CN109816590B - Image extrapolation processing method - Google Patents
Image extrapolation processing method Download PDFInfo
- Publication number
- CN109816590B CN109816590B CN201811598972.XA CN201811598972A CN109816590B CN 109816590 B CN109816590 B CN 109816590B CN 201811598972 A CN201811598972 A CN 201811598972A CN 109816590 B CN109816590 B CN 109816590B
- Authority
- CN
- China
- Prior art keywords
- interpolation
- image
- matrix
- pixel
- points
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Images
Landscapes
- Image Processing (AREA)
Abstract
The image extrapolation processing method comprises the steps of determining coordinate variables of an image and known function points of an interpolation frame, constructing a Van der Monte matrix and a Van der Monte vector space, calculating an inner product between subspace base vectors to obtain a metric tensor of a subspace, obtaining the metric tensor of a dual space of the subspace by a matrix inversion method, obtaining a base of the dual space by matrix operation, and transposing the base matrix of the dual space to obtain a pseudo-inverse matrix of the Van der Monte matrix. Determining the position of the interpolated interval in the interpolation frame point; and acquiring a Van der Monte matrix with the same terms as the interpolation frame according to the abscissa of the interpolation point set. And multiplying the vandermonde matrix of the insertion point set by the pseudo-inverse matrix to obtain an extrapolation matrix. And obtaining the pixel value of a new pixel point according to the extrapolation matrix, moving the interpolation grid by grid according to the pixel grid in one dimension of the image pixel, converting the dimension, and then performing interpolation in another dimension after completing the dimension conversion of the image until completing all the interpolation. The image is more accurate and vivid, and is beneficial to developing research, public security solution and military reconnaissance.
Description
Technical Field
The embodiment of the invention relates to the technical field of image processing, in particular to an image extrapolation processing method.
Background
The existing interpolation technology is commonly existed in professional Image Processing software (such as IrfanView) and in an Image Processing tool box of a computer high-level language (such as Image Processing Toolbox of Matlab language).
For IrfanView, although the source code of IrfanView cannot be really known, two times of interpolation amplification exist in the running process, and because the interpolation method destroys the inherent property of an addition group of a two-dimensional Euclidean plane, the outer edge of a pixel after the first interpolation amplification obviously exists in an image after the second interpolation amplification, and new noise is added. In the IrfanView running process, because x and y variables are mutually dependent, diagonal twill noise can appear after two times of interpolation amplification, and the inherent property of an addition group of a two-dimensional Euclidean plane is damaged. In addition, due to the high technical cost adopted by the IrfanView, the picture interpolated and amplified in the running process cannot be stored in a disk due to the consideration of economic benefits of merchants.
In the specification of Matlab, an advanced computer language, and other information gathered, linear interpolation is the coarsest interpolation method commonly used, and the most precise interpolation is interpolation of a bivariate Cubic (Bi-Cubic) polynomial in a 16-pixel grid, although two dimensions can be interpolated simultaneously, the simple and clear characteristics of an exchange group are destroyed.
When pixels are interpolated by interpolation, the conventional image processing documents are mostly used for local repair or for enlarging a pattern. There is no technical solution for increasing pixels in large area to improve the picture accuracy by tens of hundreds of times. The Lagrange interpolation method in the existing mathematical textbook and handbook only provides a few low-order interpolation coefficients, and the interpolation effect is not good. Therefore, a new image processing technical scheme is needed.
Disclosure of Invention
Therefore, the embodiment of the invention provides an image extrapolation processing method, which can be used for image processing and video image processing, so that the image becomes more accurate, more vivid, more insights into autumn hair and more clearly shows spider silk trail, and is more favorable for developing scientific research, public security case solving and military reconnaissance.
