technique to get the maximum likelihood estimates

[2,4-5]

The key issue of EM algorithm is model selection

problem that is how to determine the number of compo-

nents in order to avoid over-fitting or under-fitting. If

the choice of number is inappropriate, the speed of

convergence will be very slow and the result of

clustering may be poor. Many information rules are

selected to try to solve this problem

[6-10]

, such as

Bayesian Information Criterion (BIC), Akaike Infor-

mation Criterion (AIC) which compute relative loss

information. But they do not know what the true model

is like, so with these rules we cannot explain the

accuracy in an absolute sense. Even if all the candidate

models are not fit well, these rules will not give any

hints. Another crucial problem is how to guarantee EM

algorithm to get the global optimum which is depends

on the initial value of models. Currently improved

method is to use K-means to get a rough estimate, and

then use this estimate as the initial value of EM

Received date: 2013−06−09. JOURNAL OF NINGBO UNIVERSITY ( NSEE ): http://journallg.nbu.edu.cn/

Foundation items: Supported by the National Natural Science Foundation of China (61175026); Discipline Project of Ningbo University (XKL09154).

The first author: ZHANG Yuan-yuan ( 1981− ), female, Ninghai Zhejiang, PhD, experimentalist, research domain: machine learning and computer vision.

E-mail: zhangyuanyuan@nbu.edu.cn

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