Normalized Kemeny and Snell distance: a novel metric for quantitative evaluation of rank-order similarity of images

There are needs for evaluating rank order-based similarity between images. Region importance maps from image understanding algorithms or human observer studies are ordered rankings of the pixel locations. We address three problems with Kemeny and Snell´s distance (d_KS), an existing measure from ordinal ranking theory, when applied to images: its high-computational cost, its bias in favor of images with sparse histograms, and its image-size dependent range of values. We present a novel computationally efficient algorithm for computing d_KS between two images and we derive a normalized form d_KS with no bias whose range is independent of image size. For evaluating similarity between images that can be considered as ordered rankings of pixels, d_KS is subjectively superior to cross correlation.