Abstract
In this article, we address the problem of interpolating data points lying on a regular grid by C 1-continuous L 1-bicubic spline surfaces. Our algorithm is based on a local univariate L 1 minimization method which enable us to calculate first derivative values for C 1-cubic spline curves. In order to construct the interpolation surface, we calculate four derivative values at each data point using this local method. At is was shown in [17], our local interpolation L 1 cubic spline curve algorithm preserves well the shape of the data even for abrupt changes.The sequential computational complexity of this local method is linear and the parallel computational complexity is O(1). Consequently, we can address in this manner data on large grids. In order to keep this linear complexity for spline surface interpolation, we define an interpolation scheme based on four linear directions so as to construct our L 1-bicubic surface. Some image interpolation examples show the efficiency of this non linear interpolation scheme.
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Nyiri, E., Gibaru, O., Auquiert, P. (2012). Nonlinear L 1 C 1 Interpolation: Application to Images. In: Boissonnat, JD., et al. Curves and Surfaces. Curves and Surfaces 2010. Lecture Notes in Computer Science, vol 6920. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27413-8_33
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DOI: https://doi.org/10.1007/978-3-642-27413-8_33
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