1. A New PCA-based Compression Method for Natural Color Images Arash Abadpour Dr. Shohreh Kasaei Mathematics Science Department Computer Engineering Department Sharif University of Technology, Tehran, Iran

2. Outline  Introduction Colorizing, Quad-Tree Decomposition, Color Space Dimension Reduction.  Method Homogeneity Criteria, Quad-Tree Decomposition, Bi-Tree Decomposition, Color Image Compression, Decompression.  Experimental Results Block Count Growth, Block Count, Samples, Peak Signal to Noise Ratio, Compression Ratio, Elapsed Time.

3. Colorizing  Many Modern Systems Produce Gray- Scale Images: MRI, CT-SCAN, Infrared, …  Color Images are More Preferred: Larger Amount of Information.  Conversion: Color to Grayscale: Trivial. Grayscale to Color: Complicated, Needs User Intervention.

4. Colorizing (Cntd.)  Literature Review: Pseudocoloring: Not Realistic. A Few Other Reports. We Proposed Elsewhere:  PCA-Based Colorizing: Have you ever seen Barabara in Color? Faster, Subjectively Better.

5. Quad-Tree Decomposition  Splitting an Image into Homogenous Blocks. Recursively. Until Enough Homogenous or Too Small.  To Avoid Over-Segmentation.  Generalized Quad-Tree: Shape (e.g. Triangle), Dimension (Hypercube)

6. Quad-Tree Decomposition (Cntd.)  Rectangular Block is Preferred. Computationally Inexpensive. No Round-Off Error.  Quad-Tree Produces Too Many Blocks: One-Split-to-Four.  Declining the Performance of Proceeding Operations.

7. Color Space Dimension Reduction  Illumination Rejection: Used Frequently.  Principal Component Analysis (PCA). A Proper Tool for Color Image Processing.  Spring or Autumn, this is the problem.

8. Homogeneity Criteria  Reconstruction Error.  Normalization.  Homogeneity Criteria.

9. Quad-Tree Decomposition  Splitting Decision.  Minimum Size of Block.  Tree Depth: Asked From User. Computed as:

10. Bi-Tree Decomposition  Bi_11-Tree Deciding Whether to Cut Vertically or Horizontally:  Bi_12-Tree Decision:

11. Color Image Compression  Lowpass filtering. To Avoid Aliasing.  Bi-Tree Decomposition. Storing the Result:  Sizes: Original Image: After Compression: Compression Ratio:  Sending the image: Block Information Plus the Grayscale Version. The Grayscale Version is 7-bit quantized. The Extra Bit Holds the Block Information.

12. Decompression  Easy Way: Colorize each block with Corresponding Color Information.  Enhanced Way: Interpolate the Vectors and then use them.  Splitting all blocks to the smallest size.  Using Lowpass filtering.

13. Block Count Growth

14. Block Count

15. Elapsed Time

16. Compression Results

17. Peak Signal to Noise Ratio

18. Compression Ratio

19. Conclusions  A New Tree Decomposition Method is Proposed that Out-Performs the Conventional Method.  A New Compression Method is Proposed that Reaches to the Theoretical Margins

20. Any Questions?