Colour Image Compression by Grey to Colour Conversion Mark S. Drew 1, Graham D. Finlayson 2, and Abhilash Jindal 3 1 Simon Fraser University 2 University of East Anglia 3 IIT Kanpur,

1. The problem: Can we use a map from Grey, onto Colour, so as to transmit/store just Grey + some parameters, and re- generate full Colour? Here we utilize a polynomial map, from achromatic information to each of R,G,B

2. Color Spaces Log-Geometric-Mean Luminance Mean Luminance HSV Color Space YIQ Color Space YCbCr Color Space AC1C2 Color Space HSV-Hue HSV-SatHSV-Value

3. Windowing Method Divide image into fixed-size windows Plot chrominance (2-D) vs. luminance for each window Polynomial regression of luminance onto chrominance Quantize coefficients obtained from regression Compress luminance information (e.g. JPEG)

4. Observation: Good performance for smooth color variations Error in case of an edge compressed 1: no edge 2: contains edge original chrom_1 chrom_2 { Box_1 (smooth)  Good regression!

2: contains edge chrom_1 chrom_2 { Box_2 (edge)  worse regression! 5. Observation: cont.

6. Pyramid Approach Polynomial regression of chrominance vs. luminance If PSNR < threshold Break image into four parts Repeat regression for each part If PSNR > threshold Go to next part

7. Segmentation Method: Segment input image Choose the pixels in one segment Polynomial regression of chrominance vs. luminance

8. Separate Sorting: Sort Chrominances of the image separately Make chunks of fixed number of pixels Polynomial regression of chrominance vs. luminance Sorted chrominance components (in log-geometric-mean colour space). Here, the original RGB image is shown with addressing according to sorting respectively the first and second chrominance channels.

9. Evaluation of Results: Peak Signal to Noise Ratio PSNR Spatial-CIELAB (S-CIELAB) Error ΔE S == a spatial blurring is applied to the colour image data to simulate the human visual system. Also, the blurring function is adjusted differently for three different colour planes according to human psychophysical measurements of colour appearance. Compression Rate  the Shannon entropy == quantize polynomial regression coefficients linearly over their maximum and minimum limit. Then use LB = Shannon entropy.

10. Comparision of Colour Spaces: PSNR vs. bits per pixel S-CIELAB Error ΔE vs. bits per pixel. Using simple windowing method: log-geometric-mean colour space is best colour space

11. Comparision of algorithms: performance for the idea of separately sorting each chrominance component is much better than all the other methods (using log-geometric-mean colour space)

12. Main conclusions: → Developed a much faster and quite efficient algorithm for image compression → Instead of de-correlating image luminance from chrominance, use the correlation between the luminance component of an image and its chromatic components → log-geometric-mean color space is best color space → separate sorting is best algorithm Future Work → Extend to video