CN117151991A - Remote sensing image RPC repairing method - Google Patents

Remote sensing image RPC repairing method Download PDF

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CN117151991A
CN117151991A CN202310826448.8A CN202310826448A CN117151991A CN 117151991 A CN117151991 A CN 117151991A CN 202310826448 A CN202310826448 A CN 202310826448A CN 117151991 A CN117151991 A CN 117151991A
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CN117151991B (en
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杜慧丽
张玥珺
邹圣兵
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Beijing Shuhui Spatiotemporal Information Technology Co ltd
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Abstract

The invention discloses a remote sensing image RPC restoration method, which comprises the following steps: s1, obtaining information such as an image to be repaired and a reference image; s2, carrying out feature extraction and matching on the image to be repaired and the reference image by adopting a SIFT algorithm to obtain a matching point pair and a corresponding first pixel coordinate; s3, acquiring longitude and latitude coordinates; s4, obtaining a geodetic coordinate and a control point; s5, constructing an RFM model, carrying out forward calculation on the original RPC parameters of the image to be repaired and the geodetic coordinates RPC to obtain second pixel coordinates of the geodetic coordinates corresponding to the remote sensing image, and respectively calculating the average value of the error distances between the corresponding pixel coordinates; s6, introducing constraint conditions by using an L1 regularization optimization method to obtain an optimized RFM model; s7, judging according to the mean value of the error distance and a preset threshold value, selecting different repairing strategies, and re-calculating or correcting the RPC parameters. According to the method, the RFM model is optimized by using the L1 regularization method, different restoration strategies are selected, RPC parameters are corrected or estimated, and the geometric positioning accuracy of satellite images is improved.

Description

Remote sensing image RPC repairing method
Technical Field
The invention relates to the field of remote sensing treatment, in particular to a remote sensing image RPC repairing method.
Background
Geometric imaging models of high resolution satellite imagery are generally divided into two categories: rigorous imaging models and generic imaging models. All parameters of the rigorous imaging model have a definite geometric meaning and therefore the positioning accuracy based thereon is highest. However, the establishment of a rigorous imaging model requires the use of satellite orbit positions, attitude observations and sensor structural parameters, and lacks versatility, so the model is less used as a data release form of satellite images. As the mathematical simulation of the strict imaging model, the RFM (Rational FunctionModel) general imaging model based on the cubic rational polynomials has the advantages of confidentiality of sensor parameters, strong universality, simple form, convenience and rapidness in calculation and the like, and is widely researched and applied. Currently, the RPC (Rational Polynomial Coefficient) parameters of the RFM model have become the standard for high resolution satellite images. Regarding model parameter solving, since the general model contains 78 rational polynomial coefficients (RPCs for short), a sufficiently large and reasonably distributed control point array is required to perform iterative solving calculation.
Satellite images with RPC parameters are usually subjected to geometric preprocessing, including on-orbit geometric calibration, sensor system error correction and the like, have certain direct ground positioning precision, and can be used for subsequent processing of geometric positioning, orthographic image correction, stereogram and the like. However, RFM still has certain drawbacks in practical applications, mainly reflected in both the intrinsic problems and external effects of RPC. Firstly, the RPC has intrinsic problems of excessive parameterization, strong correlation among parameters, residual errors when a strict imaging model is fitted, and the like; secondly, due to technical limitations of sensors and the like, the stability of many satellite platforms is not high, the instantaneous attitude measurement accuracy is limited, and obvious system errors exist in satellite images and RPC parameters thereof due to external factors, such as errors caused by high-frequency flutter of the satellite platforms.
These problems directly lead to difficulty in eliminating the vertical parallax of satellite images in applications such as stereography and image matching, difficulty in stereoscopic observation and decline in positioning accuracy.
Disclosure of Invention
Based on the technical problems, the remote sensing image RPC restoration method provided by the invention optimizes the RFM model by using the L1 regularization method, adopts different RPC parameter restoration strategies, corrects or estimates the original RPC parameters, reduces the over-fitting by controlling the complexity of the RFM model, eliminates the problems of reduced geometric positioning accuracy and the like caused by model errors in the RFM, and improves the geometric positioning accuracy of the high-resolution satellite image.
In order to achieve the technical purpose, the invention provides a remote sensing image RPC repairing method, which comprises the following steps:
s1, acquiring an image to be repaired, a reference image, geographic information data and DEM data;
s2, carrying out feature extraction and matching on the image to be repaired and the reference image by adopting a SIFT algorithm to obtain a matching point pair and a corresponding first pixel coordinate;
s3, carrying out geographic coordinate conversion on the first pixel coordinates of the matching point pairs according to the geographic information data to obtain longitude and latitude coordinates of the matching point pairs;
s4, interpolating longitude and latitude coordinates of the matching point pairs according to the DEM data to obtain geodetic coordinates, and taking the matching point pairs corresponding to the geodetic coordinates as control points;
s5, constructing an RFM model, performing RPC forward calculation on the original RPC parameters of the image to be repaired and the geodetic coordinates to obtain second pixel coordinates of the geodetic coordinates corresponding to the remote sensing image, and respectively calculating the average value of error distances of the corresponding first pixel coordinates and second pixel coordinates;
s6, on the basis of a least square adjustment principle, using an L1 regularization optimization method, and introducing a set linear constraint condition to obtain an optimized RFM model;
s7, judging according to the mean value of the error distance and a preset threshold value, selecting different repairing strategies, and re-calculating or correcting the RPC parameters.
