A framework for comparing different image segmentation methods and its use in studying equivalences between level set and fuzzy connectedness frameworks.
A framework for comparing different image segmentation methods and its use in studying equivalences between level set and fuzzy connectedness frameworks.
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DOI：
10.1016/j.cviu.2011.01.003
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发表时间：
2011-06-01
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.
关键词：
在当前大量的图像分割文献中，算法之间似乎存在相当大的冗余，而严重缺乏允许它们的理论比较来建立它们的相似性、等效性或独特性的方法。本文试图填补这一空白。为了实现这一目标，我们认为：（1）每一个数字分割算法应该有一个定义良好的连续对应，称为其模型，这构成了一个渐近的图像分辨率时，走向无穷大;（2）两个这样的模型的平等，并建立了一个理论（渐近）等价的数字对应和。这样的比较是充分的理论价值，只有当每个涉及的算法，其模型被证明是一个渐近的。到目前为止，这样的证明并没有出现在文献中的任何地方，即使是在连续模型的数字化算法的情况下，如水平集分割算法。本文的主要目标是探索一条线的调查正式配对的数字分割算法与他们的渐近模型，证明这种关系的数学证明，并使用结果比较分割算法在这个一般的理论框架。作为实现这一总体目标的第一步，我们在这里证明了基于梯度的阈值模型是渐近的模糊连通性Udupa和Samarasekera分割算法与基于梯度的亲和力。我们还认为，在某种意义上说，是渐近的Malladi，Sethian和Vemuri的原始前传播水平集算法，从而建立了这两个特定的算法之间的理论等价性。这最后的等价性的实验证据也提供。
In the current vast image segmentation literature, there seems to be considerable redundancy among algorithms, while there is a serious lack of methods that would allow their theoretical comparison to establish their similarity, equivalence, or distinctness. In this paper, we make an attempt to fill this gap. To accomplish this goal, we argue that: (1) every digital segmentation algorithm should have a well defined continuous counterpart , referred to as its model, which constitutes an asymptotic of when image resolution goes to infinity; (2) the equality of two such models and establishes a theoretical (asymptotic) equivalence of their digital counterparts and . Such a comparison is of full theoretical value only when, for each involved algorithm , its model is proved to be an asymptotic of . So far, such proofs do not appear anywhere in the literature, even in the case of algorithms introduced as digitizations of continuous models, like level set segmentation algorithms. The main goal of this article is to explore a line of investigation for formally pairing the digital segmentation algorithms with their asymptotic models, justifying such relations with mathematical proofs, and using the results to compare the segmentation algorithms in this general theoretical framework. As a first step towards this general goal, we prove here that the gradient based thresholding model is the asymptotic for the fuzzy connectedness Udupa and Samarasekera segmentation algorithm used with gradient based affinity . We also argue that, in a sense, is the asymptotic for the original front propagation level set algorithm of Malladi, Sethian, and Vemuri, thus establishing a theoretical equivalence between these two specific algorithms. Experimental evidence of this last equivalence is also provided.
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