In order to achieve the above object, the embodiments of the present invention provide the following technical solutions: an image extrapolation processing method, comprising:
1) Determining the sequence and coordinate system of the coordinate variables of the image;
2) Determining n +1 known function points as an interpolation frame, wherein the known function points comprise known coordinate points and known function values, and n is an order;
3) Constructing a Van der Waals matrix V from the known function points 1 ；
4) Using the vandermonde matrix V 1 The n +1 lines of (1) constitute an m-dimensional vandermonde vector space as row vectors, and the base of the n + 1-dimensional subspace of the m-dimensional vandermonde vector space as the row vector is denoted as e 0 ,e 1 ,…,e n Vandermonde matrix is denoted V 1 ＝(e 0 ,e 1 ,…,e n ) Wherein m is more than or equal to n +1, m and n are natural numbers;
5) Calculating the inner product between the subspace base vectors to obtain the metric tensor g of the subspace ij ＝e i ·e j ；
6) Obtaining a metric tensor g of a dual space of the subspace through a matrix inversion method ij * The matrix of the dual space is the inverse of the metric number of the subspace, i.e. (g) ij * )＝(g ij ) -1 ；
7) Obtaining the base of the dual space through matrix operation, wherein the base of the dual space is (e) 0 ,e 1 ,…,e n )＝(e 0 ,e 1 ,…,e n )(g ij * )；
8) Transposing the basis matrix of the dual space to obtain a pseudo-inverse V of the vandermonde matrix 1 -1 I.e. V 1 -1 ＝(e 0 ,e 1 ,…,e n ) T Wherein T represents a transpose operation of the matrix;
9) Determining the position of the interpolated interval in n +1 points of an interpolation frame;
10 Given the number of insertion points between two adjacent pixels, d-1 new pixel points are inserted between two adjacent pixels, wherein d represents the equal division of the insertion points to the insertion interval;
11 Determine the abscissa of the set of insertion points;
12 Obtain a Van der Waals matrix V having the same number of terms as the interpolation frame from the abscissa of the set of interpolation points 2 ；
13 An extrapolation matrix E for constructing (d-1) × (n + 1) dn ；
14 According to the extrapolation matrix E dn Obtaining the pixel value z of d-1 new pixel points i Wherein i =1, \8230;, d-1;
15 Constructing an interpolation transformation G (x) = G (f (x)), wherein f (x) is a one-dimensional variable function, and G (x) is a function obtained after interpolation;
16 Starting from the first row or column in one dimension of the image pixels, moving the grid-wise interpolation by pixel grid forward in the first row or column;
17 Changing to the next line or the next column of the image pixels, repeating the step 16) to complete the interpolation of the next line or the next column, and repeatedly executing the step 16) and the step 17) to complete the interpolation of the last line of the pixels of the image in the corresponding dimension;
18 And) converting to another dimension, and repeating the step 16) and the step 17) to finish the interpolation of the other dimension after the dimension conversion of the image until the whole interpolation of the image is finished.
As a preferable scheme of the image extrapolation processing method, the image is a two-dimensional image, a three-dimensional image or a high-dimensional image, and the dimension of the high-dimensional image is larger than three dimensions.
As a preferred scheme of the image extrapolation processing method, in the step 2), the known function value adopts a gray value of an image pixel point; constructing coefficients of an interpolation polynomial from the known function values;
the known function values are obtained by calculating or in a predetermined manner for the interpolated function.
In a preferred embodiment of the image extrapolation method in step 9), n intervals are present in the n +1 points, and when n is an odd number, the n intervals have a central interval.
As a preferable embodiment of the image extrapolation processing method, in the step 13), the formula of the extrapolation matrix is E dn ＝V 2 V 1 -1 。
As the preferred scheme of the image extrapolation processing method, the pixel value z of d-1 new pixel points is determined by the pixel transplanter in the step 14) i Calculating;
this formula is z = E dn y, the y is an in-situ interpolation component of the pixel transplanter;
wherein z = (z) 1 ,…,z d-1 )
y＝(y 1 ,…,y n+1 )
And y is a coordinate variable of the image.
As a preferred scheme of the image extrapolation processing method, in the step 16), the original pixel points of the image are skipped without interpolation, or interpolation is performed again at the positions of the original pixel points;
the interpolation matrix is moved forward by grid within the same row or column by the interpolation transformation G (x) = G (f (x)) until the last pixel. With the shift function, the interpolation transformation G (x) = G (f (x)) is a pixel transplanter.
As a preferred embodiment of the image extrapolation processing method, for the color image, further comprising step 19),
step 19): step 16), step 17) and step 18) are repeatedly performed to successively complete interpolation in accordance with the component order of the color image.
As a preferable scheme of the image extrapolation processing method, for the high-dimensional image, the step 16), the step 17), the step 18), and the step 19) are repeatedly performed, and interpolation of the high-dimensional image is sequentially performed in one dimension.
The embodiment of the invention has the following advantages: the interpolation method can be used for two-dimensional, three-dimensional and high-dimensional image processing, two-step interpolation is equivalent to one-step interpolation, no trace noise of the first interpolation can be seen after the second interpolation, because each-dimensional interpolation is independently carried out, no twill noise between different dimensions exists after one-dimensional interpolation by a one-dimensional interpolation method, interpolation of data and graphics of any dimension can be conveniently completed by one-dimensional interpolation by the one-dimensional interpolation method, the image can become more accurate, more vivid, more insights autumn hair can be observed, spider silk trail can be more clearly shown, development of scientific research, public security case solving and military reconnaissance is facilitated, the image processing effect is improved, and the interpolation image processing becomes more accurate, more accurate and easier.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below. It should be apparent that the drawings in the following description are merely exemplary, and that other embodiments can be derived from the drawings provided by those of ordinary skill in the art without inventive effort.
The reference numbers of L65, E83 and E85 representing interpolation series in the technical scheme are as follows:
l65, 6 equal division 5-order polynomial interpolation by a Lagrange interpolation method;
e65, an extrapolation method 6 equally divides the pseudo 5-order polynomial interpolation;
e83, an extrapolation method 8 equally divides the pseudo 3-order polynomial interpolation;
e85 extrapolation method 8 equally divides pseudo 5 th order polynomial interpolation, and so on.
