CN108765286A - A kind of digital image interpolation algorithm of radiation modulation function fidelity - Google Patents
A kind of digital image interpolation algorithm of radiation modulation function fidelity Download PDFInfo
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- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
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Abstract
The invention discloses a kind of digital image interpolation algorithms of radiation modulation function fidelity.Sub-pixel interpolation processing is carried out for digital picture, for arbitrary sub-pixel location, the pixel value that sub-pixel location is calculated using the horizontal and vertical interpolation coefficient formula of special designing carries out digital image interpolation；The lateral interpolation coefficient and longitudinal interpolation coefficient are calculated using same procedure, are obtained by solving the calculating of non-binary constraint optimization problem.The interpolation coefficient of the present invention has the interpolation function of traditional interpolation algorithm, while avoiding the degeneration of image radiation modulation function (MTF), has ensured the details resolving power of interpolation image.The present invention solves the disadvantage that traditional interpolation algorithm reduces image detail resolving power.
Description
Technical field
The invention belongs to digital image processing fields, are related to the operations such as digital image scaling, perspective transform, geometric correction
A kind of interpolation algorithm, and in particular to digital image interpolation algorithm of radiation modulation function fidelity.
Background technology
Radiation modulation function (MTF) is the function for describing image details resolving power under different space frequency, is mainly examined
Look into reduction degree of the modulation degree compared to the modulation degree of signal in ideal image system of signal in image.In remote sensing and medicine shadow
Fields, the radiation modulation functions (MTF) such as picture are the important indicators of evaluation image details resolving power.
When executing digital image scaling, perspective transform, the operations such as geometric correction, need to original image sub-pixel location into
Row interpolation.Traditional interpolation method has：Closest interpolation, linear interpolation, cube difference, B-spline interpolation.These common interpolation
Method is substantially that the pixel value of new position is estimated using the linear combination of adjacent pixels value, this is equivalent to image filtering operations.
And traditional interpolation algorithm will produce the effect of low-pass filtering, and image radiation modulation function (MTF) is caused to be degenerated, high-frequency information is lost
It loses, reduces image detail resolving power.
Invention content
Technical problem present in for the above-mentioned prior art, the present invention provide a kind of number of radiation modulation function fidelity
Image interpolation algorithm can realize the picture element interpolation of any position, and compared to traditional interpolation method, the invention avoids image radiations
The degeneration of modulation function (MTF) has ensured the details resolving power of interpolation image.
As shown in Figure 1, the technical scheme is that：
Sub-pixel interpolation processing is carried out for digital picture, for arbitrary sub-pixel location, is inserted using horizontal and vertical
The pixel value that value coefficient R (m, △ r) and R (n, △ c) calculates sub-pixel location using following formula carries out digital image interpolation：
Wherein, △ r, △ c indicate sub-pixel location with respect to original image pixel F (r, c) along image vertical and horizontal respectively
Offset, △ r, △ c ∈ [0,1),Indicate that the pixel value of sub-pixel location, F (r+m, c+n) indicate former
With the pixel value of sub-pixel location neighborhood pixels, R (m, △ r) and R (n, △ c) it is respectively longitudinal interpolation coefficient of image in image
With lateral interpolation coefficient；M indicates the serial number of longitudinal interpolation coefficient, and m=-2, -1 ..., 3, n indicate the serial number of lateral interpolation coefficient,
N=-2, -1 ..., 3.
Position of the sub-pixel location between adjacent pixel, pixel value are unknown, the above methods through the invention
Interpolation obtains.
The lateral interpolation coefficients R (n, △ c) and longitudinal direction interpolation coefficient R (m, △ r) is calculated using same procedure, logical
It crosses solution non-binary constraint optimization problem and calculates acquisition.
