ENLARGEMENT OR REDUCTION OF DIGITAL IMAGES WITH MINIMUM LOSS OF INFORMATION

The purpose of this paper is to derive optimal spline algorithms for t he enlargement or reduction of digital images by arbitrary (noninteger ) scaling factors, In our formulation, the original and rescaled signa ls are each represented by an interpolating polynomial spline of degre e n with step size one and Delta, respectively, The change of scale is achieved by determining the spline with step size Delta that provides the closest approximation of the original signal in the L(2)-norm. We show that this approximation can be computed in three steps: i) a dig ital prefilter that provides the B-spline coefficients of the input si gnal, ii) a resampling using an expansion formula with a modified samp ling kernel that depends explicitly on Delta, and iii) a digital postf ilter that maps the result back into the signal domain, We provide exp licit formulas for n = 0, 1, and 3 and propose solutions for the effic ient implementation of these algorithms, We consider image processing examples and show that the present method compares favorably with stan dard interpolation techniques, Finally, we discuss some properties of this approach and its connection with the classical technique of bandl imiting a signal, which provides the asymptotic limit of our algorithm as the order of the spline tends to infinity.