CN103927783A - Graph cut method for contrasting filled and excavated space by using three-dimensional triangulation network - Google Patents
Graph cut method for contrasting filled and excavated space by using three-dimensional triangulation network Download PDFInfo
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Abstract
The invention relates to a graph cut method for contrasting filled and excavated space by using a three-dimensional triangulation network. According to the method, the three-dimensional triangulation network is directly constructed on the basis of the graph cut method, and network construction problems are regarded as mark optimization problems. Firstly, initial landform splashes and actual landform splashes are obtained and combined, and then a normal vector of each splash is estimated; tetrahedrons are constructed through the combined splashes by the adoption of the point-by-point insertion algorithm, the space is decomposed, and the tetrahedrons contain the triangulation network which users want to obtain; according to intersecting information of the normal vectors of the splashes and the tetrahedrons, and area information of each triangular surface of the tetrahedrons, the weight of an s-t graph is added; final surfaces are obtained by the minimum cut-maximum flow algorithm, the filled and excavated space is obtained, and the quantity of filled and excavated earth work is obtained by adding up the volumes of the tetrahedrons. According to the graph cut method, projection on a two-dimensional plane is not needed, and the defects caused when the triangulation network is constructed with a two-dimensional projection method are overcome; the quantity of earth work is calculated through the tetrahedrons, so that precision is higher.
Description
Technical field
The invention belongs to field of three-dimension modeling, particularly relate to a kind of THREE DIMENSIONAL TRIANGULATION NET and build the figure segmentation method of filling out between hollowing out.
Background technology
In Geotechnical Engineering, relate generally to fill out hollow out between the cubic metre of earth and stone measurement.The measurement of the cubic metre of earth and stone, calculating are the important evidence of quantities budget in engineering construction, establishment job design and reasonable arrangement working-yard.Existing cubic metre of earth and stone computing method have the method for section, square grid method and DTM method.
Method of section computational accuracy is relevant with the length of section spacing, and spacing is less, and precision is just higher; When the method for section is calculated earthwork, will note choosing of transversal section, choosing of section has considerable influence to precision; But this method calculated amount is large, especially more obvious in the situation that the larger accuracy requirement of scope is high.
The precision of square grid method calculating earthwork depends on the size of image data density, and simultaneously relevant with the size of square grid, square grid is less, and precision is higher; Some topographic relief minor grades change the suitable square grid method of using in mild place.
DTM method can adapt to complicated irregular terrain profiles well, thereby can express better real terrain surface specifications, adopts sciagraphy to build respectively initial landform TIN and real model TIN; With triangular prism method or Grid Method fill in border, excavation side design a model and real model between difference space, calculate afterwards earthwork.This method computational accuracy is high, but also has some problems: while building TIN with sciagraphy, the TIN that different projecting planes builds there are differences (even wrong TIN), and precision is had to considerable influence; Sciagraphy can not build more complicated real model (existing overlapping on projecting plane); During by triangular prism method volume calculated, can decompose triangular facet, precision is had to considerable influence.
Summary of the invention
Technical matters to be solved by this invention is to provide a kind of THREE DIMENSIONAL TRIANGULATION NET to build the figure segmentation method of filling out between hollowing out.By the method, can build three-dimensional model more accurately to complicated Geotechnical Engineering, to obtain more high-precision quantity of earth work.
In order to achieve the above object, the present invention is based on figure and cut method, network forming problem is considered as optimizing mark problem.First obtain the loose point of initial landform and the loose point of real landform, after being merged, estimate each point normal vector; Loose point after being combined adopts Incremental insertion algorithm structure tetrahedron to decompose space, and we want the triangulation network obtaining to be included in tetrahedron; According to each loose some normal vector and each triangular facet area information in tetrahedral crossing information and tetrahedron, add weights in s-t figure; With finally surface of minimal cut-max-flow Algorithm for Solving, between obtaining filling out and hollowing out, the each tetrahedron volume in space is added and obtains filling out the quantity of earth work digging.
