A PDE approach to image smoothing and magnification using the Mumford-Shah functional

A. Tsai, A. Yezzi, A. Willsky
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引用次数: 3

Abstract

We first address the problem of simultaneous image segmentation and smoothing by approaching the Mumford-Shah (1989) paradigm from a curve evolution perspective. In particular we let a set of deformable contours define the boundaries between regions in an image where we model the data via piecewise smooth functions and employ a gradient flow to evolve these contours. Next, we generalize the data fidelity term of the original Mumford-Shah functional to incorporate a spatially varying penalty. This more general model leads us to a novel partial differential equation (PDE) based approach for simultaneous image magnification, segmentation, and smoothing.
使用Mumford-Shah函数的图像平滑和放大的PDE方法
我们首先通过从曲线演化的角度接近Mumford-Shah(1989)范式来解决同时图像分割和平滑的问题。特别是,我们让一组可变形的轮廓定义图像中区域之间的边界,我们通过分段平滑函数对数据进行建模,并使用梯度流来进化这些轮廓。接下来,我们推广原始Mumford-Shah函数的数据保真度项,以纳入空间变化的惩罚。这个更一般的模型使我们得到了一种新的基于偏微分方程(PDE)的方法,用于同时进行图像放大、分割和平滑。
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