CN109727196A - Image interpolation processing method - Google Patents
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Abstract
Image interpolation processing method, determine the coordinate variable of image, the known function point of interpolation frame, construct generalized circular matrix, vandermonde vector space, the inner product calculated between subspace base vector obtains the metric tensor of subspace, matrix inversion method obtains the metric tensor of the dual spaces of subspace, the base that dual spaces are obtained by matrix operation, obtains the pseudo inverse matrix of generalized circular matrix for the basic matrix transposition of dual spaces.Determine the position in interpolation frame point for being inserted section；The generalized circular matrix having with the same item number of interpolation frame is obtained according to the abscissa of insertion point set.The generalized circular matrix for being inserted into point set is obtained into interpolation matrix multiplied by pseudo inverse matrix.The pixel value that new pixel is obtained according to interpolation matrix converts dimension in one dimension of image pixel by the mobile single-frame interpolation of pixel compartments, completes another dimension interpolation after image conversion dimension, until completing whole interpolation.Keep image more acurrate lively, is conducive to scientific research exploration, the imaging that public security is solved a case with military surveillance.
Description
Technical field
The present embodiments relate to technical field of image processing, and in particular to a kind of image interpolation processing method.
Background technique
It is high that the software (such as IrfanView) that existing interpolation technique is prevalent in the image procossing of profession neutralizes computer
In the image processing toolbox of grade language (the Image Processing Toolbox of such as Matlab language).
For IrfanView, although can not really know its source code, there is interpolation twice in the process of running and put
Greatly, since interpolation method itself destroys the property of the intrinsic module in two-dimentional Euclidean plane, after first time interpolation amplification
Pixel outer is clearly present in the image after second of interpolation amplification, increases new noise.In IrfanView operational process
In interdepended due to two variable of x, y, will appear the twill noise of diagonal line style after interpolation amplification twice, while also destroying two
Tie up the property of the intrinsic module in Euclidean plane.Further, since the technical costs that IrfanView is used is high, businessman for
The considerations of economic interests, interpolated amplified picture cannot deposit in operational process.
In the specification of high-level [computer Matlab and in other information summarized, linear interpolation is commonly used
Most coarse interpolation method, and most accurate interpolation is exactly that two arguments cube (Bi-Cubic) in 16 pixel grids are polynomial
Interpolation, although bidimensional can simultaneously interpolation, destroy abelian group characteristic simple and easy.
It is mentioned in existing image processing literature when inserting pixel with interpolation method, is mostly the repairing for locality, or to put
Big figure and use.Large area be improve tens times of hundred times of picture precision increase pixel technical solution there is no.It is existing
Lagrange's interpolation only provides the interpolation coefficient of several low orders in some mathematical textbooks and handbook, and interpolation is simultaneously bad.
Therefore a kind of new image processing techniques scheme is needed.
Summary of the invention
For this purpose, the embodiment of the present invention provides a kind of image interpolation processing method, it can be used for image procossing and video image
Processing makes image become more acurrate, more continuous, is conducive to scientific research exploration, the imaging that public security is solved a case with military surveillance, can also be with
Applied to daily life photo.
To achieve the goals above, the embodiment of the present invention provides the following technical solutions: a kind of image interpolation processing method, packet
It includes:
1) the coordinate variable sequence and its coordinate system of interpolation image are determined；
2) determine n+1 known function point, make it as interpolation frame, the known function point include known coordinate point and
Known function value, wherein n is order；
3) generalized circular matrix V is constructed by the known function point1；
4) the generalized circular matrix V is used1N+1 row as row vector constitute n+1 rank square matrix, wherein n be natural number；
5) it according to the first interpolation theorem of Guo Shi, inverts to obtain n+1 rank Lagrange interpolation polynomial using vandermonde square matrix
Coefficient matrix, and each column vector of the matrix is made of the coefficient vector of the lagrange polynomial of each point respectively；
6) position in n+1 point of interpolation frame for being inserted section is determined；
7) number for giving insertion point between adjacent two pixel is inserted into d-1 new pixels, wherein d between adjacent two pixel
Insertion point is represented to the isodisperse in insertion section；
8) abscissa of insertion point set is determined；
9) the generalized circular matrix V having with the same item number of interpolation frame is obtained according to the abscissa of insertion point set2；
10) the interpolation matrix L of (d-1) × (n+1) is constructeddn；
11) according to the interpolation matrix LdnObtain the pixel value z of d-1 new pixelsi, wherein i=1 ..., d-1；
12) Interpolating transform g (x)=G (f (x)) is constructed, wherein f (x) is one-dimensional variable function, and g (x) is obtained after interpolation
Function；
13) in a dimension of image pixel since the first row or first row, in the first row or first row forward
By the mobile single-frame interpolation of pixel compartments；
14) next line or next column of image pixel are changed to, step 13) is repeated and completes next line or next column interpolation, instead
Step 13) is executed again and step 14) completes pixel last line interpolation of the image in corresponding dimension；
15) it is transformed into another dimension, another dimension after repeating step 13) and step 14) completion image conversion dimension is inserted
Value, until completing image whole interpolation.