Specifically, S51 constructs an RFM model:
wherein P is i (i=1, 2,., 4) is third orderThe polynomial (l, s) is normalized second pixel coordinate, the (X, Y, Z) is normalized control point geodetic coordinate, and the values are all [ -1,1]Between them;
s52 expands (l, S) into two equations in linear form according to the Taylor series:
P 1 (X,Y,Z)-lP 2 (X,Y,Z)=0
P 3 (X,Y,Z)-sP 4 (X,Y,Z)=0;
s53, constructing two equations in a linear form into an equation set form by using the geodetic coordinates of the control points, and solving the equations:
y=Ax 0 +e
wherein y is E R m×1 For observing vector, A epsilon R m×n For coefficient matrix and e.epsilon.R m×1 Is the residual vector, x 0 ∈R n×1 Is the RPCs vector; m=2k, where k is the number of geodetic coordinates of the control point and n is 78;
solving the equation set:
x 0 =N -1 A T y
wherein n=a T A is a regular matrix, x 0 ∈R n×1 Is the RPCs vector;
s54, based on the RFM model, performing RPC forward calculation on the original RPC parameters of the remote sensing image and the geodetic coordinates of the control points to obtain second pixel coordinates of the control points corresponding to the geodetic coordinates of the remote sensing image;
s55 calculates the mean value of the error distances of the first pixel coordinates and the second pixel coordinates.
Specifically, the preset linear constraint condition in step S6 is:
wherein, |x| 1 Is the sum of the absolute values of the vectors x, and γ is the regularization parameter.
Specifically, in step S7, the selection of different repair strategies is:
when the average value of the error distances accords with a first judging condition, selecting a first repairing strategy, and performing RPC re-calculation according to the original RPC parameters of the image to be repaired and the optimized RFM model to obtain repaired RPC parameters;
and when the mean value of the error distance meets a second judging condition, selecting a second repairing strategy, and performing RPC correction according to the geodetic coordinates, the original RPC parameters of the image to be repaired and the optimized RFM model to obtain repaired RPC parameters.
Specifically, the first repair policy in step S7 includes:
in the optimized RFM model, the preset linear constraint condition is updated as follows:
min x,e ||x|| 1 +||e|| 1
under the updated linear constraint condition, according to the geodetic coordinates of the control points, constructing an equation set:
y=Ax+e
solving the equation set:
x=N -1 A T y
wherein x is the RPC parameter after repair.
Specifically, the second repair policy in step S7 includes:
taking the original RPC parameter as an initial value x initial
In the optimized RFM model, the preset linear constraint condition is updated as follows:
min Δx,e ||Δx|| 1 +||e|| 1
under the updated linear constraint condition, according to the geodetic coordinates of the control points, constructing an equation set:
y=Ax initial +AΔx+e;
solving the equation set:
Δx=N -1 A T y-Ax initial
wherein Δx is the optimal solution of the offset transform;
at an initial value x initial On the basis of (1), add Δx, i.e. x=x initial +Δx, where x is the RPC parameter after repair.
Specifically, step S2 includes:
s21, determining a frame of image in the same space as a reference image according to the remote sensing image, and carrying out image enhancement on the two images to enable the two images to have interaction characteristics in gray scale;
s22, performing block matching on the two images by utilizing the constraint of the space geographic information of the remote sensing images, dividing the remote sensing images into a plurality of sub-area image blocks to be matched, and obtaining corresponding reference sub-area image blocks according to the projection coordinates of each image block;
s23, moving an area search window in all directions by using a shi_Tomasi algorithm, observing an energy expansion average value of the window, and determining a central pixel point with the energy change of the window larger than a defined threshold value as a corner point;
s24, establishing a feature descriptor to describe the features of the detected feature points by using SIFT descriptors with scale and rotation invariance;
s25, after the SIFT descriptor is constructed, performing feature rough matching based on a K-D tree nearest neighbor query algorithm, performing shortest distance searching by adopting a K-D tree, and removing disordered feature points existing in the unknown points;
s26, carrying out initial matching on homonymous points by using a bidirectional matching strategy, and then removing homonymous points of which the reliability of the rest part cannot be determined by using an integral relaxation method;
s27, adopting a random sampling consistency algorithm and a least square iteration method to remove mismatching pairs in the candidate matching point set;
and S28, carrying out homogenization treatment on the characteristic points by using a greedy algorithm to obtain finally uniformly distributed matching point pairs, and obtaining first pixel coordinates corresponding to each matching point in the remote sensing image.
Specifically, the calculating method of the error distance in step S4 is any one of euclidean distance, similarity, and angle cosine.
The beneficial effects of the invention at least comprise:
(1) According to the method, the L1 regularization method is utilized to optimize the RFM model, the complexity of the RFM model is controlled according to preset constraint conditions, the overfitting is reduced, the problems of geometric positioning accuracy reduction and the like caused by model errors in the RFM are solved, and the geometric positioning accuracy of the high-resolution satellite image is improved.
