Abstract
Let an image be distorted by a nonlinear transformationT, and then be restored back to its original by the inverse transformationT −1. Such a cycle conversion,T −1 T, of digital images can be facilitated by the combination (CSIM) given in [6] using the splitting-shooting method and the splitting-integrating method forT andT −1 respectively. Since there is no need to solve nonlinear equations, CSIM has been widely applied to specific areas of image processing and pattern recognition, even those with complicated transformations, e.g., the harmonic transformation [12]; however, no strict error analysis has been provided so far. In this paper, a priori error estimates and convergence rates are derived for pixel greyness obtained from CSIM; also the analytical results are extended to the harmonic transformation. Numerical and graphical experiments are provided to support the theoretical analysis.
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Communicated by C. Brezinski
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Li, Z.C. Analysis of discrete techniques for image transformation. Numer Algor 13, 225–263 (1996). https://doi.org/10.1007/BF02207696
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DOI: https://doi.org/10.1007/BF02207696
Keywords
- numerical integration
- error analysis
- harmonic transformation
- finite element method
- digital image
- image transformation