CN107220665B - Image interpolation method and two-dimensional empirical mode decomposition method based on same - Google Patents
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Abstract
The invention discloses an image interpolation method, which comprises the steps of decomposing a scattered point set to be interpolated, which is defined on an M-dimensional grid, to form a plurality of point sets; respectively expanding the plurality of point sets to obtain a plurality of expanded point sets; performing scattered point interpolation based on a radial basis function on a plurality of expanded point sets to obtain an interpolation function; obtaining sparse grids which are sparser than M-dimensional grids, calculating a weight function value from a grid point on each sparse grid to the center of one or more expansion point sets to which the grid point belongs, and distributing an interpolation result of each grid point calculated by a radial basis function according to the weight function value; and obtaining interpolation results of all grid points on the M-dimensional grid through the obtained interpolation result on each sparse grid to obtain the whole envelope surface. The invention also discloses a two-dimensional empirical mode decomposition method, and the image interpolation method not only has higher calculation speed, but also has better decomposition quality when being applied to the two-dimensional empirical mode decomposition method.
Description
Technical Field
The invention relates to the technical field of image signal processing, in particular to an image interpolation method and a two-dimensional empirical mode decomposition method based on the image interpolation method.
Background
Popularization of one-dimensional Empirical Mode Decomposition (EMD) is applied to two-dimensional empirical mode decomposition (2D-EMD) methods in computer vision, image processing and processing of various two-dimensional signals. However, due to the excessive data amount in the two-dimensional case, the complexity of the discrete point interpolation calculation required in the EMD algorithm increases exponentially as the image scale increases, so that the calculation speed of the algorithm is extremely slow on a general computer, and further application of the algorithm is limited.
At present, researchers search different calculation paths to realize 2D-EMD to realize acceleration of the algorithm, and mainly include a differential equation method, a piecewise scatter interpolation method and a method for directly calculating an average value of an envelope surface based on a local extreme value average value; the method using the differential equation comprises a method using a nonlinear diffusion equation and a method for solving a thin plate spline function equation, and the calculation complexity is still high; the method of using the piecewise scatter interpolation method and the method of directly calculating the average value of the envelope surface based on the local extremum mean value have insufficient accuracy, and still cannot achieve higher operation speed under large-size images. The application of 2D-EMD is therefore still very limited.
TFT-LCD liquid crystal panels are widely used in modern display applications, including smart phones, tablets, notebook computers, liquid crystal televisions, and the like. In each process of manufacturing liquid crystal and in the connection process between processes, the final display may be bad, so the final product of TFT-LCD has many kinds of display defects and various expression forms: of which there are mainly point defects, line defects and Mura, which is the most complex meaning. How to distinguish various defects and effectively and quickly determine the defects becomes one of the difficulties in liquid crystal detection.
The above background disclosure is only for the purpose of assisting understanding of the concept and technical solution of the present invention and does not necessarily belong to the prior art of the present patent application, and should not be used for evaluating the novelty and inventive step of the present application in the case that there is no clear evidence that the above content is disclosed at the filing date of the present patent application.
Disclosure of Invention
In order to solve the technical problems, the invention provides an image interpolation method, a two-dimensional empirical mode decomposition method based on the image interpolation method and a liquid crystal screen defect detection method based on the two-dimensional empirical mode decomposition method.
In order to achieve the purpose, the invention adopts the following technical scheme:
the invention discloses an image interpolation method, which comprises the following steps:
s1: decomposing a scattered point set to be interpolated, which is defined on an M-dimensional grid, to form a plurality of point sets;
s2: respectively expanding the point sets to obtain a plurality of expanded point sets;
s3: performing scattered point interpolation based on a radial basis function on a plurality of the expanded point sets to obtain an interpolation function;
s4: obtaining sparse grids which are more sparse relative to the M-dimensional grid, calculating a weight function value from a grid point on each sparse grid to the center of one or more enlarged point sets to which the grid point belongs, and distributing an interpolation result of each grid point calculated by a radial basis function according to the weight function value;
s5: and obtaining interpolation results of all grid points on the M-dimensional grid through the obtained interpolation result on each sparse grid to obtain the whole envelope surface.