(2) According to the method, different RPC parameter restoration strategies are selected according to the error distance of the original RPC of the calculated remote sensing image, the original RPC parameters are corrected or estimated, and the geometric positioning accuracy of the high-resolution satellite image is further improved.
(3) The control point automatic extraction method based on the combination of ideas such as geographic constraint blocking processing, shi_Tomasi algorithm corner detection, triangular network model, small face element correction and the like and SIFT algorithm is used for improving matching precision by combining various matching strategies on the basis of geographic constraint blocking strategies, so that uniformly distributed control points are obtained.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are needed in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a schematic diagram of a method according to an embodiment of the present invention;
fig. 2 is a technical flowchart of an embodiment of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. It should be noted that, as long as no conflict is formed, each embodiment of the present invention and each feature of each embodiment may be combined with each other, and the formed technical solutions are all within the protection scope of the present invention.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of exemplary embodiments according to the present invention. As used herein, the singular is also intended to include the plural unless the context clearly indicates otherwise, and furthermore, it is to be understood that the terms "comprises" and/or "comprising" when used in this specification are taken to specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof.
Referring to fig. 1 and 2, in an embodiment of the present invention, a remote sensing image RPC repairing method is provided, which is characterized by comprising the following steps:
s1, acquiring an image to be repaired, a reference image, geographic information data and DEM data;
DEM (Digital Elevation Model) is a data set of plane coordinates (X, Y) and elevations (Z) of regular lattice points within a certain range, and is mainly formed by describing the spatial distribution of regional landform morphology, and performing data acquisition (including sampling and measurement) through contour lines or similar three-dimensional models and then performing data interpolation. DEM is a virtual representation of the morphology of the terrain from which information such as contours, slope maps, etc. can be derived.
S2, carrying out feature extraction and matching on the image to be repaired and the reference image by adopting a SIFT algorithm to obtain a matching point pair and a corresponding first pixel coordinate;
in an embodiment of the present invention, step S2 includes:
s21, determining a frame of image in the same space as a reference image according to the remote sensing image, and carrying out image enhancement on the two images to enable the two images to have interaction characteristics in gray scale;
in the embodiment of the invention, the two images are subjected to image enhancement by adopting a mode of linear stretching of enhancement coefficients.
S22, performing block matching on the two images by utilizing the constraint of the space geographic information of the remote sensing images, dividing the remote sensing images into a plurality of sub-area image blocks to be matched, and obtaining corresponding reference sub-area image blocks according to the projection coordinates of each image block;
in the embodiment of the invention, the remote sensing images are subjected to standard blocking, each image is divided into M multiplied by N pixels, and four corners of the sub-area images are respectively marked as A 1 ,A 2 ,A 3 A is a 4 And calculate the upper left boundary point A respectively 1 And a lower right boundary point A 3 The image coordinates of the two boundary points are recorded as(I 1 ,J 1 ) And (I) 3 ,J 3 );
Converting the image coordinates into corresponding geographic coordinates, expressed by the following formula,
wherein, (X i ,Y i ) Representing geographic coordinates, (X) 0 ,Y 0 ) Representing the geographic coordinates of the upper left corner of the input image, (I) i ,J i ) The image coordinates of the i-th point are represented, and a, b, c, and d represent transformation model parameters.
Obtaining the geographic coordinate (X) of the upper left boundary point A1 of the image block of the sub-region to be matched through the mapping relation between the image coordinate and the geographic coordinate 1 ,Y 1 ) And the lower right boundary point A3 geographic coordinates (X 2 ,Y 2 );
Obtaining an upper left boundary point B1, a lower right boundary point B3 and corresponding image coordinates (I 'of the reference sub-region image block through geographic coordinate back calculation' 1 ,J’ 1 )、(I’ 3 ,J’ 3 ) And obtaining the image coordinates of the upper right boundary point B2 and the lower left boundary point B4 of the reference subarea image block according to the image coordinates of the upper left boundary point B1 and the lower right boundary point B3.
The constraint of the space geographic information of the remote sensing image is utilized for block matching, redundant control points can be effectively reduced, and matching precision is improved.
On the basis of obtaining corresponding sub-region image blocks to be matched and reference sub-region image blocks, extracting characteristic points of each image block by utilizing a shi_Tomasi algorithm, firstly moving an area search window in each direction by utilizing the shi_Tomasi algorithm, observing an energy expansion average value of the window, and then determining a central pixel point with the window energy change larger than a defined threshold value as a corner point, namely detecting the corner point.
S23, moving an area search window in all directions by using a shi_Tomasi algorithm, observing an energy expansion average value of the window, and determining a central pixel point with the energy change of the window larger than a defined threshold value as a corner point;
in the embodiment of the present invention, step S23 specifically includes:
wherein, (x, y) represents the window center coordinates, (u, v) represents the window translation amount, I represents the image gray scale, w (x, y) represents the window, and w (x, y) represents the window by a gaussian function, and the formula is as follows:
wherein σ represents the standard deviation.
For the partial small translation amount, the gray level change taylor expansion generated after the window translation can be approximately expressed as a formula containing an autocorrelation matrix, expressed as the following formula,
wherein M represents an autocorrelation matrix, expressed by the following formula:
wherein I is x ,I y The gradient values of the image gray scale in the x and y directions are respectively represented.
