CN104599224B

CN104599224B - A kind of concerning security matters point-like geographic element camouflage deposited based on information point and restoring method

Info

Publication number: CN104599224B
Application number: CN201510038934.9A
Authority: CN
Inventors: 吴雪荣; 李安波; 蒋伟; 杨孝丽
Original assignee: Nanjing Normal University
Current assignee: Nanjing Normal University
Priority date: 2015-01-26
Filing date: 2015-01-26
Publication date: 2017-12-15
Anticipated expiration: 2035-01-26
Also published as: CN104599224A

Abstract

The invention discloses a kind of vertex type GIS vector data camouflage deposited based on information point and restoring method, including following process：(1) for vertex type GIS vector data camouflage process, including the steps such as the determination of scope, the pseudo- generation decorateeed are pretended；(2) it is directed to vertex type GIS vector data reduction process, including the process such as the identifying of camouflaged target, pseudo- reduction decorateeed.The method of the present invention has higher disguise and not by the advantage of capacity limit, new approaches are provided for the information disguising of vector geographic data, security of the effective guarantee secret point data in data transfer, Communication hiding on the basis of secret information existence is hidden.

Description

A kind of concerning security matters point-like geographic element camouflage deposited based on information point and restoring method

Technical field

The invention belongs to field of geographic information safety, and in particular to a kind of to deposit technology progress vertex type based on information point GIS vector data pretends the method with reduction.

Background technology

The security protection of geography information is related to national security and social benefit, is the current country for being badly in need of solving and society's weight Big needs of problems.On the basis of being hidden to the secret GIS vector data information content, the presence of secret information is further hidden, It is the emphasis of current geographic information security study and application.

At present, the information point technology of depositing is mainly used in image domains, and image point, which is deposited, to be meant that image information being divided into tool There are the n width images of certain visual effect, if it is known that the m (m in image information<N) width subgraph, then the image can obtain extensive Multiple, if image is less than m width, image can not be restored.Use for reference to divide and deposit application of the technology in image domains, technology is deposited by point Vector geographic data information disguising is applied to, complete vector geographic data is stored to multiple points using certain method point Pretended in scattered vector geographic data, make the still meaningful vector geographic data of the data after camouflage.With it is existing Camouflage method is compared, and has both been taken into account the concealed advantage of precision crippled mode, turn avoid scrambled fashion and easily cause attacker Pay attention to and the defects of carrier Stealth Modus is to the high request of capacity.

The content of the invention

It is an object of the invention to：Camouflage is deposited based on information point, proposed a kind of for concerning security matters in GIS point diagram layer datas The camouflage of point-like geographic element and restoring method, can safety of the effective guarantee concerning security matters point data in data transfer, Communication hiding Property.

To achieve these goals, the technical scheme that the present invention takes mainly includes：

A kind of concerning security matters point-like geographic element camouflage deposited based on information point and restoring method, are comprised the following steps that：

(1) vertex type GIS vector data camouflage process

Step 11：A width point figure layer map vector is loaded, and inputs camouflage radius factor c, c ∈ (0,1)；

Step 12：Concerning security matters point set P={ P are selected from original point figure layer data R_i| i=1,2 ..., m }, m is concerning security matters point Number；For each concerning security matters point P in point set P_i, circulate perform step 13 to step 17 successively；

Step 13：It is determined that current concerning security matters point P_iIntend the interior angle of generation camouflage triangle_i1、α_i2、α_i3,

(a) using recurrence growth method current point figure layer data are generated with the triangle net collective T of TIN data formats, from set T Middle traversal includes current concerning security matters point P_iTriangle sets T'={ T_j' | j=1,2 ..., n }, wherein T' ∈ T, n are to include P_i's The number of triangle；

(b) to three interior angles of set T' intermediate cam shapes_i1、α_i2、α_i3Sorted from small to large, and angularly from it is small to Big order is stored in set A1, A2, A3 successively, wherein A1={ A1_j| j=1,2 ..., n }, A2={ A2_j| j=1,2 ..., N }, A3={ A3_j| j=1,2 ..., n }, wherein n is the number of triangle；

(c) three interior angles for pretending triangle can be obtained by set A1, A2, A3 being averaged respectively based on formula (1) α_i1、α_i2、α_i3：

Step 14：It is determined that current concerning security matters point P_iCamouflage radius r_i',

(a) the interior angle ratio for the camouflage triangle for intending generation is calculated according to formula (2), is designated as 1:m:N, wherein n>m>1,

