基于局部主成分分析的曲线演化:分而治之方法。

Vikram Appia, Balaji Ganapathy, Anthony Yezzi, Tracy Faber
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引用次数: 13

摘要

提出了一种新的基于局部主成分分析(PCA)的曲线演化方法,该方法在图像的各个目标区域(分割)内对分割曲线进行半局部演化,然后将这些局部精确的分割曲线组合在一起得到全局分割。我们方法的训练数据由训练形状和相关的辅助(目标)掩模组成。掩模表明形状的各个区域在局部表现出高度相关的变化,这可能与全球形状的遥远部分的变化相当独立。因此,从某种意义上说,我们正在聚类训练数据集中显示的变化。然后,我们使用参数模型隐式地将每个局部分割曲线表示为通过表示训练形状和掩模作为有符号距离函数集合获得的局部形状先验的组合。我们还提出了一种参数化模型,将局部进化的分割曲线组合成单一的混合(全局)分割。最后,我们结合这些半局部和全局参数的演化来最小化目标能量函数。由此产生的算法提供了一个全局精确的解决方案,它保留了局部形状的变化。我们给出了一些结果来说明我们的方法如何比具有全全局PCA的传统方法表现得更好。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Localized Principal Component Analysis based Curve Evolution: A Divide and Conquer Approach.

We propose a novel localized principal component analysis (PCA) based curve evolution approach which evolves the segmenting curve semi-locally within various target regions (divisions) in an image and then combines these locally accurate segmentation curves to obtain a global segmentation. The training data for our approach consists of training shapes and associated auxiliary (target) masks. The masks indicate the various regions of the shape exhibiting highly correlated variations locally which may be rather independent of the variations in the distant parts of the global shape. Thus, in a sense, we are clustering the variations exhibited in the training data set. We then use a parametric model to implicitly represent each localized segmentation curve as a combination of the local shape priors obtained by representing the training shapes and the masks as a collection of signed distance functions. We also propose a parametric model to combine the locally evolved segmentation curves into a single hybrid (global) segmentation. Finally, we combine the evolution of these semilocal and global parameters to minimize an objective energy function. The resulting algorithm thus provides a globally accurate solution, which retains the local variations in shape. We present some results to illustrate how our approach performs better than the traditional approach with fully global PCA.

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