A geometric hidden Markov tree wavelet model
A geometric hidden Markov tree wavelet model
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DOI：
10.1117/12.506853
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发表时间：
2003-08
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影响因子：
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通讯作者：
J. Romberg;M. Wakin;Hyeokho Choi;Richard Baraniuk
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文献类型：
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作者：
J. Romberg;M. Wakin;Hyeokho Choi;Richard Baraniuk
在过去的几年里，人们已经清楚地看到，传统的基于小波的图像处理算法和模型在处理边缘轮廓方面存在显着缺陷。标准建模范式利用了这样一个事实，即表示图像中平滑区域的小波系数往往具有较小的幅度，并且小波变换的多尺度性质意味着这些小系数将跨尺度持续存在（典型的例子是古老的零树编码器）。然而，图像中的边缘轮廓导致越来越多的大幅度小波系数，因为我们通过尺度向下移动到更精细的分辨率。但是如果轮廓是平滑的，当我们放大它们时，它们会变得简单，并且在精细尺度上可以很好地近似于直线。标准小波模型利用图像平滑区域的灰度规则性，但不利用轮廓的几何规则性。在本文中，我们建立了一个模型，占这种几何规律，通过捕捉沿着轮廓的复杂小波系数之间的依赖关系。几何隐马尔可夫树（GHMT）为每个小波系数（或小波系数的空间簇）分配对应于局部轮廓结构的线性近似的隐藏状态。复数小波变换的移位和旋转不变性属性允许GHMT对给定在指定方向存在线性边缘的每个系数的行为进行建模-给定状态的小波系数的行为。通过在四叉树中将状态连接在一起，GHMT将沿着轮廓的小波系数沿着联系在一起，并且还对轮廓本身跨尺度的行为进行建模。我们证明了该模型的有效性，将其应用到特征提取。
In the last few years, it has become apparent that traditional wavelet-based image processing algorithms and models have significant shortcomings in their treatment of edge contours. The standard modeling paradigm exploits the fact that wavelet coefficients representing smooth regions in images tend to have small magnitude, and that the multiscale nature of the wavelet transform implies that these small coefficients will persist across scale (the canonical example is the venerable zero-tree coder). The edge contours in the image, however, cause more and more large magnitude wavelet coefficients as we move down through scale to finer resolutions. But if the contours are smooth, they become simple as we zoom in on them, and are well approximated by straight lines at fine scales. Standard wavelet models exploit the grayscale regularity of the smooth regions of the image, but not the geometric regularity of the contours. In this paper, we build a model that accounts for this geometric regularity by capturing the dependencies between complex wavelet coefficients along a contour. The Geometric Hidden Markov Tree (GHMT) assigns each wavelet coefficient (or spatial cluster of wavelet coefficients) a hidden state corresponding to a linear approximation of the local contour structure. The shift and rotational-invariance properties of the complex wavelet transform allow the GHMT to model the behavior of each coefficient given the presence of a linear edge at a specified orientation --- the behavior of the wavelet coefficient given the state. By connecting the states together in a quadtree, the GHMT ties together wavelet coefficients along a contour, and also models how the contour itself behaves across scale. We demonstrate the effectiveness of the model by applying it to feature extraction.