(b) it is respectively P to set three points for intending pretending generation_i1、P_i2、P_i3, the Thiessen polygon of current concerning security matters point is designated as ABCDEF, the camouflage center of circle are o, and maximum camouflage radius is r, P_iWith other original points P_jMinimum range be R, j ≠ i, P_i1P_i2Away from L, P are designated as from maximum_i1Point and P_iMinimum range be designated as l_i；According to the structure of TIN rule, ensuring to intend puppet Decorate on the premise of same triangle, the maximum camouflage radius r of current concerning security matters point is obtained based on formula (3)_i：

(c) the camouflage radius r of current concerning security matters point is calculated according to formula (4)_i', wherein, c is customer parameter：

r_i'=c*r_i,c∈(0,1) (4)

Step 15：Intend the calculating of camouflage point coordinates value, current concerning security matters point P_iCoordinate is designated as (x_i,y_i),

(a) central angle corresponding to each side of camouflage triangle is designated as β successively according to order from small to large₁、β₂、β₃, calculate public Formula is such as shown in (5)：

(b) first puppet is decorateeed：Arbitrarily taken on camouflage circle and a little decorate P as first puppet_i1(x_i1, y_i1), such as formula (6) shown in：

(c) second puppet decorates P_i2(x_i2, y_i2), it is assumed that P_i2With P_i1Central angle corresponding to the chord length of formation is β₁, it is based on P_i1Rotation β in the direction of the clock₁, P_i2Coordinate calculation formula such as shown in (7)：

(d) the 3rd puppet decorates P_i3(x_i3, y_i3)：According to the structure rule of the TIN triangulation networks and the interior angle of camouflage triangle Than for 1：m:Two conditions of n the 3rd puppet of traversal on camouflage circle is decorateeed, and the 3rd camouflage can be found according to counter clockwise direction Point, calculation formula is such as shown in (8)：

Step 16：Three puppets of generation are decorateeed into P_i1、P_i2、P_i3Substitute current concerning security matters point P_iUpdate original point figure layer number According in R；

Step 17：By current concerning security matters point P_iCamouflage radius r_i' it is the key information k generated after enciphering transformation_iIt is added to close In key file KeyFile；

Step 18：Repeat step 13, until realizing the processing of the camouflage to each concerning security matters point key element, preserves camouflage to step 17 Data file afterwards is R'；

(2) it is directed to vertex type GIS vector data reduction process

Step 21：The data file R' after camouflage is opened, opens key file KeyFile；For each concerning security matters point P_i Reduction, circulation successively performs step 22 to step 26：

Step 22：The three of TIN data formats is built according to recurrence growth method to the vector point diagram layer data after current camouflage Angle net collective T；

Step 23：To pretending triangle S_iIdentification, the triangle formed by three points after pretending in triangle net collective T Referred to as pretend triangle；

(a) current i-th group key k in key file KeyFile is read_i, current camouflage triangle is can obtain after decryption reduction Shape S_iCircumradius r_i'；

(b) its circumscribed circle center of circle O is asked to each triangle in set T_iCoordinate (x_i,y_i), remember each Atria summit Coordinate is respectively P_i1(x_i1,y_i1),P_i2(x_i2,y_i2),P_i3(x_i3,y_i3), calculation formula is such as shown in (9)；In the known circumscribed circle center of circle O_iOn the basis of coordinate, circumradius r is calculated according to formula (10)_i：

(c) each triangle in T is traveled through, searches its circumradius r_iWith r_i' equal all triangles, it is designated as collecting Close A={ A_i| i=1,2 ..., n }, wherein n is the triangle number for meeting the condition；

If (d) n is 1, then the triangle is camouflage triangle S_i, three summits of the triangle are that puppet is decorateeed； If n is more than 1, step (e) is transferred to；

(e) triangle S is pretended than further screening according to interior angle_i；To current triangle A_iCirculation performs following grasp successively Make：

(i) current triangle A is calculated respectively_iThree interior angles, and be designated as α respectively according to order from small to large_i1、 α_i2、α_i3；

(ii) ephemeral data R is created_tmp, and data file R' is assigned to data R_tmp；

(iii) by current triangle A_iCorresponding circumscribed circle center of circle O_iInstead of three vertex updates of the triangle to temporarily Data R_tmpIn, regenerate the triangle net collective T' of TIN data formats；