Calculating eigenvalues lambda of autocorrelation matrix M 12 And taking the minimum value to be compared with the set threshold value T, if min (lambda 12 )>And T, reserving the characteristic point, and taking the characteristic point as the shi_Tomasi corner point. The characteristic points extracted by the algorithm are stable, and the extraction of the points can be well completed under the conditions that the image rotates, the illumination angle and the like are changed, noise is generated in the image and the like. Meanwhile, the algorithm can reduce the aggregation of the control points, so that redundant control points are avoided, and the characteristic points are distributed more reasonably and uniformly.
S24, establishing a feature descriptor to describe the features of the detected feature points by using SIFT descriptors with scale and rotation invariance;
in the embodiment of the present invention, step S24 specifically includes:
calculating each direction parameter designated by the extreme point neighborhood pixels by using the distribution characteristic of the gradient direction, respectively calculating the gradient value m (x, y) and the gradient direction theta (x, y) of the characteristic point in the scale image L (x, y) according to the following two formulas,
and determining the main direction of the feature points by utilizing gradient values and gradient directions in an 8X 8 region with the feature points as the center, rotating coordinate axes of the image, determining a 4X 4 region with each key point as the center, setting 8 directions in each region, calculating gradient histograms of each sub-region to form the best SIFT descriptors, namely 4X 8 feature vectors, and finally carrying out normalization processing on the feature vectors to remove the influence of illumination change.
S25, after the SIFT descriptor is constructed, performing feature rough matching based on a K-D tree nearest neighbor query algorithm, performing shortest distance searching by adopting a K-D tree, and removing disordered feature points existing in the unknown points;
in the embodiment of the invention, the N data points exist in the K-dimensional space, the data space is equally divided into two parts at the ith dimension with the largest data change, the truncated data m is the average value of the (k+1)/2 data of the ith dimension, and the ith dimension of the search data and the truncated data m of the ith dimension of the K-d tree are compared according to the construction sequence of the original K-d tree so that the number of the data falling into the two ends of m is different by not more than 1. The search points are divided into sub-nodes by size until there is only one data to participate in the comparison. However, part of the shortest distance points are divided by adjacent other data points, and M times (M < N) of searching is still needed to be carried out on the adjacent nodes after the k-d tree searching is carried out, so that the position of the minimum distance is determined.
S26, carrying out initial matching on homonymous points by using a bidirectional matching strategy, and then removing homonymous points of which the reliability of the rest part cannot be determined by using an integral relaxation method;
in an embodiment of the present invention, the step of bi-directional matching strategy includes:
taking a certain characteristic point (x) r ,y r ) Searching two points closest to Euclidean distance corresponding to the reference subarea, wherein the points are homonymous points (xm, ym) of the images to be matched when the closest distance DN and the next closest distance DSN are met in the two feature points; the present embodiment preferably sets Threshold T to 0.8; taking the homonymous points (xm, ym) of the subareas to be matched as target points to obtain homonymous points (x 'on the remote sensing image' r ,y’ r ) The method comprises the steps of carrying out a first treatment on the surface of the Comparison (x) r ,y r ) And (x' r ,y’ r ) And if the distance between the two pixels is smaller than one pixel, rejecting the pixel if the distance between the two pixels is larger than the one pixel. After the two-way matching is checked, the reliability of the rest homonymous points can not be determined, and the points are screened by adopting the integral relaxation method to match, so that the matching points are combined with the points in the adjacent areas.
In the embodiment of the invention, the homonymous points of which the reliability of the rest parts cannot be determined are removed by using an integral relaxation method, the constraint and consistency among objects are considered by utilizing the context information in the neighborhood, and the most consistent and compatible result in the whole is finally obtained by iterative calculation.
The method comprises the following specific steps: determining a conjugate point i of a certain point j of the remote sensing image in the reference image, regarding the target point j as a category, and regarding a conjugate alternative point as a target A i The image matching is regarded as classification, namely overall fuzzy classification, and the category set is as follows: c= { C 1 ,C 2 ,...,C m ,C 0 }
Where Cj denotes the image point to be matched, j=1, 2,..m, C0 is a non-other point class. The target set determines r points i for each image point j to be matched by using a basic matching algorithm 1 ,i 2 ,....,i r As a conjugate candidate point for point j, the target set is: a= { a 11 ,A 12 ,....,A 21 ,A 22 ,.....,A i1 ,A i2 ,...,A m1 ,A m2 }, wherein target A i1 ,A i2 ,....,A ir The correlation coefficient with the remote sensing image point j is ρ 12 ,....ρ r Then A ik ∈C j The probability of (2) is:
for each image point ja to be matched and another point jb in a certain field thereof, and conjugate alternative points h and k corresponding to the image points in the reference image, and so on, the same can be said, the Phk can be determined, the Pij is continuously and iteratively corrected, and the optimization is gradually achieved:
s27, adopting a random sampling consistency algorithm and a least square iteration method to remove mismatching pairs in the candidate matching point set;
in the embodiment of the invention, an initial homography matrix H between an input remote sensing image and a reference image is initially estimated by using a RANSAC algorithm, then transformation coordinates of each point to be matched after rough matching are estimated according to the H, the transformation coordinates are expressed by the following formula,
wherein, (x) w ,y w ) Coordinates representing feature points of the remote sensing image, (X, Y) represents (X) w ,y w ) Is used to transform the coordinates.