Particularly, the inventive method comprises the steps:
(1) first obtain the loose point of real landform of filling out between hollowing out to be measured, obtain the loose point of initial landform according to reality measurement loose some border cutting the subdivision initial landform triangulation network;
(2) reality is measured after the loose point of loose point and initial landform merges and estimated each loose some normal vector;
(3) the loose point of the measurement after being combined adopts an Incremental insertion algorithm to build tetrahedron to decompose between hollowing out filling out excavation and filling;
(4) build s-t figure, comprise normal vector energy term and triangle area energy term, according to each loose some normal vector and each triangular facet area information in tetrahedral crossing information and tetrahedron, add weights in s-t figure;
(5), with finally surface of minimal cut-max-flow Algorithm for Solving, between obtaining filling out and hollowing out, the each tetrahedron volume in space is added and obtains filling out the quantity of earth work digging.
The method that the present invention builds energy function is: carry out Delaunay tetrahedron subdivision to filling out between hollowing out, using tetrahedral Delaunay dual graph (being Voronoi figure), as node and the directed edge of s-t figure, s-t figure comprises normal vector energy term and triangle area energy term.
Fill out and hollow out surface energy function E (S)=λ
normale
normal(S)+λ
areae
area(S);
S digs spatial surface for filling out;
E
normal(S) be the energy term of normal vector;
E
area(S) be the energy term of triangle area;
λ
normalfor normal vector energy term weight; λ
areafor area item energy term weight.
The present invention proposes to utilize normal vector and tetrahedral crossing information to add the weights of s-t figure.Utilize tetrahedron top P and shift value σ to determine tetrahedron, add its t weights; The triangular facet crossing with normal vector corresponding the directed edge in s-t, add limit weights; Last tetrahedron that normal vector passes adds s weights.
The present invention proposes with after the node in max-flow min-cut algorithm again mark s-t figure, will is not t by the vertex ticks of s and t mark, retains between tetrahedron corresponding to t node be and fill out and hollow out.The inventive method builds the sealing scene Direct Three-dimensional triangulation network, without projecting to two dimensional surface, has avoided two-dimensional projection's method to build the deficiency of the triangulation network; Between direct construction goes out to fill out and hollows out, can show more intuitively and fill out the spatial dimension of digging; Calculate earthwork by tetrahedron, avoided the decomposition of DTM method intermediate cam shape, precision is higher.
Brief description of the drawings
Fig. 1 is that reality is measured scatter diagram.1 is Measured Boundary point, and 2 is the loose point in surface, and 3 is the loose point of terrain feature.
Fig. 2 is for encrypting the loose point of terrain feature schematic diagram.1 for measuring loose point, 2 points for encryption, and 3 is the loose point of terrain feature before encrypting, 4 is the loose point of terrain feature after encrypting.
Fig. 3 is for to cut out and to encrypt original loose some schematic diagram according to Measured Boundary.1 is initial landform figure, and 2 is Measured Boundary, and 3 is the loose point of initial landform.
Fig. 4, for merging after the loose point of reality and the loose point of initial landform, estimates loose some normal vector schematic diagram.1 is the loose point of initial landform, and 2 is that reality is measured loose point, and 3 is loose some normal vector.
Fig. 5 is that the THREE DIMENSIONAL TRIANGULATION NET based on s-t figure is rebuild schematic diagram.1 is the triangular facet being passed by normal vector, and 2 is Voronoi polyhedron, and 3 is Delaunay tetrahedron, 4 THREE DIMENSIONAL TRIANGULATION NET surfaces for rebuilding, 5 is normal vector terminal, 6 normal vectors that are tetrahedron top, 7 is tetrahedron top, and 8 is tetrahedron top along the point after normal vector translation in the other direction σ distance.
Fig. 6 hollows out a THREE DIMENSIONAL TRIANGULATION NET reconstruction process flow diagram for filling out.
Fig. 7 is that filling out of building hollows out a schematic diagram.
