html5-img
1 / 27

Analysis of Spatio-chromatic Decorrelation for Colour Image Reconstruction

Analysis of Spatio-chromatic Decorrelation for Colour Image Reconstruction. School of Computing Science, Simon Fraser University, Canada. Mark S. Drew and Steven Bergner. {mark/sbergner}@cs.sfu.ca. I. Overview. - Use of PCA vs. ICA — what’s the difference? - How do you do ICA?

donnel
Download Presentation

Analysis of Spatio-chromatic Decorrelation for Colour Image Reconstruction

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Analysis of Spatio-chromatic Decorrelation for Colour Image Reconstruction School of Computing Science, Simon Fraser University, Canada Mark S. Drew and Steven Bergner {mark/sbergner}@cs.sfu.ca

  2. I. Overview - Use of PCA vs. ICA — what’s the difference? - How do you do ICA? - What does this have to do with images? - The objective: best characterize image blocks using ICA on color image block data == spatio (blocks are 16x16, say)-chromatic (x3); assign bits in bit allocation according to the importance of each ICA coefficient  data compression.

  3. Best characterize image colour and spatial information. Colour:we think of using PCA (Principal Component Anaysis): discover main colour axes. Is this best, given our objective? Spatial: use spatial Fourier filters? Gabor wavelets? Etc. Here, we’ll use ICA (Independent Component Anaysis) to derive best colour and spatialdecomposition at once, for decorrelation, compression, and reconstruction.

  4. II. ICA  What is it? ICA is a form of “Blind Source Separation”  To explain, consider audio signals (in an Imaging conference!). Consider 2 speakers, and 2 microphones: s2 s1 x2 x1 -sources -data

  5. Can we disentangle s1, s2from measured data x1, x2 ? == The “cocktail party problem”. An example:

  6. Order and sign not determined. ICA:

  7. What about PCA?  Writing the signals in terms of reduced set of sourcess1, s2, s3, . . ., for higher-dimensional data, we can do a better job in compression.

  8. mixing matrix separating matrix III. ICA  How to do it? (xwas 2xN in the audio example.) Model:

  9. Driving idea for finding sources:s1, s2are statistically independent == information about one gives no knowledge re. the other. Not just uncorrelated: covariance = 0 ==PCA

  10. joint pdf  for any functions , ! useful for solving. If independentas well, the pdf is separable: marginal pdf’s which implies

  11. So, to do ICA, start with uncorrelated signals (using PCA) == simplifies. Main tool: Non-Gaussian is independent. Central Limit Theorem: the sum of two independents is more like a Gaussian than is either one. So  we have sums . To get s, make a linear combination of x’s that is as non-Gaussian as possible.

  12. One way: (…many others) A Gaussian has zero kurtosis. For zero mean y, Rescale y to variance=1:  just use We seek a signal that maximizes kurtosis.

  13. Algorithm  “whiten” the data: zero mean, + linear transform to make uncorrelated,variance=1. First, PCA: orthogonal U with In the new coordinate system, Why? Now with orthogonal simpler to search for.

  14. Algorithm • whiten x • -we seek a column w of orthogonal W, with , • that maximizes kurtosis: Euler eqn.: 1. Initialize w randomly, with 2. 3. 4. stop when Code

  15. Matlab

  16. IV. ICA for Images Previous work: Greyscale and colour imagery using PCA and ICA . For colour images, x could be 3-vector pixels. But get spatial as well if use n  n tiles (nice illustration in Süsstrunk et al., CGIV’04 [using PCA on raw CFA data]) We show here that compression is better using ICA+colour+spatial info.

  17. ICA(162x1 greyscale data) 16 x 16 greyscale tiles ICA finds “sparse” features: localization in space

  18. With colour: PCA vs. ICA (3x1 data) (no spatial information)

  19. PCA vs. DCT(4x4 x3 data) • less axis-aligned • ordering by variance-accounted-for is different: pure colour axes appear first PCA (4x4 x3) • pure colour axes appear later, after luminance frequencies • separates colour from luminance DCT (4x4 x3) • Colour: luminance, • blue-yellow, red-green

  20. PCA vs. ICA • localization in frequency PCA (4x4 x3) again • colour less separate from spatial information • combined localization in space and frequency • patterns not rectangular more like Gabor functions (Gaussian-modulated sine functions) ICA (4x4 x3)

  21. ICA (4x4) ICA (5x5) ICA (8x8) ICA (16x16)

  22. Colourvs.Greyscale: Compression performance Better quality SNR Greyscale Colour (Generic basis) - Higher reconstruction quality (SNR) for larger patches - Colour has better quality than grey, at equal compression

  23. Better quality ICA vs. PCA (Specific basis: image = ) PCA ICA - ICA much better than PCA: higher compression for same SNR - ICA increased quality with larger patches, for equal compression

  24. ICA vs. PCA • ICA does better separating axes such that they influence each other least •  better entropy coding • Colour aids in compression • Large patch sizes and low rate encoding  At equal compression, SNR (quality) better for ICA

  25. ICA PSNR= 35.55 DCT: PSNR= 31.97 ICA vs. PCA: Image reconstruction (compression ratio: 1:12)

  26. Orig ICA DCT --blocking Another image  7:1 DCT: PSNR= 31.40 ICA PSNR= 39.69

  27. ICA (6x6x6) PCA (6x6x6) The Future: Video Bases [submitted]

More Related