FIG. 1 is a schematic flow chart of an image extrapolation method provided in an embodiment of the present invention;
FIG. 2 is a schematic diagram of a step S19 of an image extrapolation method according to an embodiment of the present invention;
FIG. 3 is a diagram illustrating a step S20 of an image extrapolation processing method according to an embodiment of the present invention;
FIG. 4 is a schematic diagram illustrating a comparison between black and white processing effects provided in the embodiment of the present invention;
FIG. 5 is an enlarged original drawing of a small bright hole in a street dancing girl photo according to an embodiment of the present invention;
fig. 6 is a small-bright-hole diagram in a lagrangian interpolation street dancing girl photo with a 5 th-order polynomial equally divided into 6 central intervals, provided in the embodiment of the present invention;
FIG. 7 shows an example of the present invention in which extrapolation is used when the higher-order function term is included in the first embodiment 10 A small and bright hole picture in a photo of a real street dancing girl;
FIG. 8 is a view of green laser light provided in an embodiment of the present invention being emitted from the exterior into the interior through a viewing port in the door;
FIG. 9 is an enlarged and screenshot surrounding an aperture formed as a low pixel count image with respect to the aperture provided in an embodiment of the present invention for impinging on a chamber;
FIG. 10 is a diagram illustrating interpolation of an aperture image L65 for an injection chamber according to an embodiment of the present invention;
FIG. 11 is a schematic diagram of an image of a pinhole projected into a chamber according to an embodiment of the present invention, taken through x 0 ,…,x 10 A graph after the E65 extrapolation process of the term;
FIG. 12 is a schematic view of an image of a pinhole projected into a chamber according to an embodiment of the present invention, taken through x 0 ,…,x 10 E83 extrapolation processed graph of terms;
FIG. 13 is an image of a pinhole injected into a chamber provided in an embodiment of the present invention using the present techniquesScheme passes through x 0 ,…,x 12 E85 extrapolation of the term processed graph;
fig. 14 is a ghost view of the lower edge of the eave irradiated by sunlight provided in the embodiment of the present invention.
Detailed Description
The present invention is described in terms of specific embodiments, and other advantages and benefits of the present invention will become apparent to those skilled in the art from the following disclosure. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The technical scheme adopts the following theoretical basis:
the general geometric space can be described by lie groups and lie algebraic structures. The basic structure of the lie group is a single-dimensional lie group of each dimension, and the generating element of the lie group is a tangent vector of a single-dimensional curve to form a corresponding lie algebraic element. The single-dimensional interpolation is carried out by full interpolation one by one, so that the commutative property of the switching group of the two-dimensional switching lie algebra formed by the single-dimensional lie algebra is greatly reserved.
The first interpolation theorem of guo, proposed by theoretical physicists and applied mathematicians guo dongshi.
Theorem 1: the composition is composed of x = x 0 ,x 1 ,…,x n The n +1 column vectors of the inverse matrix of the vandermonde square matrix generated at the n +1 points of (a) are the respective coefficient vectors of the lagrange interpolation polynomials at these points.
By utilizing the theorem, the calculation of the Lagrange interpolation polynomial coefficient becomes parallel calculation and is simple and feasible, and further the Lagrange polynomial interpolation method becomes simple and feasible in scientific numerical calculation. By adopting the first Guo's interpolation theorem, the calculation accuracy can be improved by 100 hundred million (10 hundred million) when the multi-electron-atom orbital wave function is researched and calculated 10 ) The effect is doubled.
Both interpolation and extrapolation of the lagrange interpolation can be achieved by the first interpolation theorem based on guo and are collectively referred to as guo interpolation, and conventional extrapolation does not exceed the functional subspace in which the interpolation is located. The interpolation method exceeding the original function subspace is called Guo's extrapolation method, and the theoretical description thereof is the second interpolation theorem of Guo's.
Theorem 2: the composition is composed of x = x 0 ,x 1 ,…,x n The n +1 column vectors of the pseudo-inverse matrix of the vandermonde rectangular matrix (column number m.gtoreq.n + 1) generated at the n +1 points of (a) are coefficient vectors of the extrapolation polynomials at these points.
On the x-y plane, n +1 x values are known, x = x 0 ,x 1 ,…,x n At respectively corresponding n +1 y values y 0 ,y 1 ,…,y n A unique m (m is more than or equal to n + 1) degree polynomial is determined by a pseudo-inverse matrix method according to theorem 2. When m = n +1, we go back to classical lagrangian interpolation described by theorem 1. The key point of the extrapolation method and the breakthrough of the extrapolation method to the classical theory lies in m>n +1. This is the core of the theory of the technical solution of the present invention.
