Abstract
Radial basis functions are widely used for image reconstruction because of grid flexibility and the fast convergence of their approximations; in other words, the RBF methods are mesh-free and high order convergent. We will present the 2D image reconstruction based on radial basis function reconstruction for sharp edged images using a MATLAB toolbox as a GUI interface. Sharp edged images reconstructed using RBF interpolations, however, tend to yield Gibbs ringing effects on the images themselves.To minimize Gibbs oscillations, the epsilon-adaptive method is employed in the developed GUI toolbox with which the shape parameter is adaptively chosen such that only the first order basis function is used near the neighborhood. To adopt this method, the functions called from the toolbox first detect the discontinuities in the image. The expansion coefficients and the concentration function derived from the first derivatives are used for the generation of an edge map. This edge map is defined where the product of the expansion coefficients and the concentration functions yield high values. We also use a domain splitting technique to develop the fast reconstruction algorithm. This technique is also used for the local image reconstruction near the discontinuity, which will be of the most interest to the user. We will present the RGB color image demonstrations using the toolbox. The non-uniform distribution in the reconstructed grid space and the Fourier filtering technique embedded in the toolbox will also be discussed.