CN104077535B - Graphic information system (GIS) vector data local decryption and restoring method - Google Patents

Abstract

The invention discloses a graphic information system (GIS) vector data local decryption and restoring method which includes the following process: (1) calculating decryption parameters through a local decryption control point and iterating the parameters to control errors in a decryption area; (2) conducting decryption on local elements according to local decryption parameters; (3) restoring the decrypted local elements through the local decryption parameters. The method has the advantages of gradual local decryption transformation, accurate transformation of the decryption control point and decryption area close support, and can meet the requirement for GIS vector data local decryption processing for external issuing and use.

Description

A kind of gis vector data local DecryptDecryption and restoration methods

Technical field

The invention belongs to field of geographic information safety is and in particular to a kind of gis vector data local DecryptDecryption and restoration methods.

Background technology

" regulation of Surveying Management Work state secret scope ", " open map content representation supplementary provisions (trying) " and Files such as " regulations (trying) of Fundamental Geographic Information System demonstration content " to the restrictive condition of open map and geography information and Secure content is made that regulation, and especially emphasizes the confidentiality of the spatial position precision of Fundamental Geographic Information System and relevant factor.

Common facility and sensitive installations have different positional accuracy index requests.Local sensitivity key element is carried out with local several What precision DecryptDecryption needs its accurate DecryptDecryption to target location to meet positional accuracy requirement.Additionally, office is carried out to sensitive key element During portion's DecryptDecryption, not should on certain limit outside key element produce impact, i.e. the compact schemes characteristic of local DecryptDecryption.Existing local DecryptDecryption Model generally adopts sectional pattern, will be divided into small range by map on a large scale, and reuse the model such as multinomial or rubber transformation of page Carry out Local treatment it is difficult to meeting control point precise transformation, converting uniformly asymptotic and three demands of deformed region compact schemes.

Content of the invention

The present invention is directed to the defect that existing gis vector data local DecryptDecryption model exists, and proposes one kind and is based on compact schemes footpath To the gis vector data local DecryptDecryption method of basic function, there are progressive, the control point precise transformation of deformation and deformed region compact schemes Feature.

The technical solution used in the present invention is as follows:

A kind of gis vector data local DecryptDecryption and restoration methods, including following process:

(1) key generation process

Step 11: determine DecryptDecryption scope

Input DecryptDecryption region minimum enclosed rectangle rectangle, wherein, rectangle rectangle lower-left angular coordinate is (x_min, y_min), upper right angular coordinate is (x_max,y_max), data x direction length xl and y direction length yl are obtained according to formula (1)；

$\left\{\begin{array}{c}\mathrm{xl}=x_{\max }-x_{\min }\\ \mathrm{yl}=y_{\max }-y_{\min }\end{array}\right.---\left(1\right)$

Step 12: determine Data Control point and DecryptDecryption converted quantity

Input source controls point set frompoints={ (fx_i,fy_i) | i=1,2 ... k } and target control point set Topoints={ (tx_i,ty_i) | i=1,2 ..., k } composition k dominating pair of vertices, meet source control point set frompoints with The condition of coincidence point is not all contained in target control point set topoints；

Step 13: determine the radius of influence r at each DecryptDecryption control point according to formula (2)；

$r\&greaterequal;100\×\max \left(\sqrt{{({\mathrm{tx}}_i-{\mathrm{fx}}_i)}^2+{({\mathrm{ty}}_i-{\mathrm{fy}}_i)}^2}\right)---\left(2\right)$

Step 14: training Compactly supported radial basis function neural network model

A) select single order compact schemes basic function as output function φ, be then c (c for center_x,c_y) basic function, its Data point p_iPlace is output as:

Euclidean distance is selected to calculate data point p and the distance of center c；

$\mathrm{dis}\tan \mathrm{ce}(p,c)=\left|\right|p-c\left|\right|=\sqrt{{(p_x-c_x)}^2+{(p_y-c_y)}^2}---\left(4\right)$

B) point set frompoints coordinate (fx is controlled with source_i,fy_i) as input layer x, DecryptDecryption converted quantity (tx_i-fx_i, ty_i-fy_i) as output layer learning sample y, k hidden node is as center the c={ (fx of basic function in hidden layer_i,fy_i) | i= 1,2 ... k }, each basic function takes identical r value, the output composition matrix h of k hidden node, the god between hidden layer to output layer Connect weight w through unit, set up Compactly supported radial basis function neutral net csrbfnet, meet the interpolation condition of formula (5)；

