扩散在持久性上运行得很快

Chao Chen, H. Edelsbrunner
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引用次数: 31

摘要

将图像解释为欧几里得平面紧子集上的函数,我们通过扩散得到它的尺度空间,将图像扩展到整个平面上。这产生了一个1参数的函数族,或者定义为具有逐渐变宽的高斯核的卷积。我们证明了相应的1参数持久性图族具有随着时间趋于无穷而迅速趋近于零的范数。这一结果为尺度空间的实验观察提供了理论依据。我们希望这将导致相关计算机视觉方法的有针对性的改进。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Diffusion runs low on persistence fast
Interpreting an image as a function on a compact subset of the Euclidean plane, we get its scale-space by diffusion, spreading the image over the entire plane. This generates a 1-parameter family of functions alternatively defined as convolutions with a progressively wider Gaussian kernel. We prove that the corresponding 1-parameter family of persistence diagrams have norms that go rapidly to zero as time goes to infinity. This result rationalizes experimental observations about scale-space. We hope this will lead to targeted improvements of related computer vision methods.
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