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.