(iV) traversal includes O in set T'_iTriangle sets B={ the B of point_i| i=1,2 ..., m }, m is to include O_iPoint Triangle number；Try to achieve average internal angle value according to the rule of the step 13 for all triangles in set B, and by from It is small to be designated as β successively to big order₁、β₂、β₃；

(V) if interior angle average value β₁、β₂、β₃With α_i1、α_i2、α_i3It is equal respectively, then current triangle A_iFor camouflage three It is angular；If interior angle average value β₁、β₂、β₃With α_i1、α_i2、α_i3, circulate and perform step (i) to (V), meet until traversing The camouflage triangle of condition；

Step 24：Camouflaged target reduces, and travels through obtained camouflage triangle S_iThree summit point coordinates be respectively P_i1、 P_i2、P_i3, original concerning security matters point coordinates P can be calculated by formula (9)_i(x_i,y_i)；

Step 25：By the original concerning security matters point coordinates P after reduction_iSubstitute puppet and decorate P_i1、P_i2、P_i3Update vector data text In part R'；

Step 26：Repeat step 22-25, it is sequentially completed the reduction treatment of each concerning security matters point.

For in the above-mentioned vertex type GIS vector data camouflage method deposited based on information point, being decorateeed calculating second puppet When, in theory based on P_i1Rotation β counterclockwise₁It is equally applicable, but according to the structure rule of the TIN triangulation networks and camouflage Three interior angle ratios of triangle are 1：m:N, travel through less than the 3rd puppet and decorate.Therefore decorate can only be according to clockwise for second puppet Direction calculating.

The present invention deposits technology using information point, is counted by the way that each concerning security matters point element information minute is stored into multiple vectorial geographicals In, reach the effect of camouflage.This method morphologically keeps complete by the triangulation network after making camouflage with the original triangulation network Office's uniformity, reduces the notice of attacker, improves the disguise of camouflage, and can avoid embedding capacity in conventional camouflage The problem of too low, it can meet that the communication of GIS vector data is hidden and safe transmission demand to a certain extent.The method of the present invention With higher disguise and not by the advantage of capacity limit, new approaches are provided for the information disguising of vector geographic data, Security of the effective guarantee secret point data in data transfer, Communication hiding on the basis of hiding secret information existence.

Brief description of the drawings

Fig. 1 is the flow chart of the inventive method, and (a) is camouflage flow chart, and (b) is reduction flow chart；

Fig. 2 is the camouflage scope schematic diagram of the inventive method；

Fig. 3 is that three puppets of the inventive method decorate schematic diagram, and (a) is that second puppet decorates schematic diagram, and (b) is the 3rd Puppet decorates schematic diagram, and (c) is that three puppets decorate schematic diagram.

Fig. 4 is initial data of the present invention and Camouflaged data TIN comparison diagram, and (a) is that the initial data triangulation network shows It is intended to, the point of wherein overstriking is decorateeed for puppet, and (b) is data triangulation network schematic diagram after camouflage, and the wherein point of overstriking is concerning security matters point, Point on circle is decorateeed for three puppets.

Fig. 5 is initial data of the present invention and Camouflaged data comparison diagram, and the point of (a) initial data schematic diagram, wherein overstriking is Original concerning security matters point, (b) are schematic diagram data after camouflage, and the wherein point of overstriking is decorateeed for the puppet of generation.

Embodiment

The present embodiment select shp form vector datas, for the reading of data, camouflage, reduction whole process, further Describe the present invention in detail.It is experimental data that this example, which selects certain simulation concerning security matters point shp data,.

(1) process is pretended

Step 11：Loading simulation concerning security matters point shp data, and c=0.5 is inputted as initial key parameter.

Step 12：Select concerning security matters point set P={ (813.91989999999987, -1033.2102999999997) }.

Step 13：It is determined that current concerning security matters point intends the interior angle of generation camouflage triangle_i1、α_i2、α_i3。

(a) current point figure layer data are generated with triangulation network T, there are 4 triangles to include concerning security matters point in set T；

(b) three interior angles of set T ' intermediate cam shapes are sorted from small to large, and angularly from small to large order according to It is secondary to be stored in A1, A2, A3, wherein A1=24.336498184787121,13.579427824944508, 18.623653496634297,56.170816586114064, A2=55.463665017116085, 19.117895793786708,46.434232690564436,57.765929283815957, A3= {100.1998367980968,147.30267638126884,114.94211381280124,66.063254130069978}；

(c) based on formula (1), to A1, A2, A3, averaging can obtain three interior angle a of camouflage triangle respectively₁= 28.177599023119996 a₂=44.6954306963208, a₃=107.12697028055921.