Below to illustrate for longitudinal interpolation coefficient R (m, △ r), longitudinal interpolation coefficient R (m, △ r) passes through solution
The non-binary constraint optimization problem that following formula indicates obtains：
Wherein, MTF (ui, △ r) be longitudinal direction interpolation coefficient R (m, △ r) discrete Fourier transform in spatial frequency uiPlace
Amplitude, i.e. mtf value, ui=i/N-0.5, i indicate that the ordinal number of discrete Fourier transform down space frequency, N indicate discrete fourier
Convert the sum of down space frequency；
And establish following constraints：
A) equality constraint：
B) inequality constraints
|p+△r|<0.05 (4)
Wherein, p is equal to the value of independent variable x when longitudinal direction edge function E (x) is equal to 0.
Longitudinal edge function E (x) is expressed as
Wherein,For phase angle of the Fourier transformation at spatial frequency u of longitudinal interpolation coefficient R (m, △ r), x
Indicate the independent variable of longitudinal direction edge function E (x).
Above-mentioned formula represents the result that longitudinal interpolation coefficient acts on sign function.
Below to illustrate for lateral interpolation coefficients R (n, △ c), the lateral interpolation coefficients R (n, △ c) passes through solution
The non-binary constraint optimization problem that following formula indicates obtains：
Wherein, MTF (ui, △ c) be lateral interpolation coefficients R (n, △ c) discrete Fourier transform in spatial frequency uiPlace
Amplitude, i.e. mtf value, ui=i/N-0.5, i indicate that the ordinal number of discrete Fourier transform down space frequency, N indicate discrete fourier
Convert the sum of down space frequency；
And establish following constraints：
A) equality constraint：
B) inequality constraints
|q+△c|<0.05 (8)
Wherein, q is equal to the value of independent variable y when transverse direction edge function E (y) is equal to 0.
The lateral edge function E (y) is expressed as：
Wherein,For phase angle of the Fourier transformation at spatial frequency u of lateral interpolation coefficients R (n, △ c), y
Indicate lateral edge side argument of function.
Above-mentioned formula represents the lateral interpolation coefficient acting in the result of sign function.
The interpolation coefficient of the present invention has the interpolation function of traditional interpolation algorithm, while avoiding image radiation modulation function
(MTF) degeneration has ensured the details resolving power of interpolation image, and solving traditional interpolation algorithm reduces image detail resolving power
The shortcomings that.
The advantages of the present invention over the prior art are that：
One, this invention removes the low-pass filtering effects of traditional interpolation algorithm, avoid the degeneration of image MTF, ensure
The details resolving power of interpolation image.
Image interpolation is substantially to be filtered to original image using interpolation coefficient, therefore the MTF of image is equal to artwork after interpolation
The MTF of picture is multiplied with the MTF of interpolation coefficient.Attached drawing 2, attached drawing 3 show a series of corresponding interpolation coefficients of offset △ r
MTF, it can be seen that for the present invention compared with cube differential technique, the MTF at each frequency can make the figure after interpolation close to 1
As keeping original MTF.
Two, interpolation algorithm geometric accuracy of the present invention is high.When building the non-binary constraint optimization problem about interpolation coefficient, add
Enter the constraint to geometric accuracy.Attached drawing 4 shows the geometric accuracy contrast schematic diagram of the present invention and cube interpolation method, can see
Go out, geometric accuracy of the invention is better than cube interpolation algorithm.
Description of the drawings
Fig. 1 is digital image interpolation schematic diagram；
Fig. 2 is the MTF schematic diagrames of interpolation coefficient of the present invention；
Fig. 3 is the MTF schematic diagrames of cube interpolation method interpolation coefficient；
Fig. 4 is the geometric accuracy contrast schematic diagram of the present invention and cube interpolation method；
Fig. 5 is the artwork of the embodiment of the present invention；
Fig. 6 is the comparison signal of interpolation graphs and artwork that the part 1 in artwork obtains after two kinds of interpolation method interpolation
Figure；
Fig. 7 is pair of restored map and artwork that the part 2 in artwork is obtained by two kinds of interpolation method interpolation and after restoring
Compare schematic diagram；
Fig. 8 is the Error Graph of restored map of the present invention；
Fig. 9 is a cube Error Graph for interpolation method restored map.
Specific implementation mode
Now will by taking image translation as an example detailed description of the present invention exemplary implementation, and made using cube interpolation method
To compare the advantageous effect to illustrate of the invention.
