LINEAR PROCESSING TECHNIQUES Most discrete image processing computational algorithms are linear in nature; an output image array is produced by a weighted linear combination of elements of an input array. The popularity of linear operations stems from the relative simplicity of spatial linear processing as opposed to spatial nonlinear processing. However, for image processing operations, conventional linear processing is often computationally infeasible without efficient computational algorithms because of the large image arrays | 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 9 LINEAR PROCESSING TECHNIQUES Most discrete image processing computational algorithms are linear in nature an output image array is produced by a weighted linear combination of elements of an input array. The popularity of linear operations stems from the relative simplicity of spatial linear processing as opposed to spatial nonlinear processing. However for image processing operations conventional linear processing is often computationally infeasible without efficient computational algorithms because of the large image arrays. This chapter considers indirect computational techniques that permit more efficient linear processing than by conventional methods. . TRANSFORM DOMAIN PROCESSING Two-dimensional linear transformations have been defined in Section in series form as Nj v P mp m2 z z F n-1 n2 T n1 n2 m1 m2 nj 1 n2 1 and defined in vector form as p Tf It will now be demonstrated that such linear transformations can often be computed more efficiently by an indirect computational procedure utilizing two-dimensional unitary transforms than by the direct computation indicated by Eq. or . 213 214 LINEAR PROCESSING TECHNIQUES FIGURE . Direct processing and generalized linear filtering series formulation. Figure is a block diagram of the indirect computation technique called generalized linear filtering 1 . In the process the input array F n1 n2 undergoes a two-dimensional unitary transformation resulting in an array of transform coefficients F u1 u2 . Next a linear combination of these coefficients is taken according to the general relation Mi M2 Fw w2 y y F u1 u2 T u1 u2 w1 w2 u1 1 u2 1 where T u1 u2 w1 w2 represents the linear filtering transformation function. Finally an inverse unitary transformation is performed to reconstruct the processed array P m1 m2 . If
