Affine-scaling for linear programs with free variables
Mathematical Programming: Series A and B
Fast B-spline Transforms for Continuous Image Representation and Interpolation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computer Aided Geometric Design
Shape-preserving, multiscale fitting of univariate data by cubic L1 smoothing splines
Computer Aided Geometric Design
An Efficient Algorithm for Generating Univariate Cubic L1 Splines
Computational Optimization and Applications
Shape-preserving properties of univariate cubic L1 splines
Journal of Computational and Applied Mathematics
A compressed primal-dual method for generating bivariate cubic L1 splines
Journal of Computational and Applied Mathematics
C1 and C2-continuous polynomial parametric Lp splines (p≥1)
Computer Aided Geometric Design
Computer Aided Geometric Design
Shape-preserving, first-derivative-based parametric and nonparametric cubic L1 spline curves
Computer Aided Geometric Design
Fast L1kCk polynomial spline interpolation algorithm with shape-preserving properties
Computer Aided Geometric Design
Image resizing via non-homogeneous warping
Multimedia Tools and Applications
Shape-preserving, multiscale interpolation by bi- and multivariate cubic L1 splines
Computer Aided Geometric Design
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In this article, we address the problem of interpolating data points lying on a regular grid by C1-continuous L1-bicubic spline surfaces. Our algorithm is based on a local univariate L1 minimization method which enable us to calculate first derivative values for C1-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 L1 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 L1-bicubic surface. Some image interpolation examples show the efficiency of this non linear interpolation scheme.