The method is initiated, and changes the thousand-ancient law of Euclidean: "a straight line can be uniquely determined between two points", but a parabola and a cubic curve cannot be uniquely determined, and a high-order curve cannot be uniquely determined. The generalized version of euclidean theorem is that n +1 points on a plane can uniquely determine an n-order polynomial curve, and is also the basis of the classical lagrangian interpolation polynomial theory. The technical scheme of the invention breaks through the limitation of the traditional technical scheme, and for the given n +1 function value points, a high-order curve of any order can be uniquely determined.
The technical scheme of the embodiment of the invention is based on the theoretical basis.
Specifically, referring to fig. 1, an image extrapolation processing method is provided, which includes the following steps:
s1: determining the sequence and coordinate system of the coordinate variables of the image;
s2: determining n +1 known function points as an interpolation frame, wherein the known function points comprise known coordinate points and known function values, and n is an order;
s3: constructing van der Waals by the known function pointsMongolian matrix V 1 ；
S4: using the vandermonde matrix V 1 The n +1 lines of (1) constitute an m-dimensional vandermonde vector space as row vectors, and the base of the n + 1-dimensional subspace of the m-dimensional vandermonde vector space as the row vector is denoted as e 0 ,e 1 ,…,e n Vandermonde matrix is denoted V 1 ＝(e 0 ,e 1 ,…,e n ) Wherein m is more than or equal to n +1, m and n are natural numbers;
s5: calculating the inner product between the subspace base vectors to obtain the metric tensor g of the subspace ij ＝e i ·e j ；
S6: obtaining a metric tensor g of a dual space of the subspace through a matrix inversion method ij * The matrix of the dual space is the inverse of the metric number of the subspace, i.e. (g) ij * )＝(g ij ) -1 ；
S7: obtaining the base of the dual space through matrix operation, wherein the base of the dual space is (e) 0 ,e 1 ,…,e n )＝(e 0 ,e 1 ,…,e n )(g ij * )；
S8: transposing the base matrix of the dual space to obtain a pseudo-inverse matrix V with a size of mx (n + 1) 1 -1 I.e. V 1 -1 ＝(e 0 ,e 1 ,…,e n ) T Wherein T represents a transpose operation of the matrix;
s9: determining the position of the interpolated interval in the n +1 points of the interpolation frame;
s10: giving the number of insertion points between two adjacent pixels, and inserting d-1 new pixel points between the two adjacent pixels, wherein d represents the equal division of the insertion point pairs in an insertion interval;
s11: determining the abscissa of the insertion point set;
s12: acquiring a Van der Monte matrix V with the same number of terms as the interpolation frame according to the abscissa of the interpolation point set 2 ；
S13: constructing an extrapolation matrix E of (d-1) × (n + 1) dn ；
S14: according to the exteriorPlug matrix E dn Obtaining the pixel value z of d-1 new pixel points i Wherein i =1, \8230;, d-1;
s15: constructing an interpolation transformation G (x) = G (f (x)), wherein f (x) is a one-dimensional variable function, and G (x) is a function obtained after interpolation;
s16: moving the grid-by-grid interpolation forward by pixel grid in the first row or the first column from the first row or the first column in one dimension of the image pixels;
s17: changing to the next row or the next column of the image pixels, repeating the step S16 to complete the interpolation of the next row or the next column, and repeatedly executing the step S16 and the step S17 to complete the interpolation of the last row of the pixels of the image in the corresponding dimension;
s18: and converting to another dimension, and repeating the step S16 and the step S17 to finish the interpolation of the other dimension after the dimension conversion of the image until the whole interpolation of the image is finished.
In an embodiment of the image extrapolation processing method, the image is a two-dimensional image, a three-dimensional image or a high-dimensional image, and the dimension of the high-dimensional image is larger than three dimensions. The image extrapolation process determines the order and coordinate system of the coordinate variables of the image, e.g. h-w (height-width) or x-y (x-y coordinate). The interpolation method is not limited to the two-dimensional image, and may be an arbitrary-dimension image. For example, a four-dimensional image, i.e., a spatially dynamic image, the coordinates can be established as x-y-z-t. Because of the adoption of the single-dimensional interpolation method, the space with higher dimension can be sequentially interpolated by various dimensions without mutual interference.
In an embodiment of the image extrapolation processing method, in step S2, the known function value is a gray value of an image pixel; constructing coefficients of an interpolation polynomial from the known function values; the known function values are obtained by calculating or in a predetermined manner for the interpolated function. Such as n +1 known function points. The known function values of these known function points will be used to construct the coefficients of the interpolating polynomial. The known function value of the known function point can be obtained by calculating the interpolated function, or can be given in advance, such as the gray value of the pixel point.
In an embodiment of the image extrapolation processing method, in step S9, n intervals exist in the n +1 points, and when n is an odd number, a central interval exists in the n intervals. For example, n =0 is the starting point, the central interval is between (n-1)/2 and (n + 1)/2. For example, n +1 is 4, n is 3; there are 3 intervals between 4 points, (n-1)/2 =1, (n + 1)/2 =2, and the central interval is located between n =1 and n = 2. If n is even, there are 2 central intervals, and the interpolation should be in the interval of n/2-1 to n/2, n/2 to n/2+ 1.
