Last updated on 10 Oct. 2013

Описание: Описание: Описание: Описание: Rambler's Top100

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

 

Deblurring

 

Dejpeg

 

Smart Edges

 

Smart Picsel

 

New Mosaic

 

Denoise

 

Deconvolution

 

Dequantization

 

Neural Spline 2 - 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

 

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.

 

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

Описание: Описание: Описание: Описание: image005

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 2
(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

Neural Spline 2
(New method)

Описание: Описание: Описание: Описание: http://www.general-cathexis.com/Images/lh_PISuperRez4X.jpg

Описание: Описание: Описание: Описание: lhrs3x4

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 2
(New method)

Time 1.0
RMSE 13.06

Time 300
RMSE 13.82*

Time 2650
RMSE 9.53

Time 9630
RMSE 8.49 

 

* - 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

Neural Spline 2

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 2
(New method)

Описание: Описание: Описание: Описание: mytestrs3x2

RMSE 11.019


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 2

RMSE 9.14

RMSE 8.54

 

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

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-spline 2

9.10

N/A

N/A

Neural Spline

8.65

N/A

N/A

Neural Spline 2

8.54

N/A

N/A

 

If someone can make is better, please tell me.

 

Your comments and questions:

resampling@yandex.ru
 

Now there is a completion of more exact modification of Neural spline which will be ready in the autumn.