Y=hw (5)

C) method of least square is utilized to calculate weight w by formula (6), w is 2*k matrix；

W=h^-1y (6)

D) uniformly choose m*n sample point in the range of minimum enclosed rectangle rectangle and form sample point set Samplepoints={ (sx_j,sy_j) | j=1,2 ..., num }, wherein m is x direction sample point quantity, and n is y direction sample point Quantity, m >=3, n >=3, num=m*n；Traversal sample point set samplepoints, calculates each sample according to formula (7) The disturbance quantity of point, generates sample point disturbance duration set samplepoints '={ (sx_j′,sy_j') | j=1,2 ..., num }；

$\left\{\begin{array}{c}{\mathrm{sx}}_i={\mathrm{\σ}}_{l=1}^k{w}_{1l}{\mathrm{\φ}}_l\left(\mathrm{dis}\tan \mathrm{ce}(x_i,c_l)\right)\\ {\mathrm{sy}}_i={\mathrm{\σ}}_{l=1}^k{w}_{2l}{\mathrm{\φ}}_l\left(\mathrm{dis}\tan \mathrm{ce}(x_i,c_l)\right)\end{array}\right.---\left(7\right)$

E) according to error rmse in formula (8) calculating；

$\mathrm{rmse}=\sqrt{\frac{\mathrm{\σ}(s{x}_i^2+s{y}_i^2)}{\mathrm{num}}}---\left(8\right)$

| offset/rmse-1 | if f) > 0.01, is unsatisfactory for the requirement of input data global transformation amount offest, makes Zoomed in and out with error of centralization rmse with the radius of influence r at each DecryptDecryption control point of formula (9) iteration, circulation step b-e, until | offset/rmse-1 |≤0.01, then complete for resolving；

$r=r\×\frac{\mathrm{offset}}{\mathrm{rmse}}---\left(9\right)$

D) source is used to control point set frompoints, target control point set topoints, each DecryptDecryption control point Radius of influence r and weight matrix w composition DecryptDecryption parameter key, carries out asymmetric encryption using rsa algorithm to key key and deposits Enter key file key.txt；

(2) local DecryptDecryption process

Step 21: read DecryptDecryption parameter key, extract key key using after the deciphering of rsa algorithm, obtain source and control point set Frompoints, target control point set topoints, the radius of influence r at each DecryptDecryption control point and weight matrix w, set up de- Close Compactly supported radial basis function neutral net csrbfnet；

Step 22: open and treat DecryptDecryption vector data d, extract the key element point coordinates of vector data d, obtain key element point coordinates collection Close p={ (x_j,y_j) | j=1,2 ..., k }, the point number that wherein k comprises for key element；

Step 23: by Compactly supported radial basis function neutral net csrbfnet of foundation, being calculated according to formula (10) will Each of vegetarian refreshments coordinate set p point coordinates p_j(x_j,y_j) through DecryptDecryption conversion after changes in coordinates amount (δ x_j,δy_j)；

$\left\{\begin{array}{c}\mathrm{\δ}{x}_j={\mathrm{csrbfnet}}_x\left(p_j\right)={\mathrm{\σ}}_{l=1}^k{w}_{1l}{\mathrm{\φ}}_l\left(\mathrm{dis}\tan \mathrm{ce}(p_j,c_l)\right)\\ \mathrm{\δ}{y}_j={\mathrm{csrbfnet}}_y\left(p_j\right)={\mathrm{\σ}}_{l=1}^k{w}_{2l}{\mathrm{\φ}}_l\left(\mathrm{dis}\tan \mathrm{ce}(p_j,c_l)\right)\end{array}\right.---\left(10\right)$

Step 24: DecryptDecryption changes in coordinates amount is applied to by point coordinates p according to formula (11)_j, obtain point coordinates set p '= {(x_j′,y_j') | j=1,2 ..., k }；

$\left\{\begin{array}{c}{x}_j^{\′}=x_j+\mathrm{\δ}{x}_j\\ y_j^{\′}=y_j+\mathrm{\δ}{y}_j\end{array}\right.---\left(11\right)$

Step 25: circulation step 23 and 24, until all key elements are disposed, preserve the data file after the DecryptDecryption of local df；

