Fully-Connected CRFs with Non-Parametric Pairwise Potential

Neill D.F. Campbell, Kartic Subr, Jan Kautz; The IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2013, pp. 1658-1665


Conditional Random Fields (CRFs) are used for diverse tasks, ranging from image denoising to object recognition. For images, they are commonly defined as a graph with nodes corresponding to individual pixels and pairwise links that connect nodes to their immediate neighbors. Recent work has shown that fully-connected CRFs, where each node is connected to every other node, can be solved efficiently under the restriction that the pairwise term is a Gaussian kernel over a Euclidean feature space. In this paper, we generalize the pairwise terms to a non-linear dissimilarity measure that is not required to be a distance metric. To this end, we propose a density estimation technique to derive conditional pairwise potentials in a nonparametric manner. We then use an efficient embedding technique to estimate an approximate Euclidean feature space for these potentials, in which the pairwise term can still be expressed as a Gaussian kernel. We demonstrate that the use of non-parametric models for the pairwise interactions, conditioned on the input data, greatly increases expressive power whilst maintaining efficient inference.

Related Material

author = {Campbell, Neill D.F. and Subr, Kartic and Kautz, Jan},
title = {Fully-Connected CRFs with Non-Parametric Pairwise Potential},
booktitle = {The IEEE Conference on Computer Vision and Pattern Recognition (CVPR)},
month = {June},
year = {2013}