The embodiment of the present invention is as follows：
The present embodiment realizes that the sub-pix of 8 gray level images translates by interpolation.In order to verify the radiation of the present invention
Original image is integrally translated up 0.375 pixel and obtains interpolation image and then incite somebody to action by modulation function fidelity performance, this implementation column
0.375 pixel of translation obtains restored image to gained interpolation image downwards, passes through the comparison of restored image and original image, Ke Yike
See the radiation modulation function fidelity performance of ground evaluation interpolation algorithm.
The sub-pix translation for implementing image according to the method for the present invention is as follows：
Step 1：Original image F (r, c) is integrally translated up to 0.375 pixel and obtains interpolation image G (r, c), structure is inserted
It is worth the mapping relations of image and original image：
When only carrying out longitudinal translation, formula (11) can be reduced to：
Therefore it only needs to solve interpolation coefficient R (m, 0.375), m=-2, -1 ..., 3.
Step 2：Structure is about interpolation coefficient R (m, 0.375), m=-2, and -1 ..., 3 non-binary constraint optimization problem：
Wherein take N=64, ui=i/N-0.5.
And it establishes constraints and is：
(1) Involving Certain Polynomial Constraints
(2) geometric accuracy constrains
|p+△c|<0.05 (14)
Wherein p is equal to the value of independent variable x when function shown in formula (15) is equal to 0.
Wherein,For phase of the discrete Fourier transform at spatial frequency u of interpolation coefficient R (m, 0.375)
Angle.
Step 3：Non-binary constraint optimization problem constructed by solution procedure 2, obtains interpolation coefficient：
Step 4：Simultaneous formula (10), formula (11) simultaneously substitute into interpolation coefficient to obtain interpolation image：
Attached drawing 5 is the artwork F (r, c) of the embodiment of the present invention, and attached drawing 6 is that two kinds of interpolation methods are passed through in the part 1 in artwork
The contrast schematic diagram of the interpolation graphs and artwork that are obtained after interpolation, comparison artwork and interpolation graphs of the present invention, it can be seen that the present invention inserts
There is offset Luminance Distribution in longitudinal direction, i.e., artwork has been translated up the effect of 0.375 pixel by interpolation method of the present invention in value figure
Fruit.
Step 5：0.375 pixel of the whole translations downwards of interpolation image G (r, c) is obtained into restored image F'(r, c).Structure
The mapping relations of restored image and interpolation image：
It can be obtained by formula (11)：
Interpolation coefficient R (m, 0.625), m=-2, -1 can be solved with reference to step 2 ..., 3.
Formula (20) shows the concrete numerical value of interpolation coefficient R (m, 0.625)：
Interpolation coefficient R (m, 0.625) is substituted into formula (19) and obtains restored image.Attached drawing 7 is that the part 2 in artwork passes through two
The contrast schematic diagram of the restored map and artwork that are obtained after kind interpolation method interpolation and recovery.It compares artwork and cube interpolation method is restored
Figure, it can be seen that after executing interpolation operation twice using cube interpolation method, the detail section of artwork is lost, and edge thickens,
I.e. cube interpolation method has the effect of low-pass filtering, leads to radiation modulation function degeneracy；Artwork and restored map of the present invention are compared, it can
To find out using after present invention execution twice interpolation operation, the detail section of artwork is still remained, i.e., interpolation method of the present invention
Advantageous effect with radiation modulation function fidelity.
It can be with the similarity of objective evaluation restored image and artwork by calculating Y-PSNR (PSNR).It is computed, this
In embodiment, the PSNR=58.3034 of restored map of the present invention, the PSNR=35.3382 of cube interpolation method restored map, therefore this hair
Bright recovery effect is more preferable.
