  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 civil
engineering.
