CN114332291A - Oblique photography model building outer contour rule extraction method - Google Patents

Oblique photography model building outer contour rule extraction method Download PDF

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CN114332291A
CN114332291A CN202111573449.3A CN202111573449A CN114332291A CN 114332291 A CN114332291 A CN 114332291A CN 202111573449 A CN202111573449 A CN 202111573449A CN 114332291 A CN114332291 A CN 114332291A
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points
line segments
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向瀚宇
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Wuhai Dashi Intelligence Technology Co ltd
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Wuhai Dashi Intelligence Technology Co ltd
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Abstract

The invention provides a method for extracting an outline rule of an oblique photography model building, which comprises the following steps: s1: and (3) performing straight line fitting on each point on the existing building contour line in the neighborhood of the set range, S2: re-evaluating the classified points belonging to certain line segments, S3: combining two line segments with smaller distance and included angle, weighting each line segment, and setting the point of the line segment with low weight to be competitive with the line segment with high weight; s4: calculating the parallel and vertical relation between the line segments, and finely adjusting the parameters of the line segments to meet the requirements of parallel and vertical; s5: and establishing a Delaunay triangulation network and reconstructing the adjacency relation among the line segments. The method lays a foundation for reconstructing the three-dimensional model monomer. On one hand, the three-dimensional model monomer generated based on the regular contour line has a more excellent visual effect; on the other hand, the single body can be suitable for various spatial analyses, and is helpful for getting through data obstacles between oblique photogrammetry technologies and smart cities.

