Computationally efficient modeling of imagery using scaled, extracted principal components

Abstract

A computationally efficient modeling system for imagery scales both the original image and corresponding principal component tiles in the same proportion to be able to extract scaled principal components. The system includes recovery of feature weights for the image model by extracting the weights from the reduced size principal component tiles. The use of the reduced size tiles to derive weights dramatically reduces computer overhead both in the generation of the files and in the generation of the weights, and is made possible by the fact that the weights from the scaled down tiles are nearly equal to the weights of the tiles associated with the full size image. The subject system thus reduces computation and the number of bits required to represent features by first scaling the image and then tiling the image in the same proportion. In one embodiment, the scaled down tiles are used as training exemplars used to generate the principal components.

1. A method for modeling an image comprising the steps of:
 tiling an image at a predetermined scale to form small tile segments of the image;  
 combining the small segments of the image into a data matrix extracting principal components of the data matrix in terms of principal component feature tiles;  
 generating a set of coefficient weights corresponding to the principal component tiles;  
 scaling the principal component tiles to reduce the data therewith;  
 transmitting from a transmitting side the scaled principal component tiles and the weights associated with each image segment to a remote location;  
 interpolating the principal component tiles at the remote location to obtain full-scale principal component tiles;  
 computing a weighted sum of full-scale principal component tiles for each segment to obtain a coarse image at full scale;  
 constructing a coarse image at the transmitting side;  
 obtaining the difference between the original image and the coarse image at the transmitting side to obtain a residual image;  
 selecting a finer scale for the residual image;  
 producing finer scale residual image tiles from the finer scale residual image;  
 obtaining from the finer scale residual image tiles a finer set of principal component tiles;  
 forming a weighted sum of the finer-scaled principal component tiles to represent each residual image segment;  
 transmitting to the remote location the newly-obtained finer principal component tiles and the new weights associated with each residual image segment;  
 reconstructing the residual image at the remote location from the transmitted new, finer principal component tiles and the new weights associated therewith; and,  
 at the remote location summing the coarse and residual images to obtain an improved image representation.  
 
     
     
       2. A method of modeling an image, the method comprising:
   generating reduced - size image tiles from an original image in a same proportion as a scaled image of the original image;        transforming the reduced - size image tiles into corresponding reduced - size principal component tiles;        extracting a set of weights corresponding to the reduced - size image tiles from the reduced - size principal component tiles; and        generating an image approximation of the original image from the reduced - size principal component tiles and the extracted weights.     
     
     
       3. The method of  claim 2 , further comprising scaling the original image before generating reduced- size image tiles.   
     
     
       4. The method of  claim 3 , wherein the scaling reduces the original image by half. 
     
     
       5. The method of  claim 2 , further comprising combining the reduced- size image tiles into a data matrix.   
     
     
       6. The method of  claim 2 , wherein extracting the set of weights corresponding to the reduced- size image tiles from the reduced - size principal component tiles comprises multiplying reduced - size principal component tiles and a corresponding segment of the original image.   
     
     
       7. The method of  claim 2 , further comprising communicating the reduced- size principal component tiles and the extracted weights.   
     
     
       8. The method of  claim 2 , further comprising obtaining from a finer scale residual image tiles a finer set of principal component tiles. 
     
     
       9. The method of  claim 8 , further comprising forming a weighted sum of the finer set of principal component tiles to represent each residual image segment. 
     
     
       10. The method of  claim 9 , further comprising communicating the finer set of principal component tiles and the new weights associated with each residual image segment. 
     
     
       11. The method of  claim 9 , further comprising reconstructing the residual image from the finer set of principal component tiles and the new weights associated therewith. 
     
     
       12. The method of  claim 11 , further comprising summing the coarse and residual images to obtain an improved image representation. 
     
     
       13. A method of modeling an image, the method comprising:
   obtaining a difference between an original image and a coarse image, the difference defining a residual image;        producing finer scale residual image tiles from a finer scale residual image of the residual image;        obtaining from the finer scale residual image tiles a finer set of principal component tiles;        forming a weighted sum of the finer set of principal component tiles to represent each residual image segment;        constructing a reconstructed image from the finer set of principal component tiles and associated weights; and        summing the coarse image and reconstructed image to obtain an improved image representation.     
     
     
       14. The method of  claim 13 , further comprising scaling the original image before obtaining the difference between the original image and a coarse image. 
     
     
       15. The method of  claim 14 , wherein the scaling reduces the original image by half. 
     
     
       16. The method of  claim 13 , further comprising communicating the finer set of principal component tiles and the new weights associated with each residual image segment. 
     
     
       17. The method of  claim 16 , wherein constructing the reconstructed image and summing the coarse image and reconstructed image are done at a remote location. 
     
     
       18. A system for modeling an image, the system comprising:
   an interface configured to receive an original image; and        a processor with programmed instructions to:        generate reduced - size image tiles from the original image in a same proportion as a scaled image of the original image;        transform the reduced - size image tiles into corresponding reduced - size principal component tiles;        extract a set of weights corresponding to the reduced - size image tiles from the reduced - size principal component tiles; and        generate an image approximation of the original image from the reduced - size principal component tiles and the extracted weights.     
     
     
       19. The system of  claim 18 , wherein the interface is configured to communicate the reduced- size principal component tiles and the extracted weights.   
     
     
       20. A computer program product including a computer readable medium having instructions stored thereon that when carried out by a computer cause the computer to perform the steps comprising:
   generating reduced - size image tiles from an original image in a same proportion as a scaled image of the original image;        transforming the reduced - size image tiles into corresponding reduced - size principal component tiles;        extracting a set of weights corresponding to the reduced - size image tiles from the reduced - size principal component tiles; and        generating an image approximation of the original image from the reduced - size principal component tiles and the extracted weights.