The quantification of uncertainties in image segmentation based on the Mumford–Shah model is studied. The aim is to address the error propagation of noise and other error types in the original image to the restoration result and especially the reconstructed edges (sharp image contrasts). Analytically, we rely on the Ambrosio–Tortorelli approximation and discuss the existence of measurable selections of its solutions as well as sampling-based methods and the limitations of other popular methods. Numerical examples illustrate the theoretical findings.

中文翻译：

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使用 Mumford-Shah 能量的 Ambrosio-Tortorelli 近似进行图像分割中的不确定性量化

研究了基于 Mumford-Shah 模型的图像分割中不确定性的量化。目的是解决原始图像中的噪声和其他错误类型对恢复结果，尤其是重建边缘（清晰的图像对比度）的错误传播。在分析上，我们依赖 Ambrosio-Tortorelli 近似并讨论其解的可测量选择的存在以及基于采样的方法和其他流行方法的局限性。数值例子说明了理论发现。