The root mean square error of the ith matching point is calculated and expressed as:
and when the residual error and the root mean square error of the matching point pair are larger than the set threshold value, removing the matching point pair. And (3) iteratively calculating residual errors and root mean square errors by using the residual matching point pairs until the residual errors and root mean square errors of all the matching point pairs are smaller than the expected threshold.
And S28, carrying out homogenization treatment on the characteristic points by using a greedy algorithm to obtain finally uniformly distributed matching point pairs, and obtaining first pixel coordinates corresponding to each matching point in the remote sensing image.
Fitting the obtained matching points to the reconstruction, calculating residual error and RMSE of each pair of control points, and sorting the RMSE of the control points to the fitted control point set according to ascending order; selecting a control point with i=1 in the sequence as a first node for numbering, and calculating the distance between the control point and all other control points by using Euclidean distance; if the Euclidean distance is smaller than the threshold value, the two control points are considered to be distributed and removed too densely, and i=i+1 is caused; further preferably, the distance threshold at the time of feature point homogenization is 1000. Repeating the above steps, stopping when all control points are traversed, and outputting homogenized matching point pairs to obtain first pixel coordinates (x) 1 ,y 1 );
And converting the first pixel coordinate corresponding to the matching point on the remote sensing image into longitude and latitude coordinates (B, L) according to the geographic parameter information.
In the embodiment of the invention, according to the geographic information of the orthographic image, an orthographic image coordinate conversion parameter is obtained, the parameter is generally an affine transformation matrix, and the conversion between the pixel coordinate and the longitude and latitude coordinate of the image can be realized, as shown in the following formula:
B=Ax 1 +By 1 +C
L=Dx 1 +Ey 1 +F
and calculating longitude and latitude coordinates corresponding to the matching points according to the formula. In (x) 1 ,y 1 ) A first pixel coordinate, (B, L) a longitude and latitude coordinate,is an orthophoto parameter. Then, the elevation corresponding to the feature point is calculated at the DEM interpolation by a raster data interpolation method such as bilinear interpolation or bicubic convolution interpolation.
S3, carrying out geographic coordinate conversion on the first pixel coordinates of the matching point pairs according to the geographic information data to obtain longitude and latitude coordinates of the matching point pairs;
s4, interpolating longitude and latitude coordinates of the matching point pairs according to the DEM data to obtain geodetic coordinates, and taking the matching point pairs corresponding to the geodetic coordinates as control points;
in the embodiment of the invention, the elevation corresponding to the point is obtained by using a bilinear polynomial interpolation method according to the obtained longitude and latitude coordinates and DEM data. From the 4 nearest data points, a bilinear polynomial can be determined:
wherein Z is the elevation of the data point, a 00 、a 01 、a 10 、a 11 Is a linear coefficient between elevation H and longitude and latitude coordinates (B, L). 4 coefficients are obtained by using 4 known data points, then the elevation of the point is interpolated according to the longitude and latitude coordinates (B, L) and the obtained coefficients, and the geodetic coordinates (B, L, H) of the control point are obtained by converting the above steps.
The RFM model is one of the general imaging geometric models of satellite remote sensing images, and is suitable for various sensors including the latest aviation and aerospace sensor models. The RFM-based imaging model does not require knowledge of the actual characteristics of the sensor and the imaging process, and is a generalized imaging model of simple form that can achieve approximately consistent accuracy with a strictly imaging model.
S5, constructing an RFM model, performing RPC forward calculation on the original RPC parameters of the image to be repaired and the geodetic coordinates to obtain second pixel coordinates of the geodetic coordinates corresponding to the remote sensing image, and respectively calculating the average value of error distances of the corresponding first pixel coordinates and second pixel coordinates;
in an embodiment of the present invention, specifically, S5 includes the steps of:
s51, constructing an RFM model:
wherein P is i (i=1, 2,) 4) is a third order polynomial, (l, s) is a normalized second pixel coordinate, (X, Y, Z) is a normalized control point geodetic coordinate, and the values are all [ -1,1]Between them;
s52 expands (l, S) into two equations in linear form according to the Taylor series:
P 1 (X,Y,Z)-lP 2 (X,Y,Z)=0
P 3 (X,Y,Z)-sP 4 (X,Y,Z)=0;
s53, constructing two equations in a linear form into an equation set form by using the geodetic coordinates of the control points, and solving the equations:
y=Ax 0 +e
wherein y is E R m×1 For observing vector, A epsilon R m×n For coefficient matrix and e.epsilon.R m×1 Is the residual vector, x 0 ∈R n×1 Is the RPCs vector; m=2k, where k is the number of geodetic coordinates of the control point and n is 78;
solving the equation set:
x 0 =N -1 A T y
wherein n=a T A is a regular matrix, x 0 ∈R n×1 Is the RPCs vector;
s54, based on the RFM model, performing RPC forward calculation on the original RPC parameters of the remote sensing image and the geodetic coordinates of the control points to obtain second pixel coordinates of the control points corresponding to the geodetic coordinates of the remote sensing image;
s55 calculates the mean value of the error distances of the first pixel coordinates and the second pixel coordinates.