In an embodiment of the image extrapolation processing method, in the step S13, the formula of the extrapolation matrix is E dn ＝V 2 V 1 -1 . In the step S14, a pixel value z of d-1 new pixel points is set by a pixel transplanter i Calculating;
this formula is z = E dn y, the value is an in-situ interpolation component of the pixel rice transplanter;
wherein z = (z) 1 ,…,z d-1 )
y＝(y 1 ,…,y n+1 )
And y is a coordinate variable of the image. Specifically, for example, a linear grid is formed between two adjacent pixels, and the linear grid is divided into d parts after interpolation (for a two-dimensional planar graph, a planar grid is changed into d 2 And (5) dividing the plane into squares. D-1 new pixel points are inserted between the two pixels. Vividly, the two-dimensional image is a two-dimensional field area, the extrapolation matrix is an in-situ immobile pixel rice transplanter, the length of the subtraction between the head and the tail of the extrapolation matrix is n, the width of the extrapolation matrix is 1, and the original pixels play the reference roles of row and column fixing and fixed value.
Specifically, the correspondence of a number to a number is called a function, and the correspondence of a function to a function is called a transformation. f (x) is a function of a one-dimensional variable, such as a dimension in a two-dimensional picture, and the independent variable x is the position number of a pixel and has a definition field of 1 to N. Because the interpolation is carried out dimension by dimension, the problem of multi-dimension simultaneous interpolation does not need to be considered, g (x) is a function obtained after the interpolation, d-1 points are inserted between two pixels, and the definition domain of the new function is 1 to d (N-1) +1. For the pixel value f (i) of the ith pixel without interpolation, the d (i-1) +1 pixel value g (d (i-1) + 1) = f (i) of the new pixel function can be defined.
In an embodiment of the image extrapolation processing method, in step S16, the original pixel points of the image are skipped without interpolation, or interpolation is performed again at the original pixel point positions; the interpolation matrix is moved forward by grid within the same row or column by the interpolation transformation G (x) = G (f (x)) until the last pixel. With the shift function, the interpolation transformation G (x) = G (f (x)) is a pixel transplanter.
Specifically, the original pixel may be skipped without interpolation, or may be interpolated to the corresponding position of the original pixel to reproduce the original value. Interpolation transformation G (x) = G (f (x)) as a pixel transplanter placed on a conveyor belt moves the difference matrix forward in the same row, grid by grid, until the last pixel.
In an embodiment of the image extrapolation processing method, for the color image, further comprising step S19,
step S19: the step S16, the step S17, and the step S18 are repeatedly performed to successively complete interpolation in accordance with the component order of the color image. For a color image, the color dimension has three components R, G and B, each being a two-dimensional image, and can be successively completed in the order of the components in steps S16, S17, S18.
In an embodiment of the image extrapolation processing method, for the high-dimensional image, the method further includes step S20, and step S20 repeatedly executes step S16, step S17, step S18, and step S19, and completes the interpolation of the high-dimensional image in order of one dimension.
Practical effects of the technical solutions in the embodiments of the present invention are explained below.
Referring to fig. 4, the technical solution in the embodiment of the present invention is applied to black and white photograph processing. The picture was taken from an exemplary standard photograph in Matlab, a head photograph named Lena. The side of the Lena hat has been enlarged to show the function of the different interpolation methods. The upper diagram in fig. 4 is an enlarged original diagram, and pixel squares are visible due to a low number of pixels. The intermediate diagram in fig. 4 uses an 8x8 interpolation method based on lagrange cubic polynomial between four points, the function base of the interpolation being 1,x, x 2 ，x 3 The image becomes smooth and continuous. The lowest graph in FIG. 4 uses 8x8 function space interpolation between four points based on the technical solution of the present invention, and the function base of the interpolation is x 0 ，…，x 6 The lines of the hat in the image become clearer.
By adopting the technical scheme in the embodiment of the invention, the beautiful girl smile can be displayed more brightly. The discontinuity caused by the pixel grids can be seen by carefully observing the low-pixel-number picture obtained by local amplification. The interpolation method of 8x8 based on Lagrange cubic polynomial between four points is adopted, and the function base of the interpolation is 1,x 2 ，x 3 The image becomes smooth and continuous. By 8x8 function space interpolation between four points, the function base of interpolation is x 0 ，…，x 7 The main character in the image is a character performing a smile that is brighter than that of the original and interpolated by interpolation, and the facial expression of each person becomes more vivid. This is because the higher order functional basis may highlight spurious changes between adjacent pixels. These variations are smoothed out in the lagrange interpolation method.