Step 14：It is determined that current concerning security matters point P_iActual camouflage radius r_i1。

(a) the interior angle ratio for the camouflage triangle for intending generation is calculated according to formula (2), is 1：1.5862043696358856： 3.801848773298977。

(b) as shown in Fig. 2 obtaining the maximum camouflage radius r of current concerning security matters point based on formula (3)₁= 88.307168093798111。

(c) the actual camouflage radius r of current concerning security matters point is calculated according to formula (4)₁₁=44.153584046899056.

Step 15：Intend the calculating of camouflage point coordinates value.

A) (a) according to formula (5) calculate central angle can obtain 28.177599023119996,44.6954306963208, 107.12697028055921。

(b) first puppet is decorateeed：According to formula (6), a point P is arbitrarily taken on camouflage circle₁₁= (825.21531441389641, -990.52596332476355).

(c) second puppet is decorateeed：It can be obtained according to calculation formula (7).P₁₂=(784.64383219137676 ,- 1000.1580559331973)。

(d) the 3rd puppet is decorateeed：P can be obtained according to calculation formula (8)₁₃=(856.72190907596212 ,- 1044.0512871897263)。

Step 16：Three puppets of generation are decorateeed into P₁₁、P₁₂、P₁₃Instead of current concerning security matters point P_iIt is stored in original point figure layer data R In.

Step 17：The result that current puppet is decorateeed after triangle camouflage radius of circle conversion is added to key file KeyFile In.

Step 18：Repeat step 13, until realizing the processing of the camouflage to each concerning security matters point key element, preserves camouflage to step 18 Data file afterwards is R'.

(2) reduction process

Step 21：The vector data R' after camouflage is opened, opens key file KeyFile.

Step 22：TIN data formats are built according to recurrence growth method to the vector point diagram layer data R' after current camouflage Triangulation network T.

Step 23：The identification of camouflaged target,

(a) current key in key file KeyFile is read, the external of current camouflage triangle is can obtain after decryption reduction Radius of circle 44.153584046899056.

(b) its circumscribed circle central coordinate of circle is asked to each triangle in T.

(c) the triangle number that the radius of the T intermediate cam shape circumscribed circles traversed is equal with current key radius is 1, should Triangle is to pretend triangle.

(d) three apex coordinates for reading camouflage triangle are respectively P₀₁(825.21531441389641 ,- 990.52596332476355)、P₀₂(784.64383219137676, -1000.1580559331973), P₀₃ (856.72190907596212, -1044.0512871897263).

Step 24：Camouflaged target is reduced, and P can be obtained according to formula (9)₀Point coordinates (813.91989999999987 ,- 1033.2102999999997)。

Step 25：By the coordinate points P after reduction₀P is decorateeed instead of puppet₀₁、P₀₂、P₀₃It is added in vector data R'.

Step 26：Repeat step 22-25, complete often also original place according to the pseudo- backward for decorateeing generation during camouflage successively Reason.

Claims

1. a kind of concerning security matters point-like geographic element camouflage deposited based on information point and restoring method, it is characterised in that specific steps are such as Under：

(1) vertex type GIS vector data camouflage process

Step 12：Concerning security matters point set P={ P are selected from original point figure layer data R_i| i=1,2 ..., m }, m is the number of concerning security matters point； For each concerning security matters point P in point set P_i, circulate perform step 13 to step 17 successively；

(a) using recurrence growth method current point figure layer data are generated with the triangle net collective T of TIN data formats, from set T time Go through and include current concerning security matters point P_iTriangle sets T'={ T_j' | j=1,2 ..., n }, wherein T' ∈ T, n are to include P_iTriangle The number of shape；

(b) to three interior angles of set T' intermediate cam shapes_i1、α_i2、α_i3Sorted from small to large, and it is angularly suitable from small to large Sequence is stored in set A1, A2, A3 successively, wherein A1={ A1_j| j=1,2 ..., n }, A2={ A2_j| j=1,2 ..., n }, A3 ={ A3_j| j=1,2 ..., n }, wherein n is the number of triangle；

(c) three interior angles for pretending triangle can be obtained by set A1, A2, A3 being averaged respectively based on formula (1)_i1、 α_i2、α_i3：

