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| About site: http://www.resampling.narod.ru/ |
Title: Programming/Graphics/Algorithms and Data Structures - M Spline A new linear best quality and fast algorithm of raster image scaling.
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Homepage of Vitaly Bursuk
Last updated on 10 Sep. 2007
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.
 RUS ENG
Resampling
Deblurring
Dejpeg
Smart Edges
Smart
Picsel
New Mosaic
Denoise
Deconvolution
Dequantization
RS-M-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 RS-M-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. The method
brought to your attention was called Magic spline
or M-spline by its author. Where here magic I shall answer a question so: magic
that I up to the end do not know why and as it works.
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
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 SmartEdge 2 LAD Deconvolution RS-M-Spline2
(New method)
   
   
   
   
Time
N/A Time N/A Time N/A Time N/A
Test - lh
Original low-resolution image - it will be enlarged by 4 times
Pseudoinverse
Enlargement
RS-M-Spline2
(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 RS-M-Spline2
(New method)
   
   
Time 1.0 Time 300 Time 2650 Time 1280
RMSE 13.06
RMSE 13.82*
RMSE 9.53 RMSE 8.60
* - subpixel shifts in
the resulting image.
Test - Clown
Original image was reduced 0.25X using a box convolution kemel.
Low resolution image was enlarged 4X by variety of
methods.
LAD Deconvolution
RS-M-Spline2
(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
M-spline
remains to the best and in this complex test:
LAD
Deconvolution
RMSE
12.9993
RS-M-Spline2
(New method)
RMSE
11.1840
Test – PDI-Target
Original image was reduced 0.25X using a box convolution kemel.
Low resolution image was enlarged 4X by RS-M-Spline and iNEDI methods.
iNEDI
RS-M-Spline2
(New method)
 
RMSE
9.14
RMSE 8.75
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.html
Results for
PDI-Target
Methods
RMSE
AAE
PSNR
Box (Nearest neighbor)
12.51
5.27
26.19
Step Interpolation
12.18
5.66
26.42
Bilinear
11.50
5.18
26.92
Bicubic
10.77
4.81
27.49
Lanczos
10.55
4.79
27.67
Triangulation
11.26
5.04
27.10
Xin Li
10.62
4.75
27.61
Zhao Xin Li
10.57
4.78
27.65
Windowless Xin
Li
10.36
4.71
27.82
Jensen Xin
Li
10.38
4.59
27.81
Jensen Zhao Xin
Li
10.26
4.58
27.90
IFS
10.09
4.40
28.05
DDL1 (Data Dependent Lanczos1)
11.39
5.05
27.00
LAD Deconvolution
9.51
4.05
28.57
DDL with SuperRez
Postprocessing
9.42
4.03
28.65
iNEDI
9.14
N/A
28.91
RS-M-Spline2
8.75
N/A
29.29
If
someone can make is better, please tell me.
Your
comments and questions:
vitalybn@fpy.ru
resampling@yandex.ru
The
algorithm is constantly improved, improvements will be, wait.
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A | new | linear | best | quality | and | fast | algorithm | of | raster | image | scaling. |
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http://www.resampling.narod.ru/
M Spline 2008 September
dvd rental
dvd
A new linear best quality and fast algorithm of raster image scaling.
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