As the preferred embodiment of image interpolation processing method, described image is two dimensional image, 3-D image or dimensional images,
The dimension of dimensional images is greater than three-dimensional.
As the preferred embodiment of image interpolation processing method, in the step 2), the known function value uses image slices
The gray value of vegetarian refreshments；The coefficient of interpolation polynomial is constructed by the known function value；
The known function value is by the way that being inserted, function is calculated or previously given mode obtains.
As the preferred embodiment of image interpolation processing method, in the step 6), there is n section in n+1 point, when n is
When odd number, there are center sections in n section.
As the preferred embodiment of image interpolation processing method, in the step 10), the formula of interpolation matrix is Ldn=V2V1 -1。
As the preferred embodiment of image interpolation processing method, using pixel rice transplanter to d-1 new pictures in the step 11)
The pixel value z of vegetarian refreshmentsiIt is calculated；
This formula is z=LdnY, this is the original place interpolation component of pixel rice transplanter；
Wherein z=(z1..., zd-1)
Y=(y1..., yn+1)
Y is the coordinate variable of image.
As the preferred embodiment of image interpolation processing method, in the step 13), pixel tripping original for image
Without interpolation, or in original pixel point position again interpolation；
By Interpolating transform g (x)=G (f (x)) make interpolating matrix in same a line or same row it is single-frame mobile forward until
The last one pixel.Because there is locomotive function, Interpolating transform g (x)=G (f (x)) is exactly our so-called pixel rice transplanters.
It further include step 16) for color image as the preferred embodiment of image interpolation processing method,
Step 16): it is gradually complete according to the component sequence of color image that step 13), step 14) and step 15) are repeated
At interpolation.
As the preferred embodiment of image interpolation processing method, for dimensional images, repeat step 13), step 14),
Step 15) and step 16) are sequentially completed the interpolation of dimensional images by dimension.
The embodiment of the present invention, which has the advantages that, can be used for two dimension, three-dimensional and higher-dimension image procossing, two step interpolation etc.
Valence can't see the trace noise of first time interpolation after a step interpolation, second of interpolation, since each dimension interpolation independently carries out,
One-dimensional interpolation method is convenient to complete to appoint by the twill noise not having after dimension interpolation between different dimensional, one-dimensional interpolation method by dimension interpolation
What data of dimension and interpolation of figure can make image become more acurrate, more lively, more see clearly autumn hair, more show spider's thread horse
Mark is conducive to scientific research exploration, the imaging that public security is solved a case with military surveillance, improves the treatment effect of image, so that interpolation image
Processing becomes more accurate, more acurrate, is easier.
Detailed description of the invention
It, below will be to embodiment party in order to illustrate more clearly of embodiments of the present invention or technical solution in the prior art
Formula or attached drawing needed to be used in the description of the prior art are briefly described.It should be evident that the accompanying drawings in the following description is only
It is merely exemplary, it for those of ordinary skill in the art, without creative efforts, can also basis
The attached drawing of offer, which is extended, obtains other implementation attached drawings.
