Scale-Sets Image Analysis
Scale-Sets Image Analysis
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DOI：
10.1007/s11263-005-6299-0
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发表时间：
2006-07
影响因子：
19.5
通讯作者：
L. Guigues;J. Cocquerez;H. L. Men
中科院分区：
文献类型：
--
作者：
L. Guigues;J. Cocquerez;H. L. Men
本文介绍了一种分段图像建模的多尺度理论，称为尺度集理论，它可以看作是一种面向区域的尺度空间理论。论文的第一部分研究了面向几何无偏区域的多尺度图像描述的一般结构，并引入了尺度集表示法，该表示法可以准确地处理这种描述。本文的第二部分讨论了根据能量最小化原理建立尺度集图像分析的方法。我们考虑划分问题的一个相当一般的公式，它涉及最小化基于两项的能量，形式为λC+D，其中D是拟合度项，C是正则化项。我们描述了这种能量是如何从近似建模的基本原理中产生的，并将它们与有损压缩问题中涉及的运算率/失真问题联系起来。然后，我们证明了这些能量的一个重要子集构成了一类多尺度能量，因为随着参数λ的增加，层级的最小割变得越来越粗。这使得我们可以设计一个快速的动态规划程序来找到这个最小割族的完整的标度集表示。然后考虑到提取最小割集的层次结构，我们最终得到了一种精确的、无参数的算法来构建尺度集图像描述，其截面构成了多尺度能量的向上全局最小值的单调序列，这被称为“尺度爬升”算法。该算法可以看作是沿尺度维度的延拓方法，也可以视为沿运行率/失真曲线的最小追踪。此外，该解决方案验证了线性标度不变性，其允许将标度参数的调整完全推迟到后续阶段。由于计算的原因，比例爬升算法被近似为一种成对区域合并方案：但是解的主要性质保持不变。文中给出了用Mumford-Shah的分段常数模型和一个变型得到的一些结果，并概述了所提出的多尺度分析的不同应用。
This paper introduces a multi-scale theory of piecewise image modelling, called the scale-sets theory, and which can be regarded as a region-oriented scale-space theory. The first part of the paper studies the general structure of a geometrically unbiased region-oriented multi-scale image description and introduces the scale-sets representation, a representation which allows to handle such a description exactly. The second part of the paper deals with the way scale-sets image analyses can be built according to an energy minimization principle. We consider a rather general formulation of the partitioning problem which involves minimizing a two-term-based energy, of the form λ C + D, where D is a goodness-of-fit term and C is a regularization term. We describe the way such energies arise from basic principles of approximate modelling and we relate them to operational rate/distorsion problems involved in lossy compression problems. We then show that an important subset of these energies constitutes a class of multi-scale energies in that the minimal cut of a hierarchy gets coarser and coarser as parameter λ increases. This allows us to devise a fast dynamic-programming procedure to find the complete scale-sets representation of this family of minimal cuts. Considering then the construction of the hierarchy from which the minimal cuts are extracted, we end up with an exact and parameter-free algorithm to build scale-sets image descriptions whose sections constitute a monotone sequence of upward global minima of a multi-scale energy, which is called the “scale climbing” algorithm. This algorithm can be viewed as a continuation method along the scale dimension or as a minimum pursuit along the operational rate/distorsion curve. Furthermore, the solution verifies a linear scale invariance property which allows to completely postpone the tuning of the scale parameter to a subsequent stage. For computational reasons, the scale climbing algorithm is approximated by a pair-wise region merging scheme: however the principal properties of the solutions are kept. Some results obtained with Mumford-Shah’s piece-wise constant model and a variant are provided and different applications of the proposed multi-scale analyses are finally sketched.