Rate-distortion optimized tree-structured compression algorithms for piecewise polynomial images

• Published in: IEEE transactions on image processing Vol. 14; no. 3; pp. 343 - 359
• Main Authors: Shukla, R., Dragotti, P.L., Do, M.N., Vetterli, M.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.03.2005; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Applied sciences; Artificial Intelligence; Binary tree; bit allocation; Bit rate; coding; Compression algorithms; Computer Graphics; Computer science; control theory; systems; Data Compression - methods; Discrete cosine transforms; Discrete wavelet transforms; Exact sciences and technology; Image coding; Image Enhancement - methods; Image Interpretation, Computer-Assisted - methods; Image processing; Image segmentation; Information, signal and communications theory; Laboratories; neighbor joining; Numerical Analysis, Computer-Assisted; Pattern Recognition, Automated - methods; Pattern recognition. Digital image processing. Computational geometry; piecewise polynomial functions; Polynomials; pruning; quadtree; Rate-distortion; Reproducibility of Results; Sensitivity and Specificity; Signal processing; Signal Processing, Computer-Assisted; Studies; Telecommunications and information theory; Transform coding; tree-structured segmentation; pruning; Tree structured method; rate-distortion; Segmentation; Image processing; piecewise polynomial functions; Rate distortion theory; Image compression; Algorithm; Optimization; Bit allocation; Polynomial function; coding; Image coding; Binary tree; Quad tree; quadtree; tree-structured segmentation; neighbor joining
• ISSN: 1057-7149; 1941-0042; 1941-0042
• DOI: 10.1109/TIP.2004.840710

This paper presents novel coding algorithms based on tree-structured segmentation, which achieve the correct asymptotic rate-distortion (R-D) behavior for a simple class of signals, known as piecewise polynomials, by using an R-D based prune and join scheme. For the one-dimensional case, our scheme is based on binary-tree segmentation of the signal. This scheme approximates the signal segments using polynomial models and utilizes an R-D optimal bit allocation strategy among the different signal segments. The scheme further encodes similar neighbors jointly to achieve the correct exponentially decaying R-D behavior (D(R)/spl sim/c/sub 0/2/sup -c1R/), thus improving over classic wavelet schemes. We also prove that the computational complexity of the scheme is of O(NlogN). We then show the extension of this scheme to the two-dimensional case using a quadtree. This quadtree-coding scheme also achieves an exponentially decaying R-D behavior, for the polygonal image model composed of a white polygon-shaped object against a uniform black background, with low computational cost of O(NlogN). Again, the key is an R-D optimized prune and join strategy. Finally, we conclude with numerical results, which show that the proposed quadtree-coding scheme outperforms JPEG2000 by about 1 dB for real images, like cameraman, at low rates of around 0.15 bpp.