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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.