Preferably, step S2 specifically includes: the coordinates of the central point of the enlarged point set and the coordinates of the central point of the corresponding point set are kept unchanged, and the coordinates (x) of the central point of each point set are calculated0,y0) And the lengths (w, h) of the long and short sides thereof, so as to enlarge all scattered points in the point set to a central point coordinate (x)0,y0) Is such that the transverse distance ofA longitudinal distance of
Preferably, in step S3, performing scatter interpolation based on radial basis function on a plurality of the expanded point sets, specifically obtaining an interpolation function Sintp(xi)＝fiAll scatter points xiSatisfies the following conditions:
and the radial basis function phi (r) satisfies the following formula:
wherein n is the total number of the scatter points in the scatter point set, and a corresponding interpolation coefficient c is obtained according to the formula (1) and the formula (2)iAnd an interpolation function fiIs described in (1).
Preferably, the sparse scale r of the sparse grid with respect to the M-dimensional network in step S4gSatisfies the following formula:
wherein:
wherein, tlIs the length in the l dimension, T, of the sparse gridlIs the length in the l dimension of the M-dimensional grid; r issIs the ratio of the number of scattered points to the total number of grid points, gmax、gminMaximum and minimum values of the difference of the column spread sequence of the scatter points respectively; preferably, rgThe value is not more than 0.5, and if the value exceeds 0.5 calculated by the formula (3), the value is 0.5.
Preferably, the step S4 of calculating the weight function value of the grid point on each sparse grid to the center of the one or more enlarged point sets to which the grid point belongs specifically includes: for the grid point x to be interpolated on the sparse grid, calculating a weight function value of the jth subset to which the grid point x to be interpolated belongs according to the following formula:
wherein N is the number of subsets to which the grid point x to be interpolated belongs, and W isj(x) And Wi(x) The calculation is made by the following formula:
wherein M is the number of dimensions, x, of the sparse gridlIs the coordinate value of the grid point x to be interpolated in the first dimension, xk,olIs the coordinate value of the central point of the kth sub-set region in the l dimension,bk,lthe length of the kth subset in the l dimension is epsilon, a minimum value, and k is j or i.
Preferably, the step S1 specifically includes decomposing the scatter gather to be interpolated, which is defined on the M-dimensional grid, by using a KD-Tree segmentation method; preferably, the step S5 specifically includes obtaining interpolation results of all grid points on the M-dimensional grid by using a grid point interpolation method for the obtained interpolation result on each sparse grid, so as to obtain the entire envelope surface.
Preferably, M is 1, 2, 3 or 4.
The invention also discloses a two-dimensional empirical mode decomposition method based on the image interpolation method, wherein all local maximum value points and minimum value points in an image to be decomposed are used as all scatter points defined in the scatter point set to be interpolated of the M-dimensional grid in the step S1, and the step S5 specifically comprises the following steps: and obtaining interpolation surfaces of all grid points through interpolation results of all grid points on the sparse grid, taking the interpolation surface of the minimum value point as a lower envelope surface, taking the interpolation surface of the maximum value point as an upper envelope surface, and obtaining the upper envelope surface and the lower envelope surface, wherein M is 2.
Preferably, the two-dimensional empirical mode decomposition method further includes step S6: calculating the average value of the upper envelope surface and the lower envelope surface, and subtracting the average value from the image to be decomposed to obtain a result Dm,k(x, y) and compared with the image to be decomposed, using as a stop condition:
wherein D ism,k-1(x, y) are images to be detected, subscripts respectively represent the number of times of the Sift process and the number of times of iteration, and R is a preset threshold value;
if the stop condition is satisfied, Dm,k(x, y) is the obtained inherent mode function, and the remainder D is detectedm,k-1(x,y)-Dm,k(x, y), if the number of the maximum value points or the minimum value points is less than 5, all the inherent mode functions are obtained; otherwise, taking the rest items as the images to be detected, and repeating the steps S1-S5 to continue decomposing;
preferably, the value of R is 0.1-0.3.
