Hyun-Jin Park and Te-Won Lee,
A Hierarchical ICA Method for Unsupervised Learning of
Nonlinear Dependencies in Natural Images,
In C. G. Puntonet and A. Prieto eds., Proceedings of the Fifth International Conference on
Independent Component Analysis and Blind Signal Separation (ICA 2004),
Granada, Spain, No. 3195 in Lecture Notes in Computer Science, pp. 1253-1261, Springer-Verlag, September 22-24 2004.Capturing dependencies in images in an unsupervised manner is important for many image-processing applications and understanding the structure of natural image signals. Linear generative models such as independent component analysis (ICA) have shown to capture low level features such as oriented edges in images. However ICA only captures linear dependency due to its linear model constraints and its modeling capability is limited. We propose a new method for capturing nonlinear dependencies in natural images. It is an extension of the linear ICA method and builds on a hierarchical representation. It makes use of lower level linear ICA representation and a subsequent mixture of Laplacian distribution for learning the nonlinear dependencies. The model is learned via the EM algorithm and it can capture variance correlation and high order structures in a consistent manner. We visualize the learned variance structure and demonstrate applications to image segmentation and denoising.