Computer Science and Engineering, Department of
Date of this Version
This paper develops two-dimensional (2-D), nonseparable, piecewise cubic convolution (PCC) for image interpolation. Traditionally, PCC has been implemented based on a one-dimensional (1-D) derivation with a separable generalization to two dimensions. However, typical scenes and imaging systems are not separable, so the traditional approach is suboptimal. We develop a closed-form derivation for a two-parameter, 2-D PCC kernel with support [-2, 2] [-2, 2] that is constrained for continuity, smoothness, symmetry, and flat-field response. Our analyses using several image models, including Markov random fields, demonstrate that the 2-D PCC yields small improvements in interpolation fidelity over the traditional, separable approach. The constraints on the derivation can be relaxed to provide greater flexibility and performance.
Published in IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 12, NO. 8, AUGUST 2003. Copyright © 2003 IEEE. Used by permission.