Embodiment
The present invention cuts the THREE DIMENSIONAL TRIANGULATION NET network construction method of method based on Delaunay tetrahedron and figure, and techniqueflow as shown in Figure 6.Utilize the loose point of the loose point of initial landform and real landform to carrying out the decomposition of Delaunay tetrahedron in space, summit and the directed edge correspondence of the tetrahedral dual graph of Delaunay (being Voronoi figure) summit and the directed edge in s-t figure, vertex representation Delaunay tetrahedron, directed edge represents to be with directive triangular facet.The computational problem of filling out between hollowing out is considered as energy function minimization problem by we, energy function comprises normal vector energy term and triangle area energy term, add the weights of s-t figure according to normal vector information and triangle area information, solution procedure is exactly to find the minimal cut of s-t figure, and the mark tetrahedron of global optimization is s or t.
Based on above principle, describe embodiments of the present invention in detail with reference to accompanying drawing.
1. obtain loose some data
1.1 measure the reality surface in certain region, obtain reality and measure loose point and the loose point of Measured Boundary, if the side slope after excavation exists terrain feature line, obtain the loose point of measurement of terrain feature, as shown in Figure 1.The object of obtaining the loose point of terrain feature measurement is to express more accurately three-dimensional model, fills out more accurately excavation quantity thereby obtain.
1.2 encrypt landform pattern measurement point, and the mean distance that makes adjacent landform pattern measurement point is 1/3rd of real surface measurement point mean distance, and object is to recover more accurately the shape of landform, as shown in Figure 2.
The 1.3 subdivision initial landform triangulation networks, object is that less triangle can approach Measured Boundary more accurately, and Measured Boundary and the initial landform triangulation network are projected to XY plane, and the triangulation network summit falling in border is taken out, measure loose point as initial landform, as shown in Figure 3.Subdivision algorithm is to cut apart each leg-of-mutton limit, get the mid point of triangle edges as cut-point, and to find triangle t1 and the t2 at this place, limit, the coordinate of cut-point be triangle t1 and the t2 mean value on 4 summits altogether, such triangle is split into four less triangles.
1.4 reality is measured to loose point and initial landform and is measured loose point and merge after the each loose some normal vector of estimation, as shown in Figure 4.For this reason, for each some p in a cloud, obtaining k the consecutive point the most close with it, is then that these points calculate a part plan P by least square.This plane can be expressed as follows:
The normal vector that wherein n is plane P, d is the distance that P arrives true origin.
2. build Delaunay tetrahedron
Building the tetrahedral object of Delaunay is that space is decomposed, and takes Incremental insertion algorithm to build Delaunay tetrahedron loose initial landform measurement point and the loose point of reality measurement.The summit of the tetrahedral dual graph of Delaunay (being Voronoi figure) and directed edge correspondence summit and the directed edge of s-t figure.The vertex representation tetrahedron of s-t figure, directed edge represents to be with directive triangular facet.
3. add the weights of s-t
3.1 add weights according to normal vector.S-t figure principle based on resurfacing is illustrated in Fig. 5, and solid black round dot P represents tetrahedron top, and black dotted lines L is the normal vector n of solid black round dot P, and black soft dot P' is tetrahedron top along the point after the mobile σ distance of opposite direction of normal vector.The tetrahedron T' at P' point place, location, is connected it and gives its t weights with the t end points in s-t figure, according to said method add all t weights; Find the triangular facet T being passed by normal vector from P point along normal vector n
iuntil the tetrahedron passing through is unlimited tetrahedron or is t tetrahedron, interpolation T
ithe weights of the directed edge of corresponding s-t figure; Last tetrahedron T that normal vector n passes through is connected with the s in s-t figure, and gives s weights, and method is added all limit weights and s weights successively.
3.2 add weights according to triangle area.Calculate each leg-of-mutton area in Delaunay tetrahedron, set it as weights and join in directed edge corresponding in s-t figure, calculate the mean value of the each triangle area of Delaunay tetrahedron simultaneously, set it as weights and join in all t weights.
3.3 reasonable distribution λ
normaland λ
areaweight, so far s-t figure has built.
