Hierarchical Context‐based Pixel Ordering

We present a context‐based scanning algorithm which reorders the input image using a hierarchical representationof the image. Our algorithm optimally orders (permutes) the leaves corresponding to the pixels, by minimizing thesum of distances between neighboring pixels. The reordering results in an improved autocorrelation betweennearby pixels which leads to a smoother image. This allows us, for the first time, to improve image compressionrates using context‐based scans. The results presented in this paper greatly improve upon previous work in bothcompression rate and running time.

[1]  Nasir D. Memon,et al.  An analysis of some common scanning techniques for lossless image coding , 1997, Conference Record of the Thirty-First Asilomar Conference on Signals, Systems and Computers (Cat. No.97CB36136).

[2]  Erik D. Demaine,et al.  K-ary Clustering with Optimal Leaf Ordering for Gene Expression Data , 2002, WABI.

[3]  Guillermo Sapiro,et al.  The LOCO-I lossless image compression algorithm: principles and standardization into JPEG-LS , 2000, IEEE Trans. Image Process..

[4]  David Salesin,et al.  Wavelets for computer graphics - theory and applications , 1996, The Morgan Kaufmann series in computer graphics and geometric modeling.

[5]  Abraham Lempel,et al.  Compression of two-dimensional data , 1986, IEEE Trans. Inf. Theory.

[6]  Jeremy S. De Bonet,et al.  Multiresolution sampling procedure for analysis and synthesis of texture images , 1997, SIGGRAPH.

[7]  Francesco Pinciroli,et al.  A Peano-Hilbert derived algorithm for compression of angiocardiographic images , 1991, [1991] Proceedings Computers in Cardiology.

[8]  Y. Fisher.  Fractal image compression: theory and application , 1995 .

[9]  Daniel Cohen-Or,et al.  Context‐based Space Filling Curves , 2000, Comput. Graph. Forum.

[10]  Tommi S. Jaakkola,et al.  Fast optimal leaf ordering for hierarchical clustering , 2001, ISMB.

[11]  Abraham Lempel,et al.  Compression of individual sequences via variable-rate coding , 1978, IEEE Trans. Inf. Theory.

[12]  Ahmad C. Ansari,et al.  Image Data Ordering And Compression Using Peano Scan And LOT , 1992 .