<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>&alpha;</mi> <mrow> <mi>i</mi> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <munderover> <mo>&Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mi>A</mi> <msub> <mn>1</mn> <mi>j</mi> </msub> </mrow> <mi>n</mi> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>&alpha;</mi> <mrow> <mi>i</mi> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <munderover> <mo>&Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mi>A</mi> <msub> <mn>2</mn> <mi>j</mi> </msub> </mrow> <mi>n</mi> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>&alpha;</mi> <mrow> <mi>i</mi> <mn>3</mn> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <munderover> <mo>&Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mi>A</mi> <msub> <mn>3</mn> <mi>j</mi> </msub> </mrow> <mi>n</mi> </mfrac> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>

(a) the interior angle ratio for the camouflage triangle for intending generation is calculated according to formula (2), is designated as 1:f:G, wherein g>f>1,

<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>f</mi> <mo>=</mo> <mfrac> <msub> <mi>&alpha;</mi> <mrow> <mi>i</mi> <mn>2</mn> </mrow> </msub> <msub> <mi>&alpha;</mi> <mrow> <mi>i</mi> <mn>1</mn> </mrow> </msub> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>g</mi> <mo>=</mo> <mfrac> <msub> <mi>&alpha;</mi> <mrow> <mi>i</mi> <mn>3</mn> </mrow> </msub> <msub> <mi>&alpha;</mi> <mrow> <mi>i</mi> <mn>1</mn> </mrow> </msub> </mfrac> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>

(b) it is respectively P to set three points for intending pretending generation_i1、P_i2、P_i3, the Thiessen polygon of current concerning security matters point is designated as ABCDEF, The camouflage center of circle is o, and maximum camouflage radius is r, P_iWith other original points P_jMinimum range be RR, j ≠ i, P_i1P_i2Distance is maximum Value is designated as L, P_i1Point and P_iMinimum range be designated as L_i；According to the structure of TIN rule, ensuring that intending puppet decorates On the premise of same triangle, the maximum camouflage radius r of current concerning security matters point is obtained based on formula (3)_i：

<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>L</mi> <mo>=</mo> <mn>2</mn> <mo>*</mo> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <mi>&pi;</mi> <mi>g</mi> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <mi>f</mi> <mo>+</mo> <mi>g</mi> </mrow> </mfrac> <mo>)</mo> </mrow> <msub> <mi>r</mi> <mi>i</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>R</mi> <mi>R</mi> <mo>=</mo> <mi>M</mi> <mi>I</mi> <mi>N</mi> <mrow> <mo>(</mo> <mo>|</mo> <mrow> <msub> <mi>P</mi> <mi>j</mi> </msub> <msub> <mi>P</mi> <mi>i</mi> </msub> </mrow> <mo>|</mo> <mo>)</mo> </mrow> <mo>,</mo> <mrow> <mo>(</mo> <mi>j</mi> <mo>&NotEqual;</mo> <mi>i</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>L</mi> <mi>i</mi> </msub> <mo>=</mo> <mi>R</mi> <mi>R</mi> <mo>-</mo> <msub> <mi>r</mi> <mi>i</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>r</mi> <mi>i</mi> </msub> <mo><</mo> <mfrac> <mrow> <mi>R</mi> <mi>R</mi> </mrow> <mrow> <mn>2</mn> <mo>*</mo> <mi>sin</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <mi>&pi;</mi> <mi>g</mi> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <mi>f</mi> <mo>+</mo> <mi>g</mi> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>+</mo> <mn>1</mn> </mrow> </mfrac> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>

(c) the camouflage radius r of current concerning security matters point is calculated according to formula (4)_i', wherein, c is camouflage radius factor：

r_i'=c*r_i,c∈(0,1) (4)

(a) central angle corresponding to each side of camouflage triangle is designated as β successively according to order from small to large₁、β₂、β₃, calculation formula is such as (5) shown in：

(b) first puppet is decorateeed：Arbitrarily taken on camouflage circle and a little decorate P as first puppet_i1(x_i1, y_i1), such as formula (6) It is shown：

<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mi>r</mi> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mi>o</mi> <mi>m</mi> <mo>&lsqb;</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>-</mo> <msup> <msub> <mi>r</mi> <mi>i</mi> </msub> <mo>&prime;</mo> </msup> <mo>,</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>+</mo> <msup> <msub> <mi>r</mi> <mi>i</mi> </msub> <mo>&prime;</mo> </msup> <mo>&rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>&PlusMinus;</mo> <msqrt> <mrow> <msup> <msub> <mi>r</mi> <mi>i</mi> </msub> <mrow> <mo>&prime;</mo> <mn>2</mn> </mrow> </msup> <mo>-</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>

