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

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.

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.

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.

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)

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.

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.

Homogeneity Criteria Reconstruction Error.

Normalization.

Homogeneity Criteria.

Quad-Tree Decomposition Splitting Decision.

Minimum Size of Block.

Tree Depth: Asked From User. Computed as:

Bi-Tree Decomposition Bi_11-Tree

Deciding Whether to Cut Vertically or Horizontally:

Bi_12-Tree Decision:

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.

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.

Block Count Growth

Block Count

Elapsed Time

Compression Results

Peak Signal to Noise Ratio

Compression Ratio

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

Any Questions?