Artwork and restored image are subtracted each other to the Error Graph that restored map can be obtained, attached drawing 8, attached drawing 9 are recovery of the present invention respectively
The Error Graph of the Error Graph of figure and cube interpolation method restored map.With reference to legend it is found that grey Representative errors are 0, white and black
Respectively represent positive error and negative sense error.Compare attached drawing 8, attached drawing 9, it can be seen that reset error smaller of the invention.Through meter
It calculates, the Error Graph mean value of restored map of the present invention is -4.5776 × 10-05, standard deviation 0.3196, cube interpolation method restored map
Error Graph mean value is 7.4768 × 10-04, standard deviation 4.3715, it can be seen that two Error Graph mean values are all close to 0, and this hair
The standard deviation of bright Error Graph is significantly less than a cube standard deviation for interpolation method Error Graph, that is, the reset error smaller invented.
Claims (6)
1. a kind of digital image interpolation algorithm of radiation modulation function fidelity, it is characterised in that：
Sub-pixel interpolation processing is carried out for digital picture, and horizontal and vertical interpolation system is utilized for arbitrary sub-pixel location
The pixel value that number R (m, △ r) and R (n, △ c) calculates sub-pixel location using following formula carries out digital image interpolation：
Wherein, △ r, △ c indicate offset of the sub-pixel location with respect to original image pixel F (r, c) along image vertical and horizontal respectively
Amount, △ r, △ c ∈ [0,1),Indicate that the pixel value of sub-pixel location, F (r+m, c+n) indicate original image
In pixel value with sub-pixel location neighborhood pixels, R (m, △ r) and R (n, △ c) are respectively the longitudinal interpolation coefficient and cross of image
To interpolation coefficient；M indicates the serial number of longitudinal interpolation coefficient, and m=-2, -1, L, 3, n indicate the serial number of lateral interpolation coefficient, n=-
2,-1,L,3。
2. a kind of digital image interpolation algorithm of radiation modulation function fidelity according to claim 1, it is characterised in that：Institute
The lateral interpolation coefficients R (n, △ c) and longitudinal direction interpolation coefficient R (m, △ r) stated are calculated using same procedure, polynary by solving
Constrained optimization problem, which calculates, to be obtained.
3. a kind of digital image interpolation algorithm of radiation modulation function fidelity according to claim 1, it is characterised in that：Institute
The longitudinal interpolation coefficient R (m, △ r) stated is obtained by solving the non-binary constraint optimization problem that following formula indicates：
Wherein, MTF (ui, △ r) be longitudinal direction interpolation coefficient R (m, △ r) discrete Fourier transform in spatial frequency uiThe width at place
Value, i.e. mtf value, ui=i/N-0.5, i indicate that the ordinal number of discrete Fourier transform down space frequency, N indicate that discrete fourier becomes
Change the sum of spatial frequency；
And establish following constraints：
A) equality constraint：
B) inequality constraints
|p+△r|<0.05
Wherein, p is equal to the value of independent variable x when longitudinal direction edge function E (x) is equal to 0.
4. a kind of digital image interpolation algorithm of radiation modulation function fidelity according to claim 3, it is characterised in that：Institute
The longitudinal edge function E (x) stated is expressed as
Wherein,For phase angle of the Fourier transformation at spatial frequency u of longitudinal interpolation coefficient R (m, △ r), x is indicated
The independent variable of longitudinal edge function E (x).
5. a kind of digital image interpolation algorithm of radiation modulation function fidelity according to claim 1, it is characterised in that：Institute
The lateral interpolation coefficients R (n, △ c) stated is obtained by solving the non-binary constraint optimization problem that following formula indicates：
Wherein, MTF (ui, △ c) be lateral interpolation coefficients R (n, △ c) discrete Fourier transform in spatial frequency uiThe width at place
Value, i.e. mtf value, ui=i/N-0.5, i indicate that the ordinal number of discrete Fourier transform down space frequency, N indicate that discrete fourier becomes
Change the sum of spatial frequency；
And establish following constraints：
A) equality constraint：
B) inequality constraints
|q+△c|<0.05
Wherein, q is equal to the value of independent variable y when transverse direction edge function E (y) is equal to 0.
6. a kind of digital image interpolation algorithm of radiation modulation function fidelity according to claim 5, it is characterised in that：Institute
The lateral edge function E (y) stated is expressed as：
Wherein,For phase angle of the Fourier transformation at spatial frequency u of lateral interpolation coefficients R (n, △ c), y is indicated
Lateral edge side argument of function.
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