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Last updated on |
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. |
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Resampling
New Mosaic
Denoise Deconvolution Dequantization |
Neural Spline - the new, linear, 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,
Catmull-Rom, non linear
(adaptive) algorithms appeared – S-Spline Pro program, iNEDI, Pxl SmartScale, SmartEdge, Genuine
Fractals etc. Notwithstanding the diversity of existing methods of scaling, S-Spline 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 postprocessing. Despite of a
high overall performance (from the point of view of visual estimations)
application of postprocessing 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) simpleness of its realization
and best quality closest to achievable limits. RS-M-spline - 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 (M-spline) 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.
RS-M-spline2 algorithm is a newer version of
RS-M-spline. 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 RS-M-spline2. 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 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: flowers lhouse lh clown To see the picture click on the
fragment Test - flowers Original low-resolution image - it will be enlarged by 2 times
Bicubic
SmartEdge2 LAD
Deconvolution Neural
Spline Time N/A Time
N/A Time
N/A Time
N/A
Original low-resolution image - it will be enlarged by 4 times Pseudoinverse
Enlargement Neural Spline (New method)
Time N/A Time N/A Test - lhouse Original image was reduced 0.5X using a box convolution kemel. Low resolution image was enlarged 2X by
variety of methods.
Bicubic
SmartEdge 2 LAD
Deconvolution Neural Spline (New
method)
Time 1.0
Time
300 Time
2650 Time
4790
RMSE
13.06 RMSE 13.82*
RMSE 9.53 RMSE 8.53 * - 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. LAD
Deconvolution Neural Spline
(New
method)
RMSE N/A RMSE N/A 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: LAD Deconvolution
RMSE 12.9993 Neural Spline
RMSE 11.008 Test – PDI-Target Original image was reduced 0.25X using a box convolution kemel. Low resolution image was enlarged 4X by
Neural Spline and iNEDI methods.
iNEDI Neural Spline
(New method) RMSE 9.14
RMSE 8.65 For comparison look the most simple and fast
methods Bicubic Nearest Neighbor RMSE 10.77 RMSE 12.51 Look
more at http://www.general-cathexis.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. |
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