Description

Oblique photography model building outer contour rule extraction method
Technical Field
The invention relates to a technology of building extraction, boundary line regularization, three-dimensional modeling and live-action three-dimension, in particular to a method for regenerating a three-dimensional building model boundary based on regularization.
Background
With the popularization of unmanned aerial vehicles, oblique photogrammetry technology is widely applied in the surveying and mapping industry. According to the technology, a high-precision three-dimensional model is reconstructed by using structures of Motion (SFM) and Multi-Stereo (MVS) methods through a plurality of unmanned aerial vehicle aerial images, but the generated triangular mesh model has large number of vertexes and high noise. On the other hand, regular building structure extraction can greatly reduce data volume, and is convenient for management, analysis and visualization.
The precision of a triangulation network model generated by the direct matching of oblique photography data is lower than that of point cloud data acquired by directly adopting laser, and the traditional algorithm for extracting the building structure by using laser scanning has a poor effect on processing the oblique photography model.
Therefore, most of the existing production building simplex models based on the oblique photography three-dimensional model adopt a manual modeling mode, namely, a physical boundary is manually acquired and edited, and geometric modeling, texture mapping and modification are carried out on the basis of the original oblique photography three-dimensional model. On the one hand, this modeling approach is inefficient; on the other hand, errors of manual modeling have uncertainty, and the data precision greatly influences the application range of the data.
The generation of the three-dimensional model monomer is based on the geographic entity in a two-dimensional form, and in the three-dimensional building model, the building outline is the geographic entity in a corresponding two-dimensional form. The unmanned aerial vehicle's shooting is accomplished from top to bottom, because the existence that shelters from each other, and the visibility of building top is higher than the bottom. Therefore, the top contour of the oblique photography three-dimensional model is accurate. However, the contour lines at any elevation have the following problems:
(1) whether the model is the top or the bottom, the oblique photography three-dimensional model always has errors, so that the accuracy of a contour line is influenced, but the direct correction on the model is obviously unrealistic;
(2) buildings should have a significant parallel-to-vertical relationship, and the contour generation should take this element into account;
(3) the contour lines are a series of indiscriminate scattered points essentially, and the regularization is to split the contour lines into single line segments which correspond to the vertical faces in the three-dimensional model monomer one by one.
Disclosure of Invention
The invention provides a method for extracting the rules of the outline of the building outside an oblique photography model, which overcomes the problems or at least partially solves the problems, wherein the outline of dense points of the building is used as input, and line segments are extracted from the outline of the dense points; and all line segments are regularized by considering the parallel and vertical relations. And finally, establishing a Delaunay triangulation network which takes the line segment end points as key nodes and the line segment boundaries as constraints, and reconstructing the adjacency relation among the line segments so as to obtain a closed and regular contour line. The method lays a foundation for reconstructing the three-dimensional model monomer. On one hand, the three-dimensional model monomer generated based on the regular contour line has a more excellent visual effect; on the other hand, the single body can be suitable for various spatial analyses, and is helpful for getting through data obstacles between oblique photogrammetry technologies and smart cities.
According to a first aspect of the present invention, there is provided a method for extracting rules of an outline of a building in an oblique photography model, comprising the steps of:
s1: performing straight line fitting on each point on the existing building contour line in the neighborhood of a set range to obtain a plurality of groups of straight line parameters; determining a possible straight line through voting, and determining points belonging to the same straight line; judging the continuity of the points on the same straight line, further dividing the straight line into a plurality of line segments, determining which points form certain line segments, and classifying the points;
s2: re-evaluating the classified points belonging to certain line segments, further adjusting the belonging relation of the classified points, and re-fitting the line segments; judging whether the unclassified point which belongs to the line segment can not be determined; if some points do not belong to any line segment, clustering the points according to positions, and fitting a new line segment;
s3: combining two line segments with smaller distance and included angle, weighting each line segment, and setting the point of the line segment with low weight to be competitive with the line segment with high weight;
s4: calculating the parallel and vertical relation between the line segments, and finely adjusting the parameters of the line segments to meet the requirements of parallel and vertical;
s5: the Delaunay triangulation is established, reconstructing the adjacency between the segments such that the outline of the polygon inside all buildings is a closed and regular building outline.
On the basis of the technical scheme, the invention can be improved as follows.
Optionally, the step S1 includes: performing least square fitting on each point on the existing building contour line in a neighborhood in a certain range, converting the point into linear parameters rho and theta under polar coordinates, voting theta, recalculating rho through new theta, voting rho, dividing the voting into a plurality of intervals according to the value range of rho or theta, wherein each point belongs to a certain interval, the interval with higher score is subjected to subsequent processing, a voting algorithm obtains a group of straight lines, a threshold is given to judge whether the straight lines are continuous at each point, and the straight lines are divided into a plurality of line segments.
Optionally, the step S2 includes: for classified points belonging to some line segments, calculating the distances from the points to the line segments to which the points belong and the adjacent line segments, and if the distances from the points to the adjacent line segments are smaller, changing the belonging relation of the points; for an unclassified point which cannot be determined to which line segment, calculating the distance from the point to an adjacent line segment, and if the distance is smaller than a given threshold value, changing the relationship of the point; a new line segment is re-fitted to a few points that still do not belong to any line segment.
Optionally, in step S3, if the distance and the included angle between the two line segments are smaller than the given threshold, the two line segments are considered to be combinable, the points of the two line segments are put together, and a new line segment is fit again.
Optionally, the stability of the line segment is measured by the length of the line segment, the parallel and vertical relation between the line segments, the fitting accuracy of the line segment, and the number of points of the line segment, and for a point of a line segment with low weight, if a line segment with better weight exists in an adjacent line segment, the point is competed by a line segment with high weight.
Optionally, the step S5 includes:
s51: establishing a Delaunay triangulation network by taking the end points of all the line segments as vertexes, calculating the lengths of all the edges in the Delaunay triangulation network, calculating the number of digits in the Delaunay triangulation network, and deleting all the edges with the lengths smaller than the median;
s52: if the end points of the two line segments are connected by the edge of the triangulation network, the adjacency relation is considered to exist, if the two line segments are parallel, a vertical line segment is generated to connect the parallel line segments, the newly generated line segment can be used for filling the missing line segment in the line segment extraction process, and if the two line segments are not parallel, the line segments are extended to be intersected, so that a closed line segment can be generated;
s53: further splitting the line segments into sub-line segments, namely, each line segment does not have end points of other line segments, searching a closed graph from the sub-line segments to obtain a plurality of sub-polygons and a large polygon containing all the sub-polygons;
s54: calculating the proportion of points inside the building in the internal points of each sub-polygon, and if the proportion is greater than a given threshold value, considering the multi-polygon as the polygon inside the building;
if the area or boundary length of some polygons is small, there may be no points inside them, or there are few points, it is necessary to determine by the length of the common boundary between them and the adjacent polygons, merge all polygons inside the building, calculate their outline to obtain a closed and regular building outline.
The method for extracting the outer contour rule of the oblique photography model building, provided by the invention, has the following beneficial effects:
(1) the method and the device have the advantages that the straight line which possibly exists is determined through the voting of the points, the initial line