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IMAGE SAMPLING AND RECONSTRUCTION In digital image processing systems, one usually deals with arrays of numbers obtained by spatially sampling points of a physical image. After processing, another array of numbers is produced, and these numbers are then used to reconstruct a continuous image for viewing. Image samples nominally represent some physical measurements of a continuous image field, for example, measurements of the image intensity or photographic density. Measurement uncertainties exist in any physical measurement apparatus | Digital Image Processing PIKS Inside Third Edition. William K. Pratt Copyright 2001 John Wiley Sons Inc. ISBNs 0-471-37407-5 Hardback 0-471-22132-5 Electronic 4 IMAGE SAMPLING AND RECONSTRUCTION In digital image processing systems one usually deals with arrays of numbers obtained by spatially sampling points of a physical image. After processing another array of numbers is produced and these numbers are then used to reconstruct a continuous image for viewing. Image samples nominally represent some physical measurements of a continuous image field for example measurements of the image intensity or photographic density. Measurement uncertainties exist in any physical measurement apparatus. It is important to be able to model these measurement errors in order to specify the validity of the measurements and to design processes for compensation of the measurement errors. Also it is often not possible to measure an image field directly. Instead measurements are made of some function related to the desired image field and this function is then inverted to obtain the desired image field. Inversion operations of this nature are discussed in the sections on image restoration. In this chapter the image sampling and reconstruction process is considered for both theoretically exact and practical systems. . IMAGE SAMPLING AND RECONSTRUCTION CONCEPTS In the design and analysis of image sampling and reconstruction systems input images are usually regarded as deterministic fields 1-5 . However in some situations it is advantageous to consider the input to an image processing system especially a noise input as a sample of a two-dimensional random process 5-7 . Both viewpoints are developed here for the analysis of image sampling and reconstruction methods. 91 92 IMAGE SAMPLING AND RECONSTRUCTION FIGURE . Dirac delta function sampling array. . Sampling Deterministic Fields Let Fj x y denote a continuous infinite-extent ideal image field representing the luminance .

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