In the embodiment of the invention, the geodetic coordinates of the control points are changed into projection plane coordinates according to a projection transformation formula, the coordinate transformation is carried out according to the original RPC parameters of the remote sensing image based on the RFM model, and the projection plane coordinates calculate the geodetic coordinates of the control points to correspond to the second pixel coordinates on the remote sensing image;
the first-level image rigorous mathematical model is based on the principle of satellite imaging, a point on the ground forms a position relationship of two points on an image plane through a satellite sensor, and the position relationship can be represented by the following formula: (x, y) =t-1 (Dlat, dlon, h) indicates that the pixel coordinates on the remote sensing image can be uniquely determined by giving a geodetic latitude and longitude coordinate, so as to realize the calculation process of the step.
In the embodiment of the invention, an RFM model is used for replacing a first-level image rigorous mathematical model. The calculation process of the step is converted into an inverse transformation formula based on the RFM model, and only the corresponding RPC parameters are directly read in, and the parameters are directly brought into the RFM model for solving.
Adjusting the elevation h in the pixel coordinates (x, y, h) to be h base Pixel coordinates (x, y, h) are calculated by the RFM forward transform formula base ) Is transformed into the geodetic coordinates (D lat1 ,D lon1 ,h base );
The forward transform formula of the RFM model can be expressed as: (D) lat ,D lon ) =t (x, y, h), the calculation procedure in the example is to read in RPC parameters and then linearize the RFM equation:
the geodetic coordinates (D lat1 ,D lon1 ,h base ) Is changed into projection plane coordinates (D east ,D north );
The process is a projective transformation process, which converts longitude and latitude coordinates into projective coordinates under a projective plane (namely an earth ellipsoid), and a projective transformation formula can be expressed as:
performing coordinate conversion according to the image information of the remote sensing image, and calculating the second pixel coordinate (x 2, y 2) of the control point corresponding to the geodetic coordinate of the control point by using the projection plane coordinate (coast Dnorth);
x 2 =(D east -a)/d x
y 2 =(D north -b)/d y
wherein a, b, d x ,d y Can be obtained from the image information of the remote sensing image. a. b is the geodetic coordinates of the upper left point of the remote sensing image, d x ,d y Is X, Y direction resolution. Since a, b, d are recorded in the remote sensing image x ,d y These geometrical parameters can therefore be used directly for coordinate transformation. The image plane coordinates can be obtained by the projection coordinates according to the formula.
In the embodiment of the invention, the Euclidean distance is used for calculating the coordinates (x 1i ,y 1i ) And each second pixel coordinate (x 2i ,y 2i ) Mean of error distances of (2)
S6, on the basis of a least square adjustment principle, using an L1 regularization optimization method, and introducing a set linear constraint condition to obtain an optimized RFM model;
in the embodiment of the invention, a new L1 regularization method is provided, based on a robust 1-norm estimation principle, the estimation principle is simultaneously applied to RPC and residual error to generate a sparse model, so that the sparse model can be used for feature selection, and to a certain extent, L1 can also prevent overfitting, and the preset linear constraint conditions in step S6 are as follows:
wherein, |x| 1 Is the sum of the absolute values of the vectors x, and γ is the regularization parameter.
Optimizing the RFM model by introducing a set linear constraint condition,
and obtaining an optimal solution.
S7, judging according to the mean value of the error distance and a preset threshold value, selecting different repairing strategies, and re-calculating or correcting the RPC parameters.
Specifically, in step S7, the selection of different repair strategies is:
when the average value of the error distances accords with a first judging condition, selecting a first repairing strategy, and performing RPC re-calculation according to the original RPC parameters of the image to be repaired and the optimized RFM model to obtain repaired RPC parameters;
and when the mean value of the error distance meets a second judging condition, selecting a second repairing strategy, and performing RPC correction according to the geodetic coordinates, the original RPC parameters of the image to be repaired and the optimized RFM model to obtain repaired RPC parameters.
In the embodiment of the invention, in step S7, the first judgment condition is that the average value of the error distances is not less than a preset threshold value; the preset threshold is 30; when the mean value of the error distanceAnd selecting a first repairing strategy, and re-calculating the RPC parameters according to the geodetic coordinates of the control points by using the optimized RFM model to obtain the repaired RPC parameters.
The corresponding first repair strategy is:
re-calculating the RPC parameters according to the geodetic coordinates of the control points by using the optimized RFM model to obtain the repaired RPC parameters;
the first repair strategy includes:
in the optimized RFM model, the preset linear constraint condition is updated as follows:
min x,e ||x|| 1 +||e|| 1
under the updated linear constraint condition, according to the geodetic coordinates of the control points, constructing an equation set:
y=Ax+e
solving the equation set:
x=N -1 A T y
wherein x is the RPC parameter after repair.
The second judgment condition is that the average value of the error distances is less than a preset threshold value;
when the error distanceMean value of separationAnd selecting a second repairing strategy, and re-calculating the RPC parameters according to the geodetic coordinates of the control points by using the optimized RFM model to obtain the repaired RPC parameters.