L65, L83 involved in the technical program represent the label of interpolation series are as follows:
L65: 5 rank multinomial interpolation of Lagrange's interpolation 6 etc. point；
L83: 3 rank multinomial interpolation of Lagrange's interpolation 8 etc. point, it is other and so on；
Fig. 1 is the image extrapolation process method flow schematic diagram provided in the embodiment of the present invention；
Fig. 2 is the image extrapolation process method and step S16 schematic diagram provided in the embodiment of the present invention；
Fig. 3 is the image extrapolation process method and step S17 schematic diagram provided in the embodiment of the present invention；
Fig. 4 is that the black and white provided in the embodiment of the present invention shines treatment effect contrast schematic diagram；
Fig. 5 is the imaging results contrast schematic diagram for keeping smile more magnificent provided in the embodiment of the present invention；
Fig. 6 is the street corner dancing girl's photo schematic diagram provided in the embodiment of the present invention；
Fig. 7 is original image of the small bright hole by amplification in the street corner dancing girl's photo provided in the embodiment of the present invention；
Fig. 8 is 5 order polynomials provided in the embodiment of the present invention between the Lagrange's interpolation street corner of 6 equal parts center
Small bright hole pattern in dancing girl's photo；
Fig. 9 is that the green laser provided in the embodiment of the present invention injects indoor figure from the outdoor peep hole by door；
Figure 10 be the embodiment of the present invention in provide injection it is indoor round aperture amplification and screenshot formed about aperture
Low pixel number figure；
Figure 11 is the indoor aperture image L65 interpolation of injection that provides treated figure in the embodiment of the present invention；
Specific embodiment
Embodiments of the present invention are illustrated by particular specific embodiment below, those skilled in the art can be by this explanation
Content disclosed by book is understood other advantages and efficacy of the present invention easily, it is clear that described embodiment is the present invention one
Section Example, instead of all the embodiments.Based on the embodiments of the present invention, those of ordinary skill in the art are not doing
Every other embodiment obtained under the premise of creative work out, shall fall within the protection scope of the present invention.
The technical program uses following theoretical basis:
General geometric space can all be described with Lie group and Lie Algebraic Structure.The basic structure of Lie group is per one-dimensional list
Lie group is tieed up, its generation member is the tangent vector of one-dimensional curve, constitutes corresponding Lie algebra member.One-dimensional interpolation is inserted by dimension is complete again,
Greatly remain the exchangeability of the abelian group for the two-dimentional commutative Lie algebra being made of one-dimensional Lie algebra.
Theoretical physicist and applied mathematician Guo Dong rise the first interpolation theorem of Guo Shi proposed.
Theorem 1: it constitutes by x=x0, x1..., xnThe n+1 of the inverse matrix of vandermonde square array that generates of n+1 point
Column vector is the respective coefficient vector of Lagrange interpolation polynomial in these points.
It is calculated as parallel computation and simple and feasible using what this theorem made Lagrange interpolation polynomial coefficient, into
And Lagrange Polynomial interpolating method is made to become simple and feasible in the calculating of scientific numerical value.It is fixed using above-mentioned the first interpolation of Guo Shi
Reason can make computational accuracy improve 10,000,000,000 (10 when research calculates many electron atoms orbital wave function10) times effect.
The interpolation and extrapolation of Lagrange's interpolation all can be by being realized based on the first interpolation theorem of Guo Shi and being referred to as Guo Shi
Interpolation method, traditional extrapolation is not departing from the function subspace where interpolation method.
The technical solution of the embodiment of the present invention is based on above-mentioned theoretical basis.
Specifically, providing a kind of image interpolation processing method referring to Fig. 1, comprising the following steps:
S1: the sequence and coordinate system of the coordinate variable of image are determined；
S2: being determined as n+1 known function point of interpolation frame, and the known function point includes known coordinate point and
Know functional value, wherein n is order；
S3: generalized circular matrix V is constructed by the known function point1；
S4: the generalized circular matrix V is used1N+1 row as row vector constitute n+1 rank square matrix, wherein n be nature
Number；
S5: it according to the first interpolation theorem of Guo Shi, inverts to obtain n+1 rank Lagrange interpolation polynomial using vandermonde square matrix
Coefficient matrix, and each column vector of the matrix is made of the coefficient vector of the lagrange polynomial of each point respectively；
S6: the position in n+1 point of interpolation frame for being inserted section is determined；
S7: giving the number of insertion point between adjacent two pixel, d-1 new pixels is inserted between adjacent two pixel, wherein d
Insertion point is represented to the isodisperse in insertion section；
S8: the abscissa of insertion point set is determined；
S9: the generalized circular matrix V having with the same item number of interpolation frame is obtained according to the abscissa of insertion point set2；
S10: the interpolation matrix L of construction (d-1) × (n+1)dn；
S11: according to the interpolation matrix LdnObtain the pixel value z of d-1 new pixelsi, wherein i=1 ..., d-1；
S12: construction Interpolating transform g (x)=G (f (x)), wherein f (x) is one-dimensional variable function, and g (x) is obtained after interpolation
Function；
S13: in a dimension of image pixel since the first row or first row, in the first row or first row forward
By the mobile single-frame interpolation of pixel compartments；
S14: changing to the next line or next column of image pixel, repeats step S13 and completes next line or next column interpolation, instead
Step S13 and step S14 is executed again completes pixel last line interpolation of the image in corresponding dimension；
S15: being transformed into another dimension, and another dimension after repeating step S13 and step S14 completion image conversion dimension is inserted
Value, until completing image whole interpolation.
