Abstract

Oftentimes when one is dealing with digital color images it is desired that some sort of image processing be performed on the spatial information. Current methods require that one process each of the channels (also called planes or colors) of an image separately, which increases the number of computations significantly. A novel, to our knowledge, approach to reducing the number of channels in a color image is presented. The channel-reduction process is intended to facilitate such color image-processing situations essentially by the separation of the spectral information from the spatial information, as in a paint-by-numbers picture. In this case the image processing need be applied only to a single channel of data and the color added afterward. With a compression ratio of slightly less than 3:1 the method is not intended to compete with existing compression methods but rather to permit the processing of images in a compressed state.

© 2000 Optical Society of America

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References

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  1. A. R. Weeks, Fundamentals of Electronic Image Processing, Vol. PM32 of SPIE Monographs and Handbooks Series (SPIE Optical Engineering Press, Bellingham, Wash., 1996), Chap. 6, pp. 228–293.
    [CrossRef]
  2. R. A. Kirk, “Image compression method and apparatus employing principal component analysis,” U.S. patent5,301,241 (5April1994).
  3. M. Partridge, R. Calvo, “Fast dimensionality reduction and simple PCA,” Intell. Data Anal. 2(3) (1998); an electronic journal at www-east.elsevier.com/ida .

1998

M. Partridge, R. Calvo, “Fast dimensionality reduction and simple PCA,” Intell. Data Anal. 2(3) (1998); an electronic journal at www-east.elsevier.com/ida .

Calvo, R.

M. Partridge, R. Calvo, “Fast dimensionality reduction and simple PCA,” Intell. Data Anal. 2(3) (1998); an electronic journal at www-east.elsevier.com/ida .

Kirk, R. A.

R. A. Kirk, “Image compression method and apparatus employing principal component analysis,” U.S. patent5,301,241 (5April1994).

Partridge, M.

M. Partridge, R. Calvo, “Fast dimensionality reduction and simple PCA,” Intell. Data Anal. 2(3) (1998); an electronic journal at www-east.elsevier.com/ida .

Weeks, A. R.

A. R. Weeks, Fundamentals of Electronic Image Processing, Vol. PM32 of SPIE Monographs and Handbooks Series (SPIE Optical Engineering Press, Bellingham, Wash., 1996), Chap. 6, pp. 228–293.
[CrossRef]

Intell. Data Anal.

M. Partridge, R. Calvo, “Fast dimensionality reduction and simple PCA,” Intell. Data Anal. 2(3) (1998); an electronic journal at www-east.elsevier.com/ida .

Other

A. R. Weeks, Fundamentals of Electronic Image Processing, Vol. PM32 of SPIE Monographs and Handbooks Series (SPIE Optical Engineering Press, Bellingham, Wash., 1996), Chap. 6, pp. 228–293.
[CrossRef]

R. A. Kirk, “Image compression method and apparatus employing principal component analysis,” U.S. patent5,301,241 (5April1994).

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Figures (5)

Fig. 1
Fig. 1

(a) Traditional method of processing the spatial information in a color image and (b) the proposed channel-reduction method. The channel-reduction method essentially removes the spectral information from an image, leaving only the spatial information to be processed. The spectral information is reapplied after processing is complete. T represents the spatial filter.

Fig. 2
Fig. 2

Example of the two types of block that are typically encountered in a color image. In block 2 the spatial information is contained in the intensity of the pixels, and projecting these pixels onto vector u2 is satisfactory. When vector u1 is used, in block 1 the spatial information is lost completely, and the color is misrepresented. However, the spatial information is preserved if vector u3 is used instead.

Fig. 3
Fig. 3

Example of a sharp image: (a) the original image, (b) the crayon method of channel reduction, (c) the crazy crayon method of channel reduction. The image size is 350 × 250 pixels, and the block size is 15 × 15 pixels.

Fig. 4
Fig. 4

(a) An uncompressed color image requires 3NM bytes, assuming an image size of N × M and a bit depth of 8. (b) Using the channel-reduction method reduces the image-storage requirements to nearly one third of the original size if nm > 3.

Fig. 5
Fig. 5

Calculation of the number of flops required for processing an N × M color image with an r × r filter by the channel-reduction method. In the channel-reduction method a block size of n × m and a subsampling factor of s within that block are assumed. The number of flops required for finding the eigenvector of interest is left as the variable W.

Equations (4)

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Xi=ri gi bi.
K=XTX=rTrrTgrTbgTrgTggTbbTrbTgbTb,
s=Xu1.
R=X-μxTX-μx.

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