Publication

Consistent And Regularized Magnification Of Images

Abstract

Because more output data must be created than is available from the input, magnification is an III-posed problem. Traditional magnification relies on resampling an interpolation model at the appropriate rate; unfortunately, this simple solution is blind to the presence of the analog fitter that was implicity present when the samples of the function to be magnified were acquired. Consistent resampling has been introduced to take this into account, but it turns out that this solution is still under-constrained. In this paper, we propose regularization as a way to devise a deterministic magnification method that fully satisfies consistency constraints in the absence of noise, and at the same time that produces and output that best fulfilled a wide class of criteria for regularity. Contrarily to many other methods, ours has been designed without ever leaving the continuous domain. We conduct experiments that show the benefit of our approach.

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Related concepts (28)
Image scaling
In computer graphics and digital imaging, image scaling refers to the resizing of a digital image. In video technology, the magnification of digital material is known as upscaling or resolution enhancement. When scaling a vector graphic image, the graphic primitives that make up the image can be scaled using geometric transformations, with no loss of . When scaling a raster graphics image, a new image with a higher or lower number of pixels must be generated.
Multivariate interpolation
In numerical analysis, multivariate interpolation is interpolation on functions of more than one variable (multivariate functions); when the variates are spatial coordinates, it is also known as spatial interpolation. The function to be interpolated is known at given points and the interpolation problem consists of yielding values at arbitrary points . Multivariate interpolation is particularly important in geostatistics, where it is used to create a digital elevation model from a set of points on the Earth's surface (for example, spot heights in a topographic survey or depths in a hydrographic survey).
Spline interpolation
In the mathematical field of numerical analysis, spline interpolation is a form of interpolation where the interpolant is a special type of piecewise polynomial called a spline. That is, instead of fitting a single, high-degree polynomial to all of the values at once, spline interpolation fits low-degree polynomials to small subsets of the values, for example, fitting nine cubic polynomials between each of the pairs of ten points, instead of fitting a single degree-ten polynomial to all of them.
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