Representing Images Using Nonorthogonal Haar-Like Bases
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Tensor Approximation Approach to Dimensionality Reduction
International Journal of Computer Vision
A prediction error compression method with tensor-PCA in video coding
MCAM'07 Proceedings of the 2007 international conference on Multimedia content analysis and mining
Spatial segmentation of temporal texture using mixture linear models
WDV'05/WDV'06/ICCV'05/ECCV'06 Proceedings of the 2005/2006 international conference on Dynamical vision
An approach to the compression of residual data with GPCA in video coding
PCM'06 Proceedings of the 7th Pacific Rim conference on Advances in Multimedia Information Processing
| Hi-index | 0.01 |
This paper introduces a simple and efficient representation for natural images. We partition an image into blocks and treat the blocks as vectors in a high-dimensional space. We then fit a piece-wise linear model (i.e. a union of affine subspaces) to the vectors at each down-sampling scale. We call this a multi-scale hybrid linear model of the image. The hybrid and hierarchical structure of this model allows us effectively to extract and exploit multi-modal correlations among the imagery data at different scales. It conceptually and computationally remedies limitations of many existing image representation methods that are based on either a fixed linear transformation (e.g. DCT, wavelets), an adaptive uni-modal linear transformation (e.g. PCA), or a multi-modal model at a single scale. We will justify both analytically and experimentally why and how such a simple multi-scale hybrid model is able to reduce simultaneously the model complexity and computational cost. Despite a small overhead for the model, our results show that this new model gives more compact representations for a wide variety of natural images under a wide range of signal-to-noise ratio than many existing methods, including wavelets.