Below we list a few representative applications of GPCA. The intent is to show how one should properly customize the basic GPCA algorithms in different contexts or for different applications. Please contact the webmaster if you would like to list your application(s) here.
Sparse Image Representation via Hybrid Linear Models |
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The first step for many applications of image processing is to find a simple and efficient representation for images. To this end, we view the collection of (non-overlapping) blocks of an image (in either the spatial domain or the wavelet domain) as a collection of 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 for the image. The model can be effectively estimated via a new algebraic method known as generalized principal component analysis (GPCA). The hybrid and hierarchical structure of this model allows us to effectively extract and exploit multi-modal correlations among the imagery data at different scales. Despite a small overhead of the model, our careful and extensive experimental 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. For more details, please visit: http://decision.csl.illinois.edu/~weihong/ImageRepresentation.htm |
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Image Segmentation via Hybrid Linear Models |
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One can use the same method in image representation for image segmentation. We can choose a window block around every pixel of the image and view the block as a vector. By fitting a piece-wise linear model (i.e. a union of affine subspaces) to the collection of blocks, we obtain a segmentation of the image: Pixels are grouped in the same segment if and only if their block vectors belong to the same subspace. The segmentation result of the tiger image (shown on the left) is obtained by using windows of a block size 20x20. |
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Motion Segmentation |
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A classic problem in visual motion analysis is to estimate a motion model for a set of 2-D feature points as they move in a video sequence. However, most real world scenes contain mutiple objects exhibiting different motions. We propose algorithms to solve the challenging problem of fitting multiple motion models to every image frame of the sequence, without knowing which pixels are moving according to the same model, the so-called motion estimation and segmentation problem. For more details, please visit: http://www.vision.jhu.edu/motion.htm |
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Dynamic Texture |
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Textures such as grass fluttering in the wind and flares of the match exhibit specific dynamics and thus can be modeled as a linear dynamical system. The classical Brightness Constancy Constraint does not hold good for such sequences as they are not rigid and lambertian. We explore methods to exploit the dynamical model and achieve segmentation and estimation of motion of a camera viewing such sequences. | |
Hybrid System Identification |
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A system is considered to be hybrid if its dynamics can be described as both continuous and discrete. We characterize the observability properties of certain classes of hybrid systems and propose algorithms to recursively identify their parameters using input-output data. For more details, please visit: http://www.vision.jhu.edu/hybrid.htm |