Sampling, Interpolation, and Quantization
This chapter deals with the conversion between real (i.e., spatially and temporally continuous) images and their discrete representation. The mathematics of the conversion processes is discussed and is found to be straightforward. The introduction of perceptual considerations makes the subject more complex, but also more rewarding. It is shown that substantial improvements in image quality, for a given amount of digital data, are possible using perceptual, rather than mathematical, criteria, particularly in the choice of presampling filters and postsampling interpolators. Similarly, perceptual considerations can be brought to bear on the design of quantizers. Appropriate placement of quantization levels and the use of randomization techniques can significantly reduce the visibility of quantization noise.
KeywordsHexagonal Convolution Sine Mirror Symmetry Aliasing
Unable to display preview. Download preview PDF.
- 4.1S.J. Mason, H.J. Zimmermann: Electronic Circuits, Signals, and Systems (Wiley, New York 1960) p. 281; A. Papoulis: Signai Analysis (McGraw-Hill, New York 1977)Google Scholar
- 4.3J.N. Ratzel: “The Discrete Representation of Spatially Continuous Images,” ScD Thesis, Massachusetts Institute of Technology, Electrical Engineering and Computer Science Department, 1980; W.F. Schreiber, D.E. Troxel: “Transformation Between Continuous and Discrete Representations of Images: A Perceptual Approach,” IEEE Trans. Pattern Analysis and Machine Intelligence, PAMI-7, No. 2, 178–186, (Mar. 1985)Google Scholar
- 4.6R.W. Grass: “An Image Compression/Enhancement System,” M.S. Thesis, Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 1978Google Scholar
- 4.7C.U. Lee: “Image Rotation by 1-D Filtering,” M.S. Thesis, Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 1985Google Scholar
- 4.9R. Mersereau: “Hexagonally Sampled 2-D Signals,” Proc. IEEE 67, No.6, (1979)Google Scholar
- 4.11N. Ziesler: “Several Binary Sequence Generators,” Massachusetts Institute of Technology Lincoln Laboratory Tech. Rep. 95, (Sept. 1955); also “Linear Sequences,” J. Soc. Industr. Appl. Math. 7, 31-48 (1959); S.W. Golomb: Shift Register Sequences (Aegean Park Press, Laguna Hills, California)Google Scholar
- 4.12D.N. Graham: “Two-Dimensional Filtering to Reduce the Effect of Quantizing Noise in Television,” M.S. thesis, Massachusetts Institute of Technology, Electrical Engineering Department, 1962; R.A. Bruce: “Optimum Pre-emphasis and De-emphasis Networks for Transmission of Television by PCM,” IEEE Trans. on Communications Systems CS-12, 91-96 (Sept. 1964); E.G. Kimme, F.F. Kuo: “Synthesis of Optimal Filters for a Feedback Quantization System,” IEEE Trans. on Circuit Theory CT-10, 405-413 (Sept. 1963); A.E. Post: B.S thesis, Massachusetts Institute of Technology, Department of Electrical Engineering, 1966Google Scholar
- 4.13K.P. Wacks: “Design of a Real Time Facsimile Transmission System,” Ph.D. thesis, Massachusetts Institute of Technology, Electrical Engineering and Computer Science Department, 1973Google Scholar