The invention also discloses a liquid crystal screen defect detection method, which comprises the following steps: the acquired image of the defect of the liquid crystal screen or the preprocessed image with the enhanced defect is subjected to the two-dimensional empirical mode decomposition method of claim 8 or 9 to obtain a plurality of intrinsic mode function images, and then each intrinsic mode function image is subjected to subsequent detection.
Compared with the prior art, the invention has the beneficial effects that: the image interpolation method of the invention adopts the scattered point interpolation based on the radial basis function with the subarea and downscale sparsity, and effectively solves the problem that the calculation speed of the scattered point interpolation in the whole image range is too slow. Furthermore, a scattered point interpolation method and a lattice point interpolation method are combined, so that the interpolation process is further accelerated; the image interpolation method of the invention can be applied to one-dimensional, two-dimensional, three-dimensional and even four-dimensional grids, and the calculation speed is effectively improved.
The image interpolation method is applied to the envelope interpolation process of the two-dimensional empirical mode decomposition, so that the calculation speed of the two-dimensional empirical mode decomposition method is effectively accelerated, and the decomposition quality is good. The invention further applies the improved two-dimensional empirical mode decomposition method to a liquid crystal screen defect detection method, can effectively separate various display defects in a liquid crystal screen and inherent characteristics in an image, facilitates subsequent detection, and has good decomposition effect on point and surface defects and Mura defects of the liquid crystal screen.
Drawings
FIG. 1 is a schematic flow diagram of an image decomposition method in accordance with a preferred embodiment of the present invention;
FIG. 2 is a schematic diagram of obtaining an enlarged set of points from a set of points;
FIG. 3 is a schematic diagram of sparse grid selection;
FIG. 4 is an artwork for two-dimensional empirical mode decomposition according to one embodiment of the present invention;
FIGS. 5 a-5 f are two-dimensional empirical mode decomposed images of FIG. 4 under a stopping condition;
FIGS. 6 a-6 e are two-dimensional empirical mode decomposed images of FIG. 4 under another stopping condition;
FIG. 7 is an original image of a liquid crystal screen image with a MURA display defect;
fig. 8a to 8f are the images of fig. 7 after decomposition.
Detailed Description
The invention will be further described with reference to the accompanying drawings and preferred embodiments.
As shown in fig. 1, the preferred embodiment of the present invention discloses an improved image interpolation method, comprising the following steps:
s1: decomposing a scattered point set to be interpolated, which is defined on an M-dimensional grid, to form a plurality of point sets;
specifically, a scatter point set to be interpolated, which is defined on an M-dimensional grid, is decomposed by using a KD-Tree segmentation method to form a plurality of point sets, so that the number of scatter points included in each point set is substantially the same, in different embodiments, M is 1, 2, 3, or 4, and in this embodiment, M takes a value of 2.
S2: respectively expanding the point sets to obtain a plurality of expanded point sets, so that an intersection exists between each expanded point set, and the coordinates of the central points of the point sets and the corresponding expanded point sets are unchanged;
wherein, the coordinates (x) of the center point of each point set are calculated0,y0) And the lengths (w, h) of the long side and the short side thereof, so as to enlarge all scattered points in the point set to the central pointCoordinate (x)0,y0) Transverse distance ofLongitudinal distanceSpecifically, as shown in fig. 2, the expanded point set 20 may be formed by obtaining a circumscribed ellipse of each point set 10 and obtaining a circumscribed rectangle of the circumscribed ellipse, and using the extreme points in the rectangle.
S3: performing scattered point interpolation based on a radial basis function on a plurality of expanded point sets to obtain an interpolation function;
wherein the scattered point interpolation based on the radial basis function is to obtain an interpolation function Sintp(xi)＝fiAll scatter points xiSatisfies the following conditions:
and the radial basis function phi (r) satisfies the following formula:
wherein n is the total number of scatter points in the scatter point set, and a corresponding interpolation coefficient c is obtained according to the formula (1) and the formula (2)iAnd an interpolation function fiIs described in (1).