4. between solving and filling out and hollow out
Utilize the max-flow min-cut algorithm state that each summit is connected with t with s in mark s-t figure again, after mark again, the summit not being connected with t with s is defined as t summit, and in s-t figure, each summit is divided into two classes like this: s summit and t summit.We retain Delaunay tetrahedron corresponding to t summit, between these tetrahedrons that are retained are and fill out and hollow out, as shown in Figure 7.Filling out earth excavation amount V is exactly each tetrahedron volume sum, being calculated as follows of earth volume:
I for fill out hollow out between tetrahedral set;
V
iit is a tetrahedral volume;
S
ifor tetrahedron base area;
H
ifor tetrahedral height.
Claims (4)
1. THREE DIMENSIONAL TRIANGULATION NET builds a figure segmentation method of filling out between hollowing out, and it is characterized in that, comprises the steps:
(1) first obtain the loose point of real landform of filling out between hollowing out to be measured, obtain the loose point of initial landform according to reality measurement loose some border cutting the subdivision initial landform triangulation network;
(2) reality is measured after the loose point of loose point and initial landform merges and estimated each loose some normal vector;
(3) the loose point of the measurement after being combined adopts an Incremental insertion algorithm to build tetrahedron to decompose between hollowing out filling out excavation and filling;
(4) build s-t figure, comprise normal vector energy term and triangle area energy term, according to each loose some normal vector and each triangular facet area information in tetrahedral crossing information and tetrahedron, add weights in s-t figure;
(5), with finally surface of minimal cut-max-flow Algorithm for Solving, between obtaining filling out and hollowing out, the each tetrahedron volume in space is added and obtains filling out the quantity of earth work digging.
2. the method for claim 1, it is characterized in that, the method that builds energy function is: Delaunay tetrahedron subdivision is carried out in space, and node and directed edge using tetrahedral Delaunay dual graph as s-t figure, s-t figure comprises normal vector energy term and triangle area energy term; Fill out and hollow out surface energy function E (S)=λ
normale
normal(S)+λ
areae
area(S), S digs spatial surface for filling out; E
normal(S) be the energy term of normal vector; E
area(S) be the energy term of triangle area; λ
normalfor normal vector energy term weight; λ
areafor area item energy term weight.
3. the method as described in claim 1 and 2, is characterized in that, utilizes normal vector and tetrahedral crossing information to add the weights of s-t figure, utilizes tetrahedron top P and shift value σ to determine tetrahedron, adds its t weights; The triangular facet crossing with normal vector corresponding the directed edge in s-t, add limit weights; Last tetrahedron that normal vector passes adds s weights.
4. method as claimed in claim 1 or 2, is characterized in that, with after the node in max-flow min-cut algorithm again mark s-t figure, will is not t by the vertex ticks of s and t mark, retains between tetrahedron corresponding to t node be and fill out and hollow out.
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CN109191581A (en) * | 2018-08-29 | 2019-01-11 | 李东帅 | A kind of Earth Volume of Road Engineering amount high-resolution method based on BIM technology |
CN109191581B (en) * | 2018-08-29 | 2023-06-30 | 李东帅 | Road engineering earthwork high-precision calculation method based on BIM technology |
CN109584365A (en) * | 2018-11-29 | 2019-04-05 | 中国科学院地理科学与资源研究所 | A kind of Voronoi diagram geological layering model building method calculated with Yu Haiyang's land reclamation engineering earth volume cost |
CN109584365B (en) * | 2018-11-29 | 2022-05-10 | 中国科学院地理科学与资源研究所 | Voronoi diagram geological layered model construction method for earth volume manufacturing cost accounting of ocean reclamation land-making engineering |
US11125914B2 (en) * | 2019-06-14 | 2021-09-21 | Doosan Infracore Co., Ltd. | Three-dimensional ground model generation and automated earthwork target model generation system based on parameter input |
CN113870267A (en) * | 2021-12-03 | 2021-12-31 | 深圳市奥盛通科技有限公司 | Defect detection method, defect detection device, computer equipment and readable storage medium |
CN113870267B (en) * | 2021-12-03 | 2022-03-22 | 深圳市奥盛通科技有限公司 | Defect detection method, defect detection device, computer equipment and readable storage medium |
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