TY - JOUR
T1 - Two-Dimensional Cubic Convolution
AU - Reichenbach, Stephen E.
AU - Geng, Frank
N1 - Funding Information:
Manuscript received December 5, 2000; revised February 12, 2003. This work was supported by the National Aeronautics and Space Administration, the Nebraska NASA Space Grant Consortium, and the National Science Foundation Digital Government Program. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Yucel Altunbasak.
PY - 2003/8
Y1 - 2003/8
N2 - 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.
AB - 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.
KW - Cubic convolution
KW - Image reconstruction
KW - Image/video processing
KW - Interpolation and spatial transformations
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U2 - 10.1109/TIP.2003.814248
DO - 10.1109/TIP.2003.814248
M3 - Article
C2 - 18237960
AN - SCOPUS:0142200831
SN - 1057-7149
VL - 12
SP - 857
EP - 865
JO - IEEE Transactions on Image Processing
JF - IEEE Transactions on Image Processing
IS - 8
ER -