Fractal Video Compression ChiaYuan Chang Department of Applied

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 er, and remove it from R. – 2) Split r into two rectangles r 1, r 2 such that er 1 + er 2 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

• Fractal dimension estimation – Basic definition • image sequence: I(x, y, t), • a group image frames: F 1, F 2, …, Fm+1, • reference frame : Fr • frame difference : Diff(x, y, t) • difference volume : V • voxel (x, y, t) • feature map : F(x, y)

– 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 Vr if Vr < Vt 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 Mr > Mt then segment Mr to smaller blocks else exit.

Motion estimation

Compression

Decompression

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