(c) second puppet decorates P_i2(x_i2, y_i2), it is assumed that P_i2With P_i1Central angle corresponding to the chord length of formation is β₁, based on P_i1By suitable Clockwise rotation β₁, P_i2Coordinate calculation formula such as shown in (7)：

(d) the 3rd puppet decorates P_i3(x_i3, y_i3)：It is according to the structure rule of the TIN triangulation networks and the interior angle ratio for pretending triangle 1：f:Two conditions of g the 3rd puppet of traversal on camouflage circle is decorateeed, and can find the 3rd puppet according to counter clockwise direction decorates, and counts Formula is calculated such as shown in (8)：

Step 16：Three puppets of generation are decorateeed into P_i1、P_i2、P_i3Substitute current concerning security matters point P_iUpdate in original point figure layer data R；

Step 17：By current concerning security matters point P_iCamouflage radius r_i' it is the key information k generated after enciphering transformation_iIt is added to key text In part KeyFile；

Step 18：Repeat step 13, until realizing the processing of the camouflage to each concerning security matters point key element, is preserved after pretending to step 17 Data file is R'；

(2) it is directed to vertex type GIS vector data reduction process

Step 21：The data file R' after camouflage is opened, opens key file KeyFile；For each concerning security matters point P_iAlso Original, successively circulation perform step 22 to step 26：

Step 22：The triangulation network of TIN data formats is built according to recurrence growth method to the vector point diagram layer data after current camouflage Set T；

Step 23：To pretending triangle S_iIdentification, the triangle formed by three points after pretending in triangle net collective T is referred to as Pretend triangle；

(a) current i-th group key k in key file KeyFile is read_i, current camouflage triangle S is can obtain after decryption reduction_i's Circumradius r_i'；

(b) its circumscribed circle center of circle O is asked to each triangle in set T_iCoordinate (x_i,y_i), remember each Atria apex coordinate Respectively P_i1(x_i1,y_i1),P_i2(x_i2,y_i2),P_i3(x_i3,y_i3), calculation formula is such as shown in (9)；In known circumscribed circle center of circle O_iSit On the basis of target, circumradius r is calculated according to formula (10)_i：

(c) each triangle in T is traveled through, searches its circumradius r_iWith r_i' equal all triangles, it is designated as set A= {A_i| i=1,2 ..., n }, wherein n is the triangle number for meeting the condition；

If (d) n is 1, then the triangle is camouflage triangle S_i, three summits of the triangle are that puppet is decorateeed；If n More than 1, then step (e) is transferred to；

(e) triangle S is pretended than further screening according to interior angle_i；

Step 24：Camouflaged target reduces, and travels through obtained camouflage triangle S_iThree summit point coordinates be respectively P_i1、P_i2、P_i3, Original concerning security matters point coordinates P can be calculated by formula (9)_i(x_i,y_i)；

Step 25：By the original concerning security matters point coordinates P after reduction_iSubstitute puppet and decorate P_i1、P_i2、P_i3Update vector data file R' In；

2. a kind of concerning security matters point-like geographic element camouflage deposited based on information point according to claim 1 and restoring method, its It is characterised by, in step 23 (e), triangle S is pretended in further screening_iDetailed process it is as follows：To current triangle A_iFollow successively Ring performs following operate：

(i) current triangle A is calculated respectively_iThree interior angles, and be designated as α respectively according to order from small to large_i1、α_i2、α_i3；

(iii) by current triangle A_iCorresponding circumscribed circle center of circle O_iInstead of three vertex updates of the triangle to ephemeral data R_tmpIn, regenerate the triangle net collective T' of TIN data formats；

(iV) traversal includes O in set T'_iTriangle sets B={ the B of point_i| i=1,2 ..., m }, m is to include O_iThe three of point Angular number；Try to achieve average internal angle value according to the rule of the step 13 for all triangles in set B, and by from it is small to Big order is designated as β successively₁、β₂、β₃；

(V) if interior angle average value β₁、β₂、β₃With α_i1、α_i2、α_i3It is equal respectively, then current triangle A_iTo pretend triangle； If interior angle average value β₁、β₂、β₃With α_i1、α_i2、α_i3, circulation performs step (i) to (V), eligible until traversing Camouflage triangle.