Algorithm GRI Smoothing-Resampling Algorithm (SRALG)  SRALG-Based Interpolation Algorithm  Free Utilities About the Author

Robust Geometric Resampling (RGR)

© Dmitry Grilikhes, 2013.    If you wish to use the materials on this page over the internet, you are obliged to preserve the link to it.

Introduction

The interpolation algorithm, which I called RGR (Robust Geometric Resampling), is based on the same approach as SRALG. Instead of searching for approximating functions, the assumed function would be approximated by a set of values calculated iteratively. When enough values have been calculated to achieve the desired resulting set, the process can be terminated. On each iteration it calculates the values of an interpolating vector-function that is defined between each pair of neighboring data points. To calculate each vector I use a single linear equation that is representing a very simple geometric construction. The algorithm has one parameter k controlling the shape of the resulting curve (or surface in the two-dimensional case). Similar to GRI, Robust Geometric Resampling was intended mainly for image scaling. Like any other method (linear, cubic etc.) it could be applied first in one direction, and then again in the other direction. In this regular grid case RGR calculation goes more efficient and every one of the iterations actually realizes an upsampling with the scale factor 2.



How does it work?

RGR



Demo on image

On the pictures below you can see the results of biRGR (bidirectional version of RGR) working on image compared with the standard solutions. They are very similar to the results of bicubic.




cut_map

Map of the cuts upscaled x8


Cut #1


linear1

linear


cubic1

cubic


rgr1

RGR


lanczos31

lanczos3


Cut #2


linear2

linear


cubic2

cubic


rgr2

RGR


lanczos32

lanczos3


Cut #3


linear3

linear


cubic3

cubic


rgr3

RGR


lanczos33

lanczos3


© Dmitry Grilikhes, 2013.   

If you wish to use the materials on this page over the internet, you are obliged to preserve the link to it.

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