The corresponding second repair strategy is:
and estimating an optimal solution of the offset conversion quantity according to the geodetic coordinates of the control points by using the optimized RFM model, and correcting the original RPC parameters to obtain the repaired RPC parameters.
The second repair strategy includes:
taking the original RPC parameter as an initial value x initial
In the optimized RFM model, the preset linear constraint condition is updated as follows:
min Δx,e ||Δx|| 1 +||e|| 1
under the updated linear constraint condition, according to the geodetic coordinates of the control points, constructing an equation set:
y=Ax initial +AΔx+e;
solving the equation set:
Δx=N -1 A T y-Ax initial
wherein Δx is the optimal solution of the offset transform;
at an initial value x initial On the basis of (1), add Δx, i.e. x=x initial +Δx, where x is the RPC parameter after repair.
The above described repair strategy can be applied to three possible cases between m and n, namely m > n, m < n, and m=n.
For example, in the case of limited GCPs (m < n), we would like to choose more RPCs than residuals, compensated by increasing the cost coefficient of residuals relative to RPCs.
When m > n, the system of equations is overfitted, the better restated version of the above linear constraint is:
min x,e ||x|| 1 +c||e|| 1
the method is constructed as a system of equations:
y=Ax+e
where c=n/m is a cost factor of e relative to x, and the linear constraint is rewritable as:
min x,e ||[x T ce T ]|| 1
the method is constructed as a system of equations:
y=Ax+c -1 ce
wherein c -1 =m/n, with v=ce (scaling vector of residual), the linear constraint is deformed to:
the method is constructed as a system of equations:
introducing z= [ x ] T ,v T ] 2 ,B=[A,c -1 I m ]The following optimization problems are obtained:
min z ||z|| 1
y=Bz
to transform the above optimization problem into a linear form we use the approach proposed by emmer-siemens, vector z, which in general has positive and negative values, can be derived from two relaxation vectors a and β:
z i =α ii
i=1,...m+n,α i ,β i ≥0
from the above equation, infer |z i |=α ii
Wherein u= [1, ], 1] T E R (m+n). Times.1, a linear version of the optimization problem is derived as follows:
after determining α and β through the above linear optimization problem, z=α - β can be calculated, and the first parameter of n=78 is the RPC parameter after repair according to the definition of z.
When the mean value of the error distanceSelecting a second repairing strategy, estimating an optimal solution of the offset conversion quantity according to the geodetic coordinates of the control points by using the optimized RFM model, and correcting the original RPC parameters to obtain repaired RPC parameters;
in an embodiment of the present invention, the second repair policy in step S7 includes:
taking the original RPC parameter as an initial value x initial
In the optimized RFM model, the preset linear constraint condition is updated as follows:
min Δx,e ||Δx|| 1 +||e|| 1
under the updated linear constraint condition, according to the geodetic coordinates of the control points, constructing an equation set:
y=Ax initial +AΔx+e;
solving the equation set:
Δx=N -1 A T y-Ax initial
wherein Δx is the optimal solution of the offset transform;
after determining α and β by the above linear optimization problem, z=α - β can be calculated, and the first parameter of n=78 is Δx, at an initial value of x, according to the definition of z initial On the basis of (1), add Δx, i.e. x=x initial +Δx, where x is the RPC parameter after repair.
The above embodiments are only for illustrating the present invention, not for limiting the present invention, and various changes and modifications may be made by one of ordinary skill in the relevant art without departing from the spirit and scope of the present invention, and therefore, all equivalent technical solutions are also within the scope of the present invention, and the scope of the present invention is defined by the claims.

Claims (8)

1. The remote sensing image RPC restoration method is characterized by comprising the following steps of:
s1, acquiring an image to be repaired, a reference image, geographic information data and DEM data;
s2, carrying out feature extraction and matching on the image to be repaired and the reference image by adopting a SIFT algorithm to obtain a matching point pair and a corresponding first pixel coordinate;
s3, carrying out geographic coordinate conversion on the first pixel coordinates of the matching point pairs according to the geographic information data to obtain longitude and latitude coordinates of the matching point pairs;
s4, interpolating longitude and latitude coordinates of the matching point pairs according to the DEM data to obtain geodetic coordinates, and taking the matching point pairs corresponding to the geodetic coordinates as control points;
s5, constructing an RFM model, performing RPC forward calculation on the original RPC parameters of the image to be repaired and the geodetic coordinates to obtain second pixel coordinates of the geodetic coordinates corresponding to the remote sensing image, and respectively calculating the average value of error distances of the corresponding first pixel coordinates and second pixel coordinates;
s6, on the basis of a least square adjustment principle, using an L1 regularization optimization method, and introducing a set linear constraint condition to obtain an optimized RFM model;
s7, judging according to the mean value of the error distance and a preset threshold value, selecting different repairing strategies, and re-calculating or correcting the RPC parameters.
