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Enlargement or Reduction of Digital Images with Minimum Loss of Information

M. Unser, A. Aldroubi, M. Eden

IEEE Transactions on Image Processing, vol. 4, no. 3, pp. 247-258, March 1995.



The purpose of this paper is to derive optimal spline algorithms for the enlargement or reduction of digital images by arbitrary (noninteger) scaling factors. In our formulation, the original and rescaled signals are each represented by an interpolating polynomial spline of degree n with step size one and Δ, respectively. The change of scale is achieved by determining the spline with step size Δ that provides the closest approximation of the original signal in the L2-norm. We show that this approximation can be computed in three steps: i) a digital prefilter that provides the B-spline coefficients of the input signal, ii) a resampling using an expansion formula with a modified sampling kernel that depends explicitly on Δ, and iii) a digital postfilter that maps the result back into the signal domain. We provide explicit formulas for n = 0, 1, and 3 and propose solutions for the efficient implementation of these algorithms. We consider image processing examples and show that the present method compares favorably with standard interpolation techniques. Finally, we discuss some properties of this approach and its connection with the classical technique of bandlimiting a signal, which provides the asymptotic limit of our algorithm as the order of the spline tends to infinity.

Erratum

  • p. 250, between Equations (17) and (18), the text "Replacing g1n(x) by its B-spline expansion (15)" should become "Replacing s1n(x) by its B-spline expansion (15)".

  • p. 250, Section III.B, Step i), the text "Determine the B-spline coefficients in (16)" should become "Determine the B-spline coefficients in (15)".


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AUTHOR="Unser, M. and Aldroubi, A. and Eden, M.",
TITLE="Enlargement or Reduction of Digital Images with Minimum Loss
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JOURNAL="{IEEE} Transactions on Image Processing",
YEAR="1995",
volume="4",
number="3",
pages="247--258",
month="March",
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