In one embodiment of image interpolation processing method, described image be two dimensional image, 3-D image or dimensional images,
The dimension of dimensional images is greater than three-dimensional.The sequence and coordinate system of the coordinate variable of image are determined in image interpolation processing method, such as
H-w (high-wide) or x-y (x coordinate-y-coordinate).Interpolation method is not limited to two dimensional image, can be any degree dimension image.As the four-dimension is schemed
As i.e. Spatial distributions image, coordinate can be asserted x-y-z-t.Due to using one-dimensional interpolation method, high space all can be all again for dimension
Dimension successively goes interpolation, does not interfere with each other.
In one embodiment of image interpolation processing method, in the step S2, the known function value uses image slices
The gray value of vegetarian refreshments；The coefficient of interpolation polynomial is constructed by the known function value；The known function value is by being inserted
Function calculates or previously given mode obtains.Such as n+1 known function point.It will be with the known letter of these known function points
Numerical value, to construct the coefficient of interpolation polynomial.The known function value of known function point can be by being inserted calculating for function
It is given in advance to being also possible to, such as the gray value of pixel.
In one embodiment of image interpolation processing method, in the step S6, there is n section in n+1 point, when n is
When odd number, there are center sections in n section.Such as n=0 be starting point, then between center be located at (n-1)/2 to (n+1)/2 it
Between.Such as it is then 3 that n+1, which is 4, n,；There are 3 sections between 4 points, (n-1)/2=1, (n+1)/2=2 are located at n=1 and n between center
Between=2.If n is even number, there is 2 centers section, interpolation should be in n/2-1 to n/2, two section n/2 to n/2+1.
In one embodiment of image interpolation processing method, in the step S10, the formula of interpolation matrix is Ldn=V2V1 -1.Using pixel rice transplanter to the pixel value z of d-1 new pixels in the step S11iIt is calculated；
This formula is z=LdnY, this is the original place interpolation component of pixel rice transplanter；
Wherein z=(z1..., zd-1)
Y=(y1..., yn+1)
Y is the coordinate variable of image.Specifically, being a linear lattice between for example two neighboring pixel, d is divided into after interpolation
Part (is exactly that a plane grid becomes d for 2-d plane graph2A plane grid.It will d-1 new pixels of insertion between two pixels
Point.For image, two dimensional image is exactly two-dimentional field, and interpolation matrix is exactly pixel rice transplanter as you were, itself is first
It is n that tail, which subtracts each other length, width 1, and original pixel plays the role of determining row and arrange surely and the reference of definite value.
Specifically, one is counted to a several corresponding relationship and is known as function, the corresponding relationship of a function a to function
Referred to as convert.F (x) is the function of an one-dimensional variable, and for example certain in two-dimension picture is one-dimensional, and independent variable x is exactly the position of pixel
Serial number is set, domain is 1 to N.Since interpolation is carried out by dimension, does not need to consider multidimensional while slotting problem, g (x) are
The function obtained after interpolation will be inserted into d-1 point between two pixels, this is that the domain of new function is 1 to d (N-1)+1.For
Do not have the pixel value f (i) of the ith pixel of interpolation, can be used to+1 pixel value g (d (i- of d (i-1) for defining new primitive definition
1)+1)=f (i).