(3) local recovery's process

Step 31: read key file key.txt, extract key key using after the deciphering of rsa algorithm, obtain source control point With target control point set, the radius of influence r and weight matrix w at each local DecryptDecryption control point, set up DecryptDecryption compact schemes radially Basis function neural network csrbfnet；

Step 32: open data df after DecryptDecryption, extract the key element point coordinates of vector data df, obtain the key element after DecryptDecryption Point coordinates set p '={ (px_i′,py_i') | i=1,2 ..., k }.And assume that the DecryptDecryption converted quantity that each is put is δ_i={ (δ x_i, δy_i) | i=1,2 ..., k }, initial value is 0；

Step 33: according to formula (12), by p '-δ_p' substituting into neutral net csrbfnet, the DecryptDecryption updating each point becomes The amount of changing δ_i(δx_i,δy_i)；

$\left\{\begin{array}{c}\mathrm{\δ}{x}_i=p{x}_i^{\′}-{\mathrm{csrbfnet}}_x(p_i^{\′}-{\mathrm{\δ}}_i)\\ \mathrm{\δ}{y}_i=p{y}_i^{\′}-{\mathrm{csrbfnet}}_y(p_i^{\′}-{\mathrm{\δ}}_i)\end{array}\right.---\left(12\right)$

Step 34: set error limit ∈, if the δ after updating_iMeet formula (13), be then considered as recovery and complete, otherwise weigh Multiple step 33；

$\left\{\begin{array}{c}p{x}_i^{\&prime;}-{\mathrm{csrbfnet}}_x(p_i^{\&prime;}-{\mathrm{\&delta;}}_i)-{\mathrm{\&delta;x}}_i<\&element;\\ y_i^{\&prime;}-{\mathrm{csrbfnet}}_y(p_i^{\&prime;}-{\mathrm{\&delta;}}_i)-{\mathrm{\&delta;y}}_i<\&element;\end{array}\right.---\left(13\right)$

Step 35: repeat step 33 and 34, process each key element successively, data file rf after saving/restoring.

The present invention proposes a kind of method carrying out local DecryptDecryption and recovery for gis vector data.This method is being safeguarded On the premise of vector data topological relation is constant, DecryptDecryption control point precise transformation to target control point can be ensured de- simultaneously The compact schemes characteristic in close region, can meet gis vector data local DecryptDecryption and process with external issue use demand.

Brief description

Fig. 1 is key product process figure in the technology of the present invention；

Fig. 2 is data local DecryptDecryption flow chart in the technology of the present invention；

Fig. 3 is Data Recovery Process figure after local DecryptDecryption in the technology of the present invention；

Fig. 4 is the original vector data that the embodiment of the present invention is selected；

Fig. 5 is the design sketch of data investigation after initial data and local DecryptDecryption in the embodiment of the present invention；

Fig. 6 is the partial enlargement design sketch of data investigation after initial data and local DecryptDecryption in the embodiment of the present invention；

Fig. 7 is the design sketch recovering data investigation after initial data and local DecryptDecryption in the embodiment of the present invention.

Specific embodiment

With reference to the accompanying drawings and examples, the present invention is described in further details.

The present embodiment selects shapefile form vector data, data is read out, DecryptDecryption and recovery operation, enters one Step describes the present invention in detail.The present embodiment selects shapefile face figure layer data (as Fig. 4) in a certain area as original vector Data.

(1) key generation process

Step 11: determine DecryptDecryption scope, input DecryptDecryption region minimum enclosed rectangle rectangle, the rectangle lower left corner Coordinate be (164417.097000,162667.721400), upper right angular coordinate be (171415.635650, 167846.074000) data x direction length xl=6998.53865m, y direction length yl=5178.3526m, are obtained；

Step 12: input 6 is to source control point and target control point set；

Step 13: determine the radius of influence r at each local DecryptDecryption control point, select r=3000m；

Step 14: training radial basis function neural network, specifically comprise the following steps that

A) select single order compact schemes basic function as output function φ；

B) with frompoints coordinate (fx_i,fy_i) as input layer x, DecryptDecryption converted quantity (tx_i-fx_i,ty_i-fy_i) conduct Output layer learning sample y, 6 hidden node are as center the c={ (fx of basic function in hidden layer_i,fy_i) | i=1,2 ... 6 }, respectively Basic function takes identical radius of influence r, and each basic function is output as h, the neuron connection weight between hidden layer to output layer W, sets up radial basis function neural network csrbfnet；

