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Medical image segmentation is one of the most challenging tasks in medical image analysis and has been widely developed for many clinical applications. Most of the existing metrics have been first designed for natural images and then extended to medical images. While object surface plays an important role in medical segmentation and quantitative analysis i.e. analyze brain tumor surface, measure gray matter volume, most of the existing metrics are limited when it comes to analyzing the object surface, especially to tell about surface smoothness or roughness of a given volumetric object or to analyze the topological errors. In this paper, we first analysis both pros and cons of all existing medical image segmentation metrics, specially on volumetric data. We then propose an appropriate roughness index and roughness distance for medical image segmentation analysis and evaluation. Our proposed method addresses two kinds of segmentation errors, i.e. (i) topological errors on boundary/surface and (ii) irregularities on the boundary/surface. The contribution of this work is four-fold: (i) detect irregular spikes/holes on a surface, (ii) propose roughness index to measure surface roughness of a given object, (iii) propose a roughness distance to measure the distance of two boundaries/surfaces by utilizing the proposed roughness index and (iv) suggest an algorithm which helps to remove the irregular spikes/holes to smooth the surface. Our proposed roughness index and roughness distance are built upon the solid surface roughness parameter which has been successfully developed in the

Roughness Index and Roughness Distance for Benchmarking Medical Segmentation