In one embodiment of image interpolation processing method, in the step S13, pixel tripping original for image
Without interpolation, or in original pixel point position again interpolation；Make interpolating matrix same by Interpolating transform g (x)=G (f (x))
It is single-frame mobile until the last one pixel forward in capable or same row.
Specifically, can not insert with tripping for original pixel, the corresponding position weight for being inserted in original pixel again can also be put down
Existing initial value.Interpolating transform g (x)=G (f (x)) seems that the pixel rice transplanter put on a moving belt makes interpolating matrix in same a line
It is single-frame mobile until the last one pixel forward.
It further include step S16 for color image in one embodiment of image interpolation processing method,
Step S16: it is gradually complete according to the component sequence of color image that step S13, step S14 and step S15 are repeated
At interpolation.For color image, it is respectively a two dimensional image that there are three components R, G and B for color dimension, can by step S13, S14,
S15 is gradually completed according to component sequence.
It further include step S17 for dimensional images, step S17 is repeated in one embodiment of image extrapolation process method
Step S13, step S14, step S15 and step S16 are executed, the interpolation of dimensional images is sequentially completed by dimension.
The practice effect of technical solution in the embodiment of the present invention is illustrated below.
Referring to fig. 4, technical solution in the embodiment of the present invention is applied to the processing that black and white is shone.Picture is taken from Matlab
An exemplary criteria shine, the head of entitled Lena shines.In order to show the function of different interpolation methods, the side of Lena cap is carried out
Amplification.Top figure is amplified original image in Fig. 4, due to the low visible pixels grid of pixel number.Middle graph in Fig. 4 uses four
The interpolation method of 8x8 based on Lagrangian cubic polynomial between point, the function base of interpolation are 1, x, x2, x3, image becomes smooth company
It is continuous.The figure of bottom has used the function space of the 8x8 between 4 points based on technical solution of the present invention to insert method, the letter of interpolation in Fig. 4
Base is x0..., x6, the cap lines in image becomes apparent from.
Referring to Fig. 5, the imaging for keeping beauty smile more magnificent using technical solution in the embodiment of the present invention.Top figure in Fig. 5
It is the low pixel number picture obtained by partial enlargement, examines it can be seen that discontinuity caused by pixel grid.In Fig. 5
Middle graph using the interpolation method of the 8x8 based on Lagrangian cubic polynomial between 4 points, the function base of interpolation is 1, x, x2, x3,
Image becomes smooth continuous.The figure of bottom inserts method using the function space of the 8x8 between 4 points in Fig. 5, and the function base of interpolation is
x0..., x7, high priest is the personage of a performance in image, and the personage smile is more bright than original image and interpolation method interpolation
It is rotten, and everyone facial expression all becomes more lively.This is because higher-order function base can highlight between adjacent pixels
Change in rain.And these variations are to have been smoothed out in Lagrange's interpolation.
The following contents verifies the effect of the technical solution processing live photo of the present embodiment.
It is the photo of street corner dancing girl, number of pixels is accurately 1720 × 2293 × 3=11831880 referring to Fig. 6.From left to right
There are two small bright holes for the overhead of 4th personage.Fig. 7 is original image of the small bright hole by amplification, it can be seen that rectangular pixel side
Lattice.Because amplifying the new picture of screenshot becomes the picture of low pixel number.Two unthreaded holes show pixel grid in figure, in addition to this simultaneously
Without other abnormal.
The bright between the glug of 6 equal parts center of 5 order polynomials is done with the point (5 sections) of 6 known function values
Day interpolation, referring to Fig. 8, figure becomes smooth, but has no new phenomenon appearance.
Fig. 9 is to inject interior from the outdoor peep hole by door with green laser, and another people claps for 4-5 meters at a distance indoors
The whole picture of Xiamen.Figure 10 is round aperture amplification and screenshot forms the low pixel number picture about aperture, and pixel square is bright
It is aobvious.Figure 11 is the L65 interpolation method processing result to aperture image, and figure is smooth.
Although above having used general explanation and specific embodiment, the present invention is described in detail, at this
On the basis of invention, it can be made some modifications or improvements, this will be apparent to those skilled in the art.Therefore,
These modifications or improvements without departing from theon the basis of the spirit of the present invention are fallen within the scope of the claimed invention.