C) weight w=[- 0.68576558 2.24318105 1.30650649- is calculated by formula (6) 0.924589651.0799589 1.09748868；3.21258749 0.86481197-0.68393027 3.34310239- 1.41045726-1.1620549]；

D) uniformly choose 50*50 sample point in the range of minimum enclosed rectangle rectangle and form sample point set Samplepoints={ (sx_j,sy_j) | j=1,2 ..., 2500 }, travel through sample point set samplepoints, according to formula (4) calculate the disturbance quantity of each sample point, generate sample point disturbance quantity set samplepoints '={ (sx_j′,sy_j′)|j =1,2 ..., 2500 }；

E) according to error rmse=0.849401552583 in formula (8) calculating；

F) due to | offset/rmse-1 | > 0.01, need the radius of influence r=at iteration local DecryptDecryption control point 4158.10214553.Then circulation step b-e, r=3706.05059411, rmse=0.993166516737 after iteration 2 times, Meet condition, obtain final weight matrix w=[- 1.84601557 2.76989104 0.95848037-2.20952748 1.79216251 1.80692918；4.42896143 -0.15784362 -1.20732732 4.89798742- 2.70956928-2.02686662]；

G) source control point, target control point set, the radius of influence r at local DecryptDecryption control point and weight matrix w are used Composition local DecryptDecryption parameter key；

(2) local DecryptDecryption process

Step 21: read DecryptDecryption parameter key, extract key key using after the deciphering of rsa algorithm, obtain source and control point set Frompoints, target control point set topoints, the radius of influence r at each DecryptDecryption control point and weight matrix w, set up de- Close Compactly supported radial basis function neutral net csrbfnet；

Step 22: open original vector data d, extract the key element point coordinates of vector data d, obtain key element point coordinates set P={ (x_j,y_j) | j=1,2 ..., k }, the point number that wherein k comprises for key element, below with 1 point of p in p (167131.647, 164958.147) as a example illustrate；

Step 23: Compactly supported radial basis function neutral net csrbfnet is set up according to key key, is calculated by formula (10) Each of p set point coordinates p_j(x_j,y_j) variable quantity (δ x_j,δy_j), the variable quantity of point p be (1.19198160762, 2.25882888931)；

Step 24: DecryptDecryption changes in coordinates amount is applied to by p according to formula (11), obtains point coordinates set p ', the DecryptDecryption of point p Recoil is designated as (167132.838982,164960.405829)；

Step 25: circulation step 23 and 24, until all key elements are disposed, preserve the data file after the DecryptDecryption of local df；

(3) local recovery's process

Step 31: read key file key.txt, extract key key using after the deciphering of rsa algorithm, obtain source control point With target control point set, the radius of influence r and weight matrix w at each DecryptDecryption control point, set up local DecryptDecryption compact schemes radially Basis function neural network csrbfnet；

Step 32: open data df after DecryptDecryption, extract the key element point coordinates of vector data df, obtain the key element after DecryptDecryption Point coordinates set p '={ (px_i′,py_i') | i=1,2 ..., k }.And assume that the DecryptDecryption converted quantity that each is put is δ_i={ (δ x_i, δy_i) | i=1,2 ..., k }, initial value is 0, below with 1 point of p ' (167132.838982,164960.405829) in p ' As a example illustrate, δ_p'=(0,0)；

Step 33: according to formula 12, by p '-δ_p' substitute into rbfnet, update the DecryptDecryption converted quantity δ of p '_p'= (1.19416476507,2.25919063147)；

Step 34: take recovery precision ∈=0.01m, the δ after renewal_iIt is unsatisfactory for formula 13, the 2nd δ_p'= (1.1919782225,2.25883077318), meet formula 13, are considered as recovery and complete；

Step 35: repeat step 33 and 34, process each key element successively, data file rf after saving/restoring.

Only taking shp formatted data as a example carry out DecryptDecryption and recovery operation, the method can also be used in the embodiment of the present invention The extended formatting vector data such as geodatabase.

The foregoing is only the preferred embodiments of the present invention, be not limited to the present invention.Obviously, those skilled in the art Member the present invention can be carried out various change and modification without departing from the spirit and scope of the present invention.So, if the present invention These modifications and modification belong within the scope of the claims in the present invention and its equivalent technologies, then the present invention is also intended to comprise these Including change and modification.

