Affinity functions in fuzzy connectedness based image segmentation II: Defining and recognizing truly novel affinities
Affinity functions in fuzzy connectedness based image segmentation II: Defining and recognizing truly novel affinities
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DOI：
10.1016/j.cviu.2009.09.005
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发表时间：
2010-01-01
影响因子：
4.5
通讯作者：
Udupa, Jayaram K.
中科院分区：
文献类型：
--
作者：
Ciesielski, Krzysztof Chris;Udupa, Jayaram K.
亲和函数-衡量图像中相邻拼块对如何强有力地挂在一起表示模糊连通性（FC）算法的核心方面（主要可变性参数），这是一类重要的图像分割模式。在本文中，我们提出了有史以来第一次的理论分析的两个标准的亲和力，同质性和对象特征，它们可以组合的方式，以及组合的版本是真正不同的。分析是基于等价亲和力的概念，其理论来自本文的同伴第一部分（Ciesielski和Udupa，在这个问题上）[11]。我们证明了基于同质性和基于对象特征的亲和力是等价的，分别，强度函数和罗森菲尔德的连通度的差商。我们还表明，这两个亲和力的定义中使用的许多参数是多余的，在这个意义上说，改变它们的值导致等效的亲和力。最后，我们分析了可能的方式相结合的不同组件的亲和力，导致非等效的亲和力。特别是，我们调查这些方法，当应用到基于同质性和基于对象特征的组件导致真正新颖的（非等价）的亲和力，以及这是如何影响不同的参数选择。由于本文的主要目标是通过正式的数学论证来识别等价的亲和函数，因此不需要大量的实验确认-它们显示出完全相同的FC分割-因此，仅提供了理论结果的相关示例。相反，我们主要集中在模糊连通性分割文献的角度内的理论结果。(C)2009 Elsevier Inc. All rights reserved.
Affinity functions - the measure of how strongly pairs of adjacent spels in the image hang together represent the core aspect (main variability parameter) of the fuzzy connectedness (FC) algorithms, an important class of image segmentation schemas. In this paper, we present the first ever theoretical analysis of the two standard affinities, homogeneity and object-feature, the way they can be combined, and which combined versions are truly distinct from each other. The analysis is based on the notion of equivalent affinities, the theory of which comes from a companion Part I of this paper (Ciesielski and Udupa, in this issue) [11]. We demonstrate that the homogeneity based and object feature based affinities are equivalent, respectively, to the difference quotient of the intensity function and Rosenfeld's degree of connectivity. We also show that many parameters used in the definitions of these two affinities are redundant in the sense that changing their values lead to equivalent affinities. We finish with an analysis of possible ways of combining different component affinities that result in non-equivalent affinities. In particular, we investigate which of these methods, when applied to homogeneity based and object-feature based components lead to truly novel (non-equivalent) affinities, and how this is affected by different choices of parameters. Since the main goal of the paper is to identify, by formal mathematical arguments, the affinity functions that are equivalent, extensive experimental confirmations are not needed - they show completely identical FC segmentations - and as such, only relevant examples of the theoretical results are provided. Instead, we focus mainly on theoretical results within a perspective of the fuzzy connectedness segmentation literature. (C) 2009 Elsevier Inc. All rights reserved.