Claims (9)
1. image interpolation processing method characterized by comprising
1) sequence and coordinate system of the coordinate variable of image are determined；
2) it is determined as n+1 known function point of interpolation frame, the known function point includes known coordinate point and known letter
Numerical value, wherein n is order；
3) generalized circular matrix V is constructed by the known function point1；
4) the generalized circular matrix V is used1N+1 row as row vector constitute n+1 rank square matrix, n is natural number；
5) according to the first interpolation theorem of Guo Shi, it is using what vandermonde square matrix inverted to obtain n+1 rank Lagrange interpolation polynomial
Matrix number, and each column vector of the matrix is made of the coefficient vector of the lagrange polynomial of each point respectively；
6) position of the section in n+1 point of interpolation frame is inserted in determination；
7) number for giving insertion point between adjacent two pixel is inserted into d-1 new pixels between adjacent two pixel, and wherein d is represented
Isodisperse of the insertion point to insertion section；
8) abscissa of insertion point set is determined；
9) the generalized circular matrix V having with the same item number of interpolation frame is obtained according to the abscissa of insertion point set2；
10) the interpolation matrix L of (d-1) × (n+1) is constructeddn；
11) according to the interpolation matrix LdnObtain the pixel value z of d-1 new pixelsi, wherein i=1 ..., d-1；
12) Interpolating transform g (x)=G (f (x)) is constructed, wherein f (x) is one-dimensional variable function, and g (x) is the letter obtained after interpolation
Number；
13) in a dimension of image pixel since the first row or first row, picture is pressed forward in the first row or first row
The mobile single-frame interpolation of plain lattice；
14) next line or next column of image pixel are changed to, step 13) is repeated and completes next line or next column interpolation, hold repeatedly
Row step 13) and step 14) complete pixel last line interpolation of the image in corresponding dimension；
15) it is transformed into another dimension, step 13) is repeated and step 14) completes another dimension interpolation after image conversion dimension, directly
To completion image whole interpolation.
2. image interpolation processing method according to claim 1, which is characterized in that described image is two dimensional image, three-dimensional
The dimension of image or dimensional images, dimensional images is greater than three-dimensional.
3. image interpolation processing method according to claim 1, which is characterized in that in the step 2), the known letter
Numerical value uses the gray value of image slices vegetarian refreshments；The coefficient of interpolation polynomial is constructed by the known function value；
The known function value is by the way that being inserted, function is calculated or previously given mode obtains.
4. image interpolation processing method according to claim 1, which is characterized in that in the step 6), have in n+1 point
N section, when n is odd number, there are center sections in n section.
5. image interpolation processing method according to claim 1, which is characterized in that in the step 10), interpolation matrix
Formula is Ldn=V2V1 -1。
6. image interpolation processing method according to claim 1, which is characterized in that inserted in the step 11) using pixel
Pixel value z of the seedling machine to d-1 new pixelsiIt is calculated；
This formula is z=EdnY, this is the original place interpolation component of pixel rice transplanter；
Wherein z=(z1..., zd-1)
Y=(y1..., yn+1)
Y is the coordinate variable of image.
7. image interpolation processing method according to claim 1, which is characterized in that in the step 13), for image original
Some pixel trippings are without interpolation, or in original pixel point position again interpolation；
Keep interpolating matrix single-frame mobile until last forward in same a line or same row by Interpolating transform g (x)=G (f (x))
One pixel.Because there is locomotive function, Interpolating transform g (x)=G (f (x)) is exactly our so-called pixel rice transplanters.
8. image interpolation processing method according to claim 1, which is characterized in that further include step for color image
16),
Step 16): step 13), step 14) and step 15) are repeated and gradually completes to insert according to the component sequence of color image
Value.
9. image interpolation processing method according to claim 8, which is characterized in that for dimensional images, repeat step
It is rapid 13), step 14), step 15) and step 16), the interpolation of dimensional images is sequentially completed by dimension.
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| CN111858142A (en) * | 2020-07-24 | 2020-10-30 | 山东云海国创云计算装备产业创新中心有限公司 | Data processing method and device, electronic equipment and storage medium |
| CN112364319A (en) * | 2020-10-12 | 2021-02-12 | 西安电子科技大学 | Biological characteristic template protection method and device based on binary tree shuffling |
| CN115526810A (en) * | 2022-11-07 | 2022-12-27 | 青岛理工大学 | Underwater image enhancement method |
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