S4: obtaining sparse grids which are sparser than M-dimensional grids, calculating a weight function value from a grid point on each sparse grid to the center of one or more expansion point sets to which the grid point belongs, and distributing an interpolation result of each grid point calculated by a radial basis function according to the weight function value;
wherein the sparse scale r of the sparse grid relative to the M-dimensional networkgSatisfies the following formula:
wherein:
wherein, tlIs the length in the l dimension, T, of the sparse gridlIs the length in the l dimension of the M-dimensional grid; r issIs the ratio of the number of scattered points to the total number of grid points, gmax、gminMaximum and minimum values of the difference of the column spread sequence of scatter points, respectively, and rgThe value is not more than 0.5, and if the value exceeds 0.5 calculated by the formula (3), the value is 0.5.
As shown in fig. 3, which is a schematic diagram of the sparse grid, it can be seen from grid lines 30 of the original grid and grid lines 40 of the sparse grid that the sparse grid is 0.5 times of the original grid. For a grid point x to be interpolated on a sparse grid, calculating a weight function value of a jth subset to which the grid point x to be interpolated belongs according to the following formula:
wherein N is the number of subsets to which the grid point x to be interpolated belongs, and W isj(x) And Wi(x) The calculation is made by the following formula:
wherein M is the number of dimensions, x, of the sparse gridlIs the coordinate value of the grid point x to be interpolated in the first dimension, xk,olIs the coordinate value of the central point of the kth sub-set region in the l dimension,bk,lis the length of the kth subset in the l dimension, epsilon is a minimum value tending to 0, k can be j ori。
S5: obtaining interpolation results of all grid points on the M-dimensional grid through the obtained interpolation result on each sparse grid to obtain the whole envelope surface;
specifically, the interpolation results of all grid points on the M-dimensional grid are obtained by using a grid point interpolation method for the obtained interpolation results on each sparse grid, so as to obtain the whole envelope surface.
Another embodiment of the present invention further discloses a two-dimensional empirical mode decomposition (2D-EMD) method based on the above improved image interpolation method, which is used to calculate the envelope surface of the extreme points in the 2D-EMD to accelerate the Sift process in the 2D-EMD, wherein in the above improved image interpolation method, all local maximum points and local minimum points in the image to be decomposed are used as all scatter points defined in the scatter point set to be interpolated in the two-dimensional grid in step S1, that is, all local maximum points and local minimum points in the image to be decomposed are used as scatter points in the method to perform interpolation calculation; wherein the step S5 specifically includes: and obtaining interpolation surfaces of all grid points through interpolation results of all grid points on the sparse grid, taking the interpolation surface of the minimum value point as a lower envelope surface, and taking the interpolation surface of the maximum value point as an upper envelope surface to obtain the upper envelope surface and the lower envelope surface.
Furthermore, the two-dimensional empirical mode decomposition method further comprises the following steps:
s6: calculating the average value of the upper envelope surface and the lower envelope surface, and subtracting the average value from the image to be decomposed to obtain a result Dm,k(x, y) and compared with the image to be decomposed, using as the stopping condition:
wherein D ism,k-1(x, y) are images to be detected, subscripts respectively represent the number of times of the Sift process and the number of times of iteration, and R is a preset threshold value;
if the stop condition is satisfied, Dm,k(x, y) is the obtained natural mode function,detecting remainder item Dm,k-1(x,y)-Dm,k(x, y), if the number of the maximum value points or the minimum value points is less than 5, all the inherent mode functions are obtained; otherwise, taking the rest items as the images to be detected, and repeating the steps S1-S5 to continue decomposing; in some embodiments, the threshold value R is 0.1-0.3, so that a satisfactory result can be obtained by decomposition, and the required decomposition time is short. And when the stop condition is met, stopping one-time Sift iteration and entering next-time Sift.
Fig. 4 is a Lena image to be decomposed, fig. 5a to 5f and fig. 6a to 6e are images obtained by decomposing the above two-dimensional empirical mode decomposition method, wherein fig. 5a to 5f and fig. 6a to 6e are decomposed images obtained under different stop conditions, respectively, and the stop condition of fig. 5a to 5f is SDm,kLess than 0.12, and the stop condition in FIGS. 6a to 6e is SDm,kIs less than 0.20. The results in fig. 5a to 5f and fig. 6a to 6e, which show the decomposition results under different stop conditions, show that the eigenmodes of the decomposition results show the change of the gray-level features in the original image from detail to outline, and that better results can be obtained under different stop conditions. On one hand, the characteristics of different scales are separated, and on the other hand, the separation result shows better continuity, and the phenomenon of gray value mutation does not exist in the boundary and the image.