2. The remote sensing image RPC repair method according to claim 1, wherein step S5 comprises:
s51, constructing an RFM model:
wherein P is i (i=1, 2,) 4) is a third order polynomial, (l, s) is a normalized second pixel coordinate, (X, Y, Z) is a normalized control point geodetic coordinate, and the values are all [ -1,1]Between them;
s52 expands (l, S) into two equations in linear form according to the Taylor series:
P 1 (X,Y,Z)-lP 2 (X,Y,Z)=0
P 3 (X,Y,Z)-sP 4 (X,Y,Z)=0;
s53, constructing two equations in a linear form into an equation set form by using the geodetic coordinates of the control points, and solving the equations:
y=Ax 0 +e
wherein y is E R m×1 For observing vector, A epsilon R m×n For coefficient matrix and e.epsilon.R m×1 Is the residual vector, x 0 ∈R n×1 Is the RPCs vector; m=2k, wherein k is the number of the geodetic coordinates of the control point and n is 78;
solving the equation set:
x 0 =N -1 A T y
wherein n=a T A is a regular matrix, x 0 ∈R n×1 Is the RPCs vector;
s54, based on the RFM model, performing RPC forward calculation on the original RPC parameters of the remote sensing image and the geodetic coordinates of the control points to obtain second pixel coordinates of the control points corresponding to the geodetic coordinates of the remote sensing image;
s55 calculates the mean value of the error distances of the first pixel coordinates and the second pixel coordinates.
3. The remote sensing image RPC repair method according to claim 2, wherein the preset linear constraint condition in step S6 is:
wherein, |x| 1 Is the sum of the absolute values of the vectors x, and γ is the regularization parameter.
4. The remote sensing image RPC repair method according to claim 1, wherein in step S7, the selecting different repair strategies is:
when the average value of the error distances accords with a first judging condition, selecting a first repairing strategy, and performing RPC re-calculation according to the original RPC parameters of the image to be repaired and the optimized RFM model to obtain repaired RPC parameters;
and when the mean value of the error distance meets a second judging condition, selecting a second repairing strategy, and performing RPC correction according to the geodetic coordinates, the original RPC parameters of the image to be repaired and the optimized RFM model to obtain repaired RPC parameters.
5. The remote sensing image RPC restoration method according to claim 4, wherein in step S7, the first determination condition is that the mean value of the error distances is equal to or greater than a preset threshold;
the corresponding first repair strategy is:
re-calculating the RPC parameters according to the geodetic coordinates of the control points by using the optimized RFM model to obtain the repaired RPC parameters;
the second judgment condition is that the average value of the error distances is less than a preset threshold value;
the corresponding second repair strategy is:
and estimating an optimal solution of the offset conversion quantity according to the geodetic coordinates of the control points by using the optimized RFM model, and correcting the original RPC parameters to obtain the repaired RPC parameters.
6. The remote sensing image RPC repair method according to claim 4, wherein the first repair strategy in step S7 includes:
in the optimized RFM model, the preset linear constraint condition is updated as follows:
min x,e ||x|| 1 +||e|| 1
under the updated linear constraint condition, according to the geodetic coordinates of the control points, constructing an equation set:
y=Ax+e
solving the equation set:
x=N -1 A T y
wherein x is the RPC parameter after repair.
7. The remote sensing image RPC repair method according to claim 4, wherein the second repair strategy in step S7 includes:
taking the original RPC parameter as an initial value x initial
In the optimized RFM model, the preset linear constraint condition is updated as follows:
min Δx,e ||Δx|| 1 +||e|| 1
under the updated linear constraint condition, according to the geodetic coordinates of the control points, constructing an equation set:
y=Ax initial +AΔx+e;
solving the equation set:
Δx=N -1 A T y-Ax initial
wherein Δx is the optimal solution of the offset transform;
at an initial value x initial On the basis of (1), add Δx, i.e. x=x initial +Δx, where x is the RPC parameter after repair.
8. The remote sensing image RPC repair method according to claim 1, wherein step S2 comprises:
s21, determining a frame of image in the same space as a reference image according to the remote sensing image, and carrying out image enhancement on the two images to enable the two images to have interaction characteristics in gray scale;
s22, performing block matching on the two images by utilizing the constraint of the geographic parameter information of the remote sensing images, dividing the remote sensing images into a plurality of sub-area image blocks to be matched, and obtaining corresponding reference sub-area image blocks according to the projection coordinates of each image block;
s23, moving an area search window in all directions by using a shi_Tomasi algorithm, observing an energy expansion average value of the window, and determining a central pixel point with the energy change of the window larger than a defined threshold value as a corner point; s24, establishing a feature descriptor to describe the features of the detected feature points by using SIFT descriptors with scale and rotation invariance;
s25, after the SIFT descriptor is constructed, performing feature rough matching based on a K-D tree nearest neighbor query algorithm, performing shortest distance searching by adopting a K-D tree, and removing disordered feature points existing in the unknown points;
s26, carrying out initial matching on homonymous points by using a bidirectional matching strategy, and then removing homonymous points of which the reliability of the rest part cannot be determined by using an integral relaxation method;
s27, adopting a random sampling consistency algorithm and a least square iteration method to remove mismatching pairs in the candidate matching point set;
and S28, carrying out homogenization treatment on the characteristic points by using a greedy algorithm to obtain finally uniformly distributed matching point pairs, and obtaining first pixel coordinates corresponding to each matching point in the remote sensing image.
The remote sensing image RPC restoration method according to claim 1, wherein the error distance calculation method in step S4 is any one of euclidean distance, similarity, and angle cosine.
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