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arXiv 2202.04680cs.CVmath.FA

基于提升的变分多类分割算法:设计、收敛性分析及在医学影像中的应用实现

Lifting-based variational multiclass segmentation algorithm: design, convergence analysis, and implementation with applications in medical imaging

University of Innsbruck(因斯布鲁克大学);VASCage-Research Centre on Vascular Ageing and Stroke(VASCage血管老化与中风研究中心);MRC Laboratory of Molecular Biology(英国医学研究委员会分子生物学实验室);Medical University of Innsbruck(因斯布鲁克医科大学)

Nadja Gruber, Johannes Schwab, Sebastien Court, Elke Gizewski, Markus Haltmeier

AI总结:

本文提出一种基于提升的变分多类分割算法,通过最小化多通道能量泛函实现图像区域划分,证明了全局极小值的存在性及对噪声的稳定性与收敛性,并在脑脓肿分类和肿瘤生长等医学影像应用中取得良好效果。

摘要:

我们提出、分析并实现了一种变分多类分割方案,该方案将给定图像划分为多个具有特定性质的区域。我们的方法通过最小化一个结合不同通道信息的能量泛函来确定多个编码分割区域的函数。多通道图像数据可以通过使用特定的多通道滤波将图像提升到更高维特征空间来获得,或者也可以由所考虑的成像模态直接提供,例如RGB图像或多模态医学数据。实验结果表明,所提出的方法在各种场景中表现良好。特别是,针对两个医学应用展示了有前景的结果,分别涉及脑脓肿分类和肿瘤生长。作为主要理论贡献,我们证明了所提出能量泛函全局极小值的存在性,并展示了其对噪声输入的稳定性和收敛性。特别地,这些结果也适用于二值分割的特殊情形,并且这些结果在该特定情形下同样是新颖的。

英文摘要:

We propose, analyze and realize a variational multiclass segmentation scheme that partitions a given image into multiple regions exhibiting specific properties. Our method determines multiple functions that encode the segmentation regions by minimizing an energy functional combining information from different channels. Multichannel image data can be obtained by lifting the image into a higher dimensional feature space using specific multichannel filtering or may already be provided by the imaging modality under consideration, such as an RGB image or multimodal medical data. Experimental results show that the proposed method performs well in various scenarios. In particular, promising results are presented for two medical applications involving classification of brain abscess and tumor growth, respectively. As main theoretical contributions, we prove the existence of global minimizers of the proposed energy functional and show its stability and convergence with respect to noisy inputs. In particular, these results also apply to the special case of binary segmentation, and these results are also novel in this particular situation.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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