1 research outputs found
Numerical Analysis of Diagonal-Preserving, Ripple-Minimizing and Low-Pass Image Resampling Methods
Image resampling is a necessary component of any operation that changes the
size of an image or its geometry.
Methods tuned for natural image upsampling (roughly speaking, image
enlargement) are analyzed and developed with a focus on their ability to
preserve diagonal features and suppress overshoots. Monotone, locally bounded
and almost monotone "direct" interpolation and filtering methods, as well as
face split and vertex split surface subdivision methods, alone or in
combination, are studied. Key properties are established by way of proofs and
counterexamples as well as numerical experiments involving 1D curve and 2D
diagonal data resampling.
In addition, the Remez minimax method for the computation of low-cost
polynomial approximations of low-pass filter kernels tuned for natural image
downsampling (roughly speaking, image reduction) is refactored for relative
error minimization in the presence of roots in the interior of the interval of
approximation and so that even and odd functions are approximated with like
polynomials. The accuracy and frequency response of the approximations are
tabulated and plotted against the original, establishing their rapid
convergence