It is known that natural light passing through a pinhole can produce Fraunhofer diffraction, which is an optical effect in nature. The fine physical phenomenon which cannot be observed by naked eyes at ordinary times can be revealed in the process of processing the life photos by the technical scheme. Therefore, the physical phenomenon is proved by designing a laser experiment for observation, which shows that unexpected new effects can be observed on a display screen of a scientific research instrument if the technical scheme of the invention is adopted. Various telescopic systems of military reconnaissance and observation can thereby find fine targets. Various forensics and observation systems of the police may discover new subtle cues and new evidence.
The following demonstrates the effect of the technical solution of the present embodiment on processing life photos.
The number of pixels is exactly 1720 × 2293 × 3=11831880. Two small bright holes are arranged above the top of the head of the fourth figure from the left. Fig. 5 is an enlarged view of the original with small bright holes, and square pixel squares can be seen. Because the enlarged screen captures a new picture as a low pixel count picture. Two apertures in the figure show a grid of pixels, unless otherwise noted.
The lagrangian interpolation of 6 equal divisions of the central interval with a 5 th order polynomial is done with 6 points of known function values (5 intervals), see fig. 6, the graph becomes smooth but no new phenomenon appears.
Referring to FIG. 7, the present embodiment includes a higher function term to x by extrapolation 10 When the light source is used, an unexpected technical effect is achieved, and a surrounding diaphragm is displayed outside the circular light hole. This is precisely the diffraction fringe of the optics, known as Fraunhofer diffraction.
In order to ensure that the surrounding aperture fringes obtained by the imaging of the technical scheme are Freund's optical diffraction, laser experiments are continuously designed for repeated verification. Referring to fig. 8, a green laser is used to shoot the green laser into the room from the outside through the observation hole on the door, and another person takes an overall picture of the door at a distance of 4-5 meters in the room. Fig. 9 is a picture enlarged around an aperture and screenshot resulting in a low pixel count for the aperture, the pixel square being apparent. FIG. 10 shows the result of L65 interpolation of the pinhole image, which is smooth but does not highlight diffraction fringes. FIG. 11 shows the present embodiment passing through x 0 ,…,x 10 The term is processed by E65 extrapolation, on a frenzov diffraction blaze screen. FIG. 12 shows the present embodiment passing through x 0 ,…,x 10 As a result of the E83 extrapolation process of the term, the frenhiff optical diffraction fringes are more pronounced. FIG. 13 shows the present embodiment passing through x 0 ,…,x 12 The term was processed by the E85 extrapolation method, and the Fraunhofer diffraction was almost the same.
The technical scheme can show the understanding of the Fraunhofer optical diffraction, and the specific reason for the ghost image is still the Fraunhofer optical diffraction as shown in FIG. 14, which is the ghost image of the lower edge of the eave irradiated by sunlight. Therefore, based on the verification, the technical scheme of the invention can enable the image to be finer and the facial expression of the character to be more vivid by an extrapolation method with a near high-order term, and is suitable for processing life photos and videos and character photos and videos. The extrapolation method with the far high-order terms can display the subtle and rare changes of the graph, the insight of autumn hair and the display of spider-silk traces, and is suitable for processing the graph and the video in the fields of scientific exploration, public security case solving, military reconnaissance and the like.
Although the invention has been described in detail with respect to the general description and the specific embodiments, it will be apparent to those skilled in the art that modifications and improvements may be made based on the invention. Accordingly, such modifications and improvements are intended to be within the scope of the invention as claimed.
Claims (5)
1. An image extrapolation processing method, comprising:
1) Determining the sequence and coordinate system of the coordinate variables of the image;
2) Determining n +1 known function points as an interpolation frame, wherein the known function points comprise known coordinate points and known function values, and n is an order;
in the step 2), the known function value adopts the gray value of an image pixel point; constructing coefficients of an interpolation polynomial through the known function values;
the known function value is obtained by calculating or presetting the inserted function;
3) Constructing a Van der Waals matrix V from the known function points 1 ；
4) Using the vandermonde matrix V 1 The n +1 lines of (1) constitute an m-dimensional vandermonde vector space as row vectors, and the base of the n + 1-dimensional subspace of the m-dimensional vandermonde vector space as the row vector is denoted as e 0 ,e 1 ,…,e n Van der Waals matrix is denoted as V 1 ＝(e 0 ,e 1 ,…,e n ) Wherein m is more than or equal to n +1, m and n are natural numbers;