The calculation process of the 2D-EMD method can be carried out by combining a CPU and a GPU, because in the interpolation process, a coefficient matrix in a radial basis interpolation equation needs to be calculated, the equation is solved, and the solved grid coordinates are substituted into the equation, the calculation speed of the CPU is low due to the extremely large data volume in the process, and the calculation process can be effectively accelerated by utilizing the parallel calculation function of the GPU.
The specific interpolation method uses the scattered point interpolation based on the radial basis function with the subarea and the downscaling, effectively solves the problem that the calculation speed of the scattered point interpolation based on the radial basis function in the whole graph range is too slow, and greatly improves the calculation efficiency; and the scattered point interpolation method and the lattice point interpolation method are combined, so that the interpolation process is further accelerated. The specific interpolation method is applied to the envelope surface interpolation process in the 2D-EMD algorithm, so that the 2D-EMD algorithm is effectively accelerated.
The invention further discloses a liquid crystal screen defect detection method based on the improved two-dimensional empirical mode decomposition method, which comprises the steps of obtaining a plurality of inherent mode function images from the acquired images of the liquid crystal screen defects or the preprocessed defect-enhanced images by the two-dimensional empirical mode decomposition method, and then carrying out subsequent detection on each inherent mode function Image (IMF).
Through the two-dimensional empirical mode decomposition method, the liquid crystal screen image is decomposed to obtain a plurality of inherent mode function images, and the inherent mode function images respectively reflect the characteristics of different sizes and scales in the original image, so that small-scale point defects and small-scale line defects in the original image are separated into the former modes, large-scale black and white clusters and uneven brightness defects are separated into the latter modes, particularly, the uneven brightness defects are usually separated into the rest items of decomposition, and the subsequent detection is facilitated.
FIG. 7 is a liquid crystal screen image with MURA display defects, and FIGS. 8a 8f are images of FIG. 7 after decomposition with the stop condition of the decomposition selected as SDm,k< 0.20, it can be seen from the decomposition result that the light and shade stripes caused by the shooting reason, the pixel lattice points of the liquid crystal screen, the MURA and the overall brightness unevenness are distributed in different decomposition images, which greatly facilitates the subsequent detection.
The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and it is not intended that the invention be limited to these specific details. For those skilled in the art to which the invention pertains, several equivalent substitutions or obvious modifications can be made without departing from the spirit of the invention, and all the properties or uses are considered to be within the scope of the invention.
Claims (11)
1. An image interpolation method, comprising the steps of:
s1: decomposing a scattered point set to be interpolated, which is defined on an M-dimensional grid, to form a plurality of point sets;
s2: respectively expanding the point sets to obtain a plurality of expanded point sets;
s3: performing scattered point interpolation based on a radial basis function on a plurality of the expanded point sets to obtain an interpolation function;
s4: obtaining sparse grids which are more sparse relative to the M-dimensional grid, calculating a weight function value from a grid point on each sparse grid to the center of one or more enlarged point sets to which the grid point belongs, and distributing an interpolation result of each grid point calculated by a radial basis function according to the weight function value;
s5: and obtaining interpolation results of all grid points on the M-dimensional grid through the obtained interpolation result on each sparse grid to obtain the whole envelope surface.
2. The image interpolation method according to claim 1, wherein the step S2 specifically includes: the coordinates of the central point of the enlarged point set and the coordinates of the central point of the corresponding point set are kept unchanged, and the coordinates (x) of the central point of each point set are calculated0,y0) And the lengths (w, h) of the long and short sides thereof, so as to enlarge all scattered points in the point set to a central point coordinate (x)0,y0) Is such that the transverse distance ofA longitudinal distance of
3. The image interpolation method according to claim 1, wherein the step S3 of performing the radial basis function-based scatter interpolation on a plurality of the dilated point sets is to obtain an interpolation function Sintp(xi)＝fiAll scatter points xiSatisfies the following conditions:
and the radial basis function phi (r) satisfies the following formula:
wherein n is the total number of the scatter points in the scatter point set, and a corresponding interpolation coefficient c is obtained according to the formula (1) and the formula (2)iAnd an interpolation function fiIs described in (1).
