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Updated: Jul 7, 2026

Three-Dimensional Reconstruction for the Whole Lung with Early Multiple Pulmonary Nodules
Published on: October 13, 2023
Two-dimensional cubic convolution
Stephen E Reichenbach1, Frank Geng
1Comput. Sci. and Eng. Dept., Univ. of Nebraska, Lincoln, NE 68588-0115, USA. reich@unl.edu
Abstract:
The paper develops two-dimensional (2D), nonseparable, piecewise cubic convolution (PCC) for image interpolation. Traditionally, PCC has been implemented based on a one-dimensional (1D) 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, 2D PCC kernel with support [-2,2] x [-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 2D 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.
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