5) Calculating the inner product between the subspace base vectors to obtain the metric tensor g of the subspace ij ＝e i ·e j ；
6) Obtaining a metric tensor g of a dual space of the subspace through a matrix inversion method ij * The matrix of the dual space is the inverse of the metric number of the subspace, i.e. (g) ij * )＝(g ij ) -1 ；
7) Obtaining the base of the dual space through matrix operation, wherein the base of the dual space is (e) 0 ,e 1 ,…,e n )＝(e 0 ,e 1 ,…,e n )(g ij * )；
8) Transposing the basis matrix of the dual space to obtain a pseudo-inverse V of the vandermonde matrix 1 -1 I.e. V 1 -1 ＝(e 0 ,e 1 ,…,e n ) T Wherein T represents a transpose operation of the matrix;
9) Determining the position of the interpolated interval in the n +1 points of the interpolation frame;
10 Given the number of insertion points between two adjacent pixels, d-1 new pixel points are inserted between two adjacent pixels, wherein d represents the equal division of the insertion points to the insertion interval;
11 Determine the abscissa of the set of insertion points;
12 Obtaining a Van der Waals matrix V having the same number of terms as the interpolation frame from the abscissa of the interpolation point set 2 ；
13 Constructing an extrapolation matrix E of (d-1) × (n + 1) dn ；
14 According to the extrapolation matrix E dn Obtaining the pixel value z of d-1 new pixel points i Wherein i =1, \8230;, d-1;
15 Constructing an interpolation transformation G (x) = G (f (x)), wherein f (x) is a one-dimensional variable function, and G (x) is a function obtained after interpolation;
16 Starting from the first row or column in one dimension of the image pixels, moving the grid-wise interpolation by pixel grid forward in the first row or column;
17 Changing to the next line or the next column of the image pixels, repeating the step 16) to complete the interpolation of the next line or the next column, and repeatedly executing the step 16) and the step 17) to complete the interpolation of the last line of the pixels of the image in the corresponding dimension;
18 Converting to another dimension, repeating the step 16) and the step 17) to finish the interpolation of the other dimension after the dimension conversion of the image is finished until the whole interpolation of the image is finished;
in the step 13), the formula of the extrapolation matrix is E dn ＝V 2 V 1 -1 ；
The pixel value z of d-1 new pixel points is measured by adopting a pixel transplanter in the step 14) i Calculating;
the in-situ interpolation component adopted by the pixel transplanter is z = E dn y；
Wherein z = (z) 1 ,…,z d-1 )
y＝(y 1 ,…,y n+1 )
y is a coordinate variable of the image;
in the step 16), the original pixel points of the image are skipped without interpolation, or interpolation is carried out again at the positions of the original pixel points;
the interpolation matrix is moved forward in the same row or column by grid until the last pixel by interpolation transformation G (x) = G (f (x)), which is the name for interpolation transformation G (x) = G (f (x)).
2. The image extrapolation processing method according to claim 1, wherein the image is a two-dimensional image, a three-dimensional image, or a high-dimensional image having a dimension larger than three dimensions.
3. The image extrapolation processing method according to claim 1, wherein in step 9), n +1 points have n intervals, and when n is an odd number, the n intervals have a central interval.
4. The image extrapolation processing method according to claim 1, further comprising a step 19 for a color image,
step 19): the step 16), the step 17), and the step 18) are repeatedly performed to successively complete interpolation in accordance with the component order of the color image.
5. The image extrapolation processing method according to claim 4, wherein the step 16), the step 17), the step 18) and the step 19) are repeated for the high-dimensional image, and the interpolation of the high-dimensional image is performed sequentially in one dimension.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201811598972.XA CN109816590B (en) | 2018-12-26 | 2018-12-26 | Image extrapolation processing method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201811598972.XA CN109816590B (en) | 2018-12-26 | 2018-12-26 | Image extrapolation processing method |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN109816590A CN109816590A (en) | 2019-05-28 |
| CN109816590B true CN109816590B (en) | 2023-03-14 |
Family
ID=66602365
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201811598972.XA Active CN109816590B (en) | 2018-12-26 | 2018-12-26 | Image extrapolation processing method |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN109816590B (en) |
Families Citing this family (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112364319B (en) * | 2020-10-12 | 2022-12-23 | 西安电子科技大学 | Biological characteristic template protection method and device based on binary tree shuffling |
Citations (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2005062196A2 (en) * | 2003-12-11 | 2005-07-07 | Geoenergy, Inc. | Method and apparatus for efficient data acquisition and interpolation |
| CN101056417A (en) * | 2006-04-10 | 2007-10-17 | 三菱电机株式会社 | Image processing apparatus, image processing method, image output apparatus, and image processing system |
| CN201084028Y (en) * | 2007-09-25 | 2008-07-09 | 薛玉起 | Electric heating type floor heating device automatic temperature control device |
