Rémi Giraud, Vinh-Thong Ta, Nicolas Papadakis. Robust Shape Regularity Criteria for Superpixel Evaluation. ICIP, 2017.

Giraud et al. propose a new measure to evaluate superpixel regularity. The main motivation of their work is that the current measure, namely compactness, which compares the superpixel area to a circle area with the same perimeter is not ideal for superpixels and images – as there is a clear prior towards rectangular or polygonal superpixels and these should also be evaluated as being regular. Giraud et al. Then introduce the shape regularity criterion (SRC) which is computed as the multiplication of three “sub-measures” (per superpixel, before averaging):

  • Solidy: solidity computes the fraction of superpixel area and convex hull (of the superpixel) area; only convex shapes have a solidity of one.
  • Balanced repartition: This measure can be seen as evaluating the distribution of pixels around the superpixel center. It is computed as the square root of the minimum of standard deviation in x and y directions divided by their maximum; therefore, it is one only if the distribution in x and y direction is the same.
  • Contour smoothness: This measure is computed as the fraction of perimeter pixels of a superpixel's convex hull and the actual perimeter pixel; it is significantly smaller than one for very noisy superpixels.

Overall, Figure 1 illustrates the newly introduced measure. Unfortunately, they do not include many algorithms in their experimental evaluation, see the paper.

Figure 1: Solidity (SO), balanced repartition ($V_{xy}$) and contour smoothness (CO) as well as the final measure (SRC) for a set of common shapes.

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