Unsupervised Learning of Compositional Sparse Code for Natural Image Representation

This article proposes an unsupervised method for learning compositional sparse code for representing natural images. Our method is built upon the original sparse coding framework where there is a dictionary of basis functions often in the form of localized, elongated and oriented wavelets, so that each image can be represented by a linear combination of a small number of basis functions automatically selected from the dictionary. In our compositional sparse code, the representational units are composite: they are compositional patterns formed by the basis functions. These compositional patterns can be viewed as shape templates. We propose an unsupervised learning method for learning a dictionary of frequently occurring templates from training images, so that each training image can be represented by a small number of templates automatically selected from the learned dictionary. The compositional sparse code approximates the raw image of a large number of pixel intensities using a small number of templates, thus facilitating the signal-to-symbol transition and allowing a symbolic description of the image. The current form of our model consists of two layers of representational units (basis functions and shape templates). It is possible to extend it to multiple layers of hierarchy. Experiments show that our method is capable of learning meaningful compositional sparse code, and the learned templates are useful for image classification. Received October 23, 2012 and, in revised form, February 10, 2013. 2000 Mathematics Subject Classification. Primary 62M40. E-mail address: [email protected] E-mail address: [email protected] E-mail address: [email protected] E-mail address: [email protected] E-mail address: [email protected] c ©2013 Brown University 373 Licensed to Univ of Calif, Los Angeles. Prepared on Fri Aug 22 16:05:31 EDT 2014 for download from IP 169.232.212.167. License or copyright restrictions may apply to redistribution; see http://www.ams.org/license/jour-dist-license.pdf 374 YI HONG, ZHANGZHANG SI, WENZE HU, SONG-CHUN ZHU, AND YING NIAN WU