| CN101436250A (en) * | 2008-11-19 | 2009-05-20 | 西安电子科技大学 | Multi-view angle human face recognizing method based on non-linear tensor resolution and view angle manifold |
| CN101626512A (en) * | 2009-08-11 | 2010-01-13 | 北京交通大学 | Method and device of multiple description video coding based on relevance optimization rule |
| CN102521794A (en) * | 2011-11-10 | 2012-06-27 | 广东威创视讯科技股份有限公司 | Image interpolation method and device based on spline surface |
| CN103530529A (en) * | 2013-11-01 | 2014-01-22 | 上海无线电设备研究所 | Massive target performance data fast reading and precise interpolation method |
| CN104915609A (en) * | 2015-05-28 | 2015-09-16 | 武汉科技大学 | Data hiding method based on Lagrange interpolation method and multiple clouds |
| EP3276577A1 (en) * | 2016-07-25 | 2018-01-31 | Technische Universität Berlin | Hölder adaptive image synthesis |
Family Cites Families (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US7826096B2 (en) * | 2005-09-16 | 2010-11-02 | Fujifilm Corporation | Image processing method and image recording apparatus |
| CN100557631C (en) * | 2007-12-17 | 2009-11-04 | 华为技术有限公司 | A kind of method and device that digital picture is carried out interpolation |
-
2018
- 2018-12-26 CN CN201811598972.XA patent/CN109816590B/en active Active
Patent Citations (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2005062196A2 (en) * | 2003-12-11 | 2005-07-07 | Geoenergy, Inc. | Method and apparatus for efficient data acquisition and interpolation |
| CN101056417A (en) * | 2006-04-10 | 2007-10-17 | 三菱电机株式会社 | Image processing apparatus, image processing method, image output apparatus, and image processing system |
| CN201084028Y (en) * | 2007-09-25 | 2008-07-09 | 薛玉起 | Electric heating type floor heating device automatic temperature control device |
| CN101436250A (en) * | 2008-11-19 | 2009-05-20 | 西安电子科技大学 | Multi-view angle human face recognizing method based on non-linear tensor resolution and view angle manifold |
| CN101626512A (en) * | 2009-08-11 | 2010-01-13 | 北京交通大学 | Method and device of multiple description video coding based on relevance optimization rule |
| CN102521794A (en) * | 2011-11-10 | 2012-06-27 | 广东威创视讯科技股份有限公司 | Image interpolation method and device based on spline surface |
| CN103530529A (en) * | 2013-11-01 | 2014-01-22 | 上海无线电设备研究所 | Massive target performance data fast reading and precise interpolation method |
| CN104915609A (en) * | 2015-05-28 | 2015-09-16 | 武汉科技大学 | Data hiding method based on Lagrange interpolation method and multiple clouds |
| EP3276577A1 (en) * | 2016-07-25 | 2018-01-31 | Technische Universität Berlin | Hölder adaptive image synthesis |
Non-Patent Citations (3)
| Title |
|---|
| Method of reconstructing sectional image based on tomosynthesis and Vandermonde matrix;Wen Junhai .etc;《Acta Electronica Sinica》;19990401;71-4 * |
| Radiographic Image Enhancement Based on Lagrange Interpolation;Gui Zhiguo .etc;《Semiconductor Technology》;20090101;1107-9 * |
| 海底地形数据网格化方法研究;刘强等;《舰船电子工程》;20130531;59-64 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN109816590A (en) | 2019-05-28 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Rabin et al. | Wasserstein barycenter and its application to texture mixing | |
| Freifeld et al. | Highly-expressive spaces of well-behaved transformations: Keeping it simple | |
| AU2020281143B1 (en) | Creating super-resolution images | |
| Yang et al. | Designing display pixel layouts for under-panel cameras | |
| Chen et al. | Hyperspectral compressive snapshot reconstruction via coupled low-rank subspace representation and self-supervised deep network | |
| CN109727196B (en) | Image interpolation processing method | |
| Rodolà et al. | Functional maps representation on product manifolds | |
| Liu et al. | Generic distortion model for metrology under optical microscopes | |
| CN109816590B (en) | Image extrapolation processing method | |
| Marquez et al. | Deep-learning supervised snapshot compressive imaging enabled by an end-to-end adaptive neural network | |
| Pelletier et al. | Preconditioning for edge-preserving image super resolution | |
| CN111079893A (en) | Method and device for obtaining generator network for interference fringe pattern filtering | |
| KR101169367B1 (en) | A high speed hologram generating device for computer generated digital hologram and the method thereof | |
| CN111130556B (en) | Method for sequencing Hadamard measurement bases | |
| CN110677555B (en) | Digital circuit for correcting vignetting effect in pixel value of image of electronic camera | |
| CN106910246A (en) | Speckle three-D imaging method and device that space-time is combined | |
| Reeger et al. | Painlevé IV: A numerical study of the fundamental domain and beyond | |
| Zhan et al. | PSF estimation method of simple-lens camera using normal sinh-arcsinh model based on noise image pairs | |
| Ngolè et al. | Point spread function field learning based on optimal transport distances | |
| Liao et al. | Visualization of hyperspectral images using moving least squares | |
| Morinaka et al. | 3D reconstruction under light ray distortion from parametric focal cameras | |
| JP7031511B2 (en) | Signal processing equipment, convolutional neural networks, signal processing methods and signal processing programs | |
| Hagen et al. | Fourier methods of improving reconstruction speed for CTIS imaging spectrometers | |
| Drouin et al. | Efficient representation of the variant PSF of structured light system | |
| CN104361629A (en) | Smoke model space editing method based on streamline deformation |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |