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  Quarterly of Applied Mathematics
Quarterly of Applied Mathematics
Online ISSN 1552-4485; Print ISSN 0033-569X


Unsupervised learning of compositional sparse code for natural image representation

Authors: Yi Hong, Zhangzhang Si, Wenze Hu, Song-Chun Zhu and Ying Nian Wu
Journal: Quart. Appl. Math. 72 (2014), 373-406
MSC (2000): Primary 62M40
Published electronically: November 14, 2013
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Abstract: 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.

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Additional Information

Yi Hong
Affiliation: Department of Computer Science, University of California, Los Angeles, California 90024

Zhangzhang Si
Affiliation: Google Inc.

Wenze Hu
Affiliation: Department of Statistics, University of California, Los Angeles, California 90024

Song-Chun Zhu
Affiliation: Department of Statistics, University of California, Los Angeles, California 90024

Ying Nian Wu
Affiliation: Department of Statistics, University of California, Los Angeles, California 90024

PII: S 0033-569X(2013)01361-5
Received by editor(s): October 23, 2012
Received by editor(s) in revised form: February 10, 2013
Published electronically: November 14, 2013
Article copyright: © Copyright 2013 Brown University

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