Claims (1)

1. a kind of gis vector data local DecryptDecryption and restoration methods, including following process:

(1) key generation process

Step 11: determine DecryptDecryption scope

Input DecryptDecryption region minimum enclosed rectangle rectangle, wherein, rectangle rectangle lower-left angular coordinate is (x_min, y_min), upper right angular coordinate is (x_max, y_max), data x direction length xl and y direction length yl are obtained according to formula (1)；

$\left\{\begin{array}{c}xl=x_{\max }-x_{\min }\\ yl=y_{\max }-y_{\min }\end{array}\right.---\left(1\right)$

Step 12: determine Data Control point and DecryptDecryption converted quantity

Input source controls point set frompoints={ (fx_i, fy_i) | i=1,2 ... k } and target control point set Topoints={ (tx_i, ty_i) | i=1,2 ..., k } k dominating pair of vertices of composition, meet source control point set frompoints with The condition of coincidence point is not all contained in target control point set topoints；

Step 13: determine the radius of influence r at each DecryptDecryption control point according to formula (2)；

$r\&greaterequal;100\&times;\max \left(\sqrt{{({\mathrm{tx}}_i-{\mathrm{fx}}_i)}^z+{({\mathrm{ty}}_i-{\mathrm{fy}}_i)}^2}\right)---\left(2\right)$

Step 14: training Compactly supported radial basis function neural network model

A) select single order compact schemes basic function as output function φ, be then c (c for center_x, c_y) basic function, it is in data Point p_iPlace is output as:

Euclidean distance is selected to calculate data pointWith center c (c_x, c_y) distance；

$dis\tan ce(p_i,c)=\left|\right|p_i-c\left|\right|=\sqrt{{(p_{i_x}-c_x)}^2+{(p_{i_y}-c_y)}^2}---\left(4\right)$

B) point set frompoints coordinate (fx is controlled with source_i, fy_i) as input layer x, DecryptDecryption converted quantity (tx_i-fx_i, ty_i- fy_i) as output layer learning sample y, k hidden node is as the center centers={ c of basic function in hidden layer_i(fx_i, fy_i) | i=1,2 ... k }, each basic function takes identical r value, and the output composition matrix h of k hidden node, between hidden layer to output layer Neuron connection weight w, set up DecryptDecryption Compactly supported radial basis function neutral net csrbfnet, meet the interpolation of formula (5) Condition；

Y=hw (5)

C) method of least square is utilized to calculate weight w by formula (6), w is 2*k matrix；

W=h^-1y (6)

D) uniformly choose m*n sample point in the range of minimum enclosed rectangle rectangle and form sample point set Samplepoints={ x_j(sx_j, sy_j) | j=1,2 ..., num }, wherein m is x direction sample point quantity, and n is y direction sample Point quantity, m >=3, n >=3, num=m*n；Traversal sample point set samplepoints, calculates each sample according to formula (7) The disturbance quantity of this point, generates sample point disturbance duration set samplepoints '={ (sx '_j, sy '_j) | j=1,2 ..., num }, Wherein, c₁For any point in the center centers of basic function；

$\left\{\begin{array}{c}{\mathrm{sx}}_j^{\&prime;}={\mathrm{\&sigma;}}_{l=1}^k{w}_{1l}{\mathrm{\&phi;}}_l\left(dis\tan ce\right(x_j,c_l\left)\right)\\ {\mathrm{sy}}_j^{\&prime;}={\mathrm{\&sigma;}}_{l=1}^k{w}_{2l}{\mathrm{\&phi;}}_l\left(dis\tan ce\right(x_j,c_l\left)\right)\end{array}\right.---\left(7\right)$

E) according to error rmse in formula (8) calculating；

$rmse=\sqrt{\frac{\&sigma;({\mathrm{sx}}_i^2+{\mathrm{sy}}_i^2)}{num}}---\left(8\right)$

| offset/rmse-1 | if f) > 0.01, is unsatisfactory for the requirement of input data global transformation amount offest, using public affairs The radius of influence r at each DecryptDecryption control point of formula (9) iteration is zoomed in and out with error of centralization rmse, circulation step b-e, until | Offset/rmse-1 |≤0.01, then complete for calculating；

$r=r\&times;\frac{offset}{rmse}---\left(9\right)$

D) source is used to control point set frompoints, target control point set topoints, the impact at each DecryptDecryption control point Radius r and weight matrix w composition DecryptDecryption parameter key, carries out asymmetric encryption using rsa algorithm and is stored in close to key key Key file key.txt；

(2) local DecryptDecryption process

Step 21: read DecryptDecryption parameter key, extract key key using after the deciphering of rsa algorithm, obtain source and control point set Frompoints, target control point set topoints, the radius of influence r at each DecryptDecryption control point and weight matrix w, set up de- Close Compactly supported radial basis function neutral net csrbfnet；

Step 22: open and treat DecryptDecryption vector data d, extract the key element point coordinates of vector data d, obtain key element point coordinates set p ={ (x_j,y_j) | j=1,2 ..., k }, the point number that wherein k comprises for key element；

Step 23: by DecryptDecryption Compactly supported radial basis function neutral net csrbfnet of step 21 foundation, according to formula (10) Each of computational element point coordinates set p point coordinates p_j(x_j,y_j) through DecryptDecryption conversion after changes in coordinates amount (δ x_j, δ y_j), c₁For any point in the center centers of basic function；

$\left\{\begin{array}{c}{\mathrm{\&delta;x}}_j={\mathrm{csrbfnet}}_x\left(p_j\right)={\&sigma;}_{l=1}^k{w}_{1l}{\mathrm{\&phi;}}_l\left(dis\tan ce\right(p_j,c_l\left)\right)\\ {\mathrm{\&delta;y}}_j={\mathrm{csrbfnet}}_y\left(p_j\right)={\&sigma;}_{l=1}^k{w}_{2l}{\mathrm{\&phi;}}_l\left(dis\tan ce\right(p_j,c_l\left)\right)\end{array}\right.---\left(10\right)$

Step 24: DecryptDecryption changes in coordinates amount is applied to by point coordinates p according to formula (11)_j, obtain point coordinates set p '={ (x_j’, y_j') | j=1,2 ..., k }；

$\left\{\begin{array}{c}{x}_j^{\&prime;}=x_j+{\mathrm{\&delta;x}}_j\\ y_j^{\&prime;}=y_j+{\mathrm{\&delta;y}}_j\end{array}\right.---\left(11\right)$

Step 25: circulation step 23 and 24, until all key elements are disposed, preserve data file df after the DecryptDecryption of local； (3) local recovery's process

Step 31: read key file key.txt, extract key key using after the deciphering of rsa algorithm, obtain source control point and mesh Mark controls point set, the radius of influence r and weight matrix w at each local DecryptDecryption control point, sets up DecryptDecryption compact schemes radial direction base letter Number neutral net csrbfnet；

Step 32: open data df after DecryptDecryption, extract the key element point coordinates of vector data df, obtain the vegetarian refreshments of wanting after DecryptDecryption and sit Mark set p '={ p '_i(px′_i, py '_i) | i=1,2 ..., k }；And assume that the DecryptDecryption converted quantity that each is put is δ_i={ (δ x_i, δy_i) | i=1,2 ..., k }, initial value is 0；

Step 33: according to formula (12), by each key element point coordinates in the key element point coordinates set p ' after DecryptDecryptionGeneration Enter DecryptDecryption Compactly supported radial basis function neutral net csrbfnet of step 31 foundation, update the DecryptDecryption converted quantity δ of each point_i (δx_i, δ y_i)；

$\left\{\begin{array}{c}{\mathrm{\&delta;x}}_i={\mathrm{px}}_i^{\&prime;}-{\mathrm{csrbfnet}}_x(p_i^{\&prime;}-{\mathrm{\&delta;}}_i)\\ {\mathrm{\&delta;y}}_i={\mathrm{py}}_i^{\&prime;}-{\mathrm{csrbfnet}}_y(p_i^{\&prime;}-{\mathrm{\&delta;}}_i)\end{array}\right.---\left(12\right)$

Step 34: set error limit ∈, if the δ after updating_iMeet formula (13), be then considered as recovery and complete, otherwise repeat to walk Rapid 33；

$\left\{\begin{array}{c}{\mathrm{px}}_i^{\&prime;}-{\mathrm{csrbfnet}}_x(p_i^{\&prime;}-{\mathrm{\&delta;}}_i)-{\mathrm{\&delta;x}}_i<\&element;\\ {\mathrm{py}}_i^{\&prime;}-{\mathrm{csrbfnet}}_y(p_i^{\&prime;}-{\mathrm{\&delta;}}_i)-{\mathrm{\&delta;y}}_i<\&element;\end{array}\right.---\left(13\right)$

Step 35: repeat step 33 and 34, process each key element successively, data file rf after saving/restoring.