Last updated on 01 Spt. 2019 
The commercial project made for presentation of
new algorithm of scaling of raster images. All rights on application of
the given algorithm belong to the author of the project. 

Resampling 
Neural Spline 3  the new
fast regression best
quality and fast
algorithm of image scaling.
Resampling  is the process of changing the
proportion of image. Until recently, there were only three linear methods
allowing the change of image proportion  copying of neighboring pixel, bi
linear and bi cube interpolation. The main advantage of these methods is high
speed of the realization. However, their application leads to a strong
artifacts which, by permanently increasing demands for quality of
interpolation, significantly limits the area of their application. Recently, on the market of professional graphic programmes, quite a
few more effective and better quality algorithms have appeared. Along with
the linear methods such as Lanczos
filter, Mitchell, CatmullRom, non linear
(adaptive) algorithms appeared  SSpline
Pro program, iNEDI, Pxl SmartScale, SmartEdge, Genuine Fractals etc. Notwithstanding the diversity of existing methods of scaling, SSpline
Pro program, Genuine Fractals, LAD Deconvolution and SmartEdge are generally recognized as ones of the best quality and the most
accurate. Modern methods of
qualitative scaling realize complex algorithms of inverse transformations.
The result of work of such algorithms depends on the chosen parameters which
quantity can reach tens. The choice of their optimum values thus is
inconvenient even to the experienced user. It essentially narrows a scope and
does these methods badly transferable for hardware realization. Also all is
usual qualitative algorithms of scaling realize various ways of post
processing. Despite of a high overall performance (from the point of view of
visual estimations) application of post processing often inevitably worsens
accuracy of scaling. Unlike the majority of methods the algorithm of Neural Spline does not demand some tinctures as it is adjusted on
reception of optimum result on any image. It is linear, simple and
qualitative simultaneously. The new linear method
which allows to carry out scaling of a better quality, better than all known
methods, both linear and adaptive. The main advantage of suggested method
over the rest of them is the speed (because it appears linear) simple of its
realization and best quality closest to achievable limits. RSMspline  algorithm is fully worked out and realized
exclusively by the author and all the rights of its use until the decision of
sale, belong to the author. The base of the
suggested algorithm (Mspline) lies in application of the new PSN&ER
metrics (peak to peak signal to noise and edges ratio) which significantly
more accurate (compared with PMS metrics) agrees with the visual valuation of
similarity and the new revolutionary approach at working out the algorithm.
Valuating the form and size of approximating function, it is also possible to
ascertain that obtained algorithms allow getting the quality of the scaling
which is maximally approximate to the achievable limit from the theory of
information point of view. There are also a few algorithm modifications. RSMspline2 algorithm is a newer version of RSMspline. New updating of algorithm which differs from the previous version
following technological decisions. Smarp Pixel  Adaptation of a spline to local features of scaled area. Smarp Function  Introduction in function of a spline of nonlinear operators. Smart Edge  Adaptation of a spline to edges of scaled area. Noise Filter  Remove noise of interpolation. New Neural spline algorithm is a newer version of RSMspline2. New updating of algorithm which differs from the previous version
following technological decisions. Smarp Pixel2  Adaptation of a spline to local features of scaled area. Smarp Function2  Introduction in function of a spline of nonlinear operators. Smart Edge2  Adaptation of a spline to edges of scaled area. Noise Filter2  Remove noise of interpolation. SuperResolution  More exact of interpolation. New Neural spline  2 algorithm is a newer version of Neural spline. New updating of algorithm which differs from the previous version
following technological decisions. Smart Edge 3  More exact edge detecting. SuperResolution 2  More exact of interpolation. Neural spline 3 algorithm is a newer version of Neural spline 2. New updating of algorithm which differs from the previous version
following technological decisions. Smart Pixel3  Smart adaptation of a spline to local features of scaled area. Smart Edge3  Variable (adaptive) angle step to edges of scaled area. Two scaling steps  Technique several consecutive approximations fore more exact of
interpolation. New. Therefore the mistake of scaling is reduced, having reached new record values. In order to confirm above, I suggest to get familiar with practical
realization of the algorithm on the well known examples of tasks and
solutions. As the test the following representation has been chosen:
To see the picture click on the fragment Test  flowers Original lowresolution image  it will be enlarged by 2 times
Test  lh Original lowresolution image  it will be enlarged by 4 times
Test  lhouse Original image was reduced 0.5X using a box
convolution kemel. Low resolution image was enlarged 2X by
variety of methods.
*  subpixel shifts
in the resulting image.
Original image was reduced 0.25X using a
box convolution kemel. Low resolution image was enlarged 4X by
variety of methods.
Test  myTest Original image was reduced 0.5X using a box
convolution kemel. Low resolution image was enlarged 2X by
variety of methods.
Very complex image
for scaling, some algorithms in this test have shown very bad results. The method Neural Spline remains to the best and in this complex test:
Original image was reduced 0.25X using a box
convolution kemel. Low resolution image was enlarged 4X by
Neural Spline and iNEDI methods.
Look
more at http://www.generalcathexis.com/interpolation/index.html
If
someone can make is better, please tell me. resampling@yandex.ru Now there is a completion of more exact modification of Neural spline which will be ready in the autumn. 