4. The image interpolation method according to claim 1, wherein the sparse scale r of the sparse grid with respect to the M-dimensional network in step S4gSatisfies the following formula:
wherein:
wherein, tlIs the length in the l dimension, T, of the sparse gridlIs the length in the l dimension of the M-dimensional grid; r issIs the ratio of the number of scattered points to the total number of grid points, gmax、gminMaximum and minimum values of the difference of the column spread sequence of the scatter points respectively; preferably, rgThe value is not more than 0.5, and if the value exceeds 0.5 calculated by the formula (3), the value is 0.5.
5. The image interpolation method according to claim 1, wherein the step S4 of calculating the weight function value of the grid point on each of the sparse grids to the center of the one or more enlarged point sets to which it belongs specifically comprises: for the grid point x to be interpolated on the sparse grid, calculating a weight function value of the jth subset to which the grid point x to be interpolated belongs according to the following formula:
wherein N is the number of subsets to which the grid point x to be interpolated belongs, and W isj(x) And Wi(x) The calculation is made by the following formula:
wherein M is the number of dimensions, x, of the sparse gridlIs the coordinate value of the grid point x to be interpolated in the first dimension, xk,olIs the coordinate value of the central point of the kth sub-set region in the l dimension,bk,lthe length of the kth subset in the l dimension is epsilon, a minimum value, and k is j or i.
6. The image interpolation method according to claim 1, wherein step S1 specifically includes decomposing a scatter gather to be interpolated, which is defined on the M-dimensional grid, by using a KD-Tree segmentation method; preferably, the step S5 specifically includes obtaining interpolation results of all grid points on the M-dimensional grid by using a grid point interpolation method for the obtained interpolation result on each sparse grid, so as to obtain the entire envelope surface.
7. The image interpolation method according to any one of claims 1 to 6, wherein M is 1, 2, 3, or 4.
8. A two-dimensional empirical mode decomposition method based on the image interpolation method of any one of claims 1 to 6, wherein the maximum value point and the minimum value point of all local gray values in the image to be decomposed are used as all scatter points defined in the scatter point set to be interpolated of the M-dimensional grid in step S1, and the step S5 specifically includes: and obtaining interpolation surfaces of all grid points through interpolation results of all grid points on the sparse grid, taking the interpolation surface of the minimum value point as a lower envelope surface, taking the interpolation surface of the maximum value point as an upper envelope surface, and obtaining the upper envelope surface and the lower envelope surface, wherein M is 2.
9. The two-dimensional empirical mode decomposition method according to claim 8, further comprising step S6: calculating the average value of the upper envelope surface and the lower envelope surface, and subtracting the average value from the image to be decomposed to obtain a result Dm,k(x, y) and compared with the image to be decomposed, using as a stop condition:
wherein D ism,k-1(x, y) are images to be detected, subscripts respectively represent the number of times of the Sift process and the number of times of iteration, and R is a preset threshold value;
if the stop condition is satisfied, Dm,k(x, y) is the obtained inherent mode function, and the remainder D is detectedm,k-1(x,y)-Dm,k(x, y), if the number of the maximum value points or the minimum value points is less than 5, all the inherent mode functions are obtained; otherwise, taking the rest items as the images to be detected, and repeating the steps S1-S5 to continue decomposing.
10. The two-dimensional empirical mode decomposition method according to claim 9, wherein R is 0.1-0.3.
11. A method for detecting defects of a liquid crystal screen, wherein a plurality of intrinsic mode function images are obtained by subjecting acquired images of defects of the liquid crystal screen or preprocessed defect-enhanced images to the two-dimensional empirical mode decomposition method according to any one of claims 8 to 10, and then each intrinsic mode function image is subjected to subsequent detection.
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