In this paper we propose a method to speed up Retinex-type algorithms, consisting of a computationally intensive nonlinear illumination estimation module followed by a relatively simple manipulation module. Speed up is obtained by way of computing the illumination on a sub-sampled image. The challenge is to interpolate a piece-wise smooth low resolution image. We present and analyze the trade o...

Division of focal plane (DoFP) polarimeters are composed of interlaced linear polarizers overlaid upon a focal plane array sensor. The interpolation is essential to reconstruct polarization information. However, current interpolation methods are based on the unrealistic assumption of noise-free images. Thus, it is advantageous to carry out denoising before interpolation. In this paper, we propo...

In this paper we study differentiability and semismoothness properties of functions defined as integrals of parameterized functions. We also discuss applications of the developed theory to the problems of shape-preserving interpolation, option pricing and semi-infinite programming.

Preserving edge structures is a challenge to the image interpolation algorithms to reconstruct a high resolution image from a low resolution counterpart. We propose a new guide edge linear interpolation technique via address filter and data fusion. For a pixel to be interpolated, two sets of observation are defined in two orthogonal directions, and each set produces an estimated value of the pi...

Conventional linear interpolation methods produce interpolated images with blurred edges, while edge directed interpolation methods make enlarged images with good quality edges but with details distortion for some cases. An adaptive rational-based algorithm for the interpolation of digital images with arbitrary scaling factors is proposed. In order to remove artifacts, we construct a new interp...

The barycentric interpolation formula defines a stable algorithm for evaluation at points in [−1, 1] of polynomial interpolants through data on Chebyshev grids. Here it is shown that for evaluation at points in the complex plane outside [−1, 1], the algorithm becomes unstable and should be replaced by the alternative modified Lagrange or “first barycentric” formula dating to Jacobi in 1825. Thi...

It is often observed that interpolation based on translates of radial basis functions or non-radial kernels is numerically unstable due to exceedingly large condition of the kernel matrix. But if stability is assessed in function space without considering special bases, this paper proves that kernel–based interpolation is stable. Provided that the data are not too wildly scattered, the L2 or L∞...

In this paper we study the existence and characterization of spaces which are images of minimal-norm projections that are required to interpolate at given functionals and satisfy additional shape-preserving requirements. We will call such spaces optimal interpolating spaces preserving shape. This investigation leads to concrete solutions in classical settings and, as examples, n will be determi...