Fractal Video Compression 碎形視訊壓縮方法 Chia-Yuan Chang 張嘉元 Department of Applied Mathematics National Sun Yat-Sen University Kaohsiung, Taiwan

Topics Introduction Our approach Simulation Conclusions

INTRODUCTION Standardization of algorithm -- MPEG Quad-tree structure Slicing floorplan tree Fractal dimension

Standardization of algorithm MPEG – video layers I-picture: Intraframe, JPEG DCT, lower compression ratio P-picture: Predicted frame, motion compensation B-picture: Bi-directional frame,higher compression ratio

–display order

–coding order

–motion compensation

–disadvantages buffer and time control encoding: the fixed block size DCT: filter high frequency (like edge)

Quad-tree structure basic definition –top-down : segment –bottom-up : merge application –Vector Quantization (VQ) disadvantage –efficiency

Slicing floorplan tree The Recursive Split Algorithm –Start with R containing a single rectangular patch that covers the entire frame –Repeat n-1 times Step 1), 2), 3) –1) Search R for the rectangle r with the largest error e r, and remove it from R. –2) Split r into two rectangles r 1, r 2 such that e r1 + e r2 is minimized. –3) Add r 1, r 2 to R.

disadvantage –each two-frames has own mask –noise effect

Fractal dimension Introduction –estimate length of coastline –general formula –the measurement, analysis, and classification of shape and texture

Box counting approach (3-D space) –image size : M x M –box size : s x s –ratio : r = s / M –box number in ( i, j) grid –total box number –FD equation

Our approach Fractal Dimension Estimation Slicing Floorplan Segmentation Compression Decompression

Mask processing

–A modified box-counting approach window volume size : mxmxm cubes size : axaxa. scaling factor s, the fractal dimension for the voxel (x, y, t)

Slicing floorplan segmentation. –Start with R containing a single rectangular patch that covers feature map F(i, j). 1) search R for the rectangle r with the largest variance V r if V r < V t then go to Step 4 else remove it from R. 2) split r into two rectangles r 1, r 2 such that is maximized 3) add r 1, r 2 to R, and go to Step 1 4) check the mean value of each block. If M r > M t then segment M r to smaller blocks else exit.

Motion estimation

Compression

Decompression

Simulation test image sequence –Claire –football –Noisy Claire (25db Gaussian noises) –Noisy football (20db Gaussian noises) comparison –MPEG

Conclusions Our algorithm can get higher compression ratio than MPEG in the same average PSNR for the same image sequence. Future research –compression speed improvement