Learning computationally efficient approximations of complex image segmentation metrics

Image segmentation metrics have been extensively used in the literature to compare segmentation algorithms among each other, or relative to a ground-truth segmentation. Some metrics are easy to compute (e.g., Dice, Jaccard), others are more accurate (e.g., the Hausdorff distance) and may reflect local topology, but they are computationally demanding. While certain attempts have been made to create computationally efficient implementations of such complex metrics, in this paper we approach this problem from a radically different viewpoint. We construct approximations of a complex metric (e.g., the Hausdorff distance), combining a small number of computationally lightweight metrics in a linear regression model. We also consider feature selection, using sparsity inducing strategies, to restrict the number of metrics employed significantly, without penalizing the predictive power of the model. We demonstrate our methodology with image data from plant phenotyping experiments. We find that a linear model can effectively approximate the Hausdorff distance using even a few features. Our approach can find many applications, but is largely expected to benefit distributed sensing scenarios where the sensor has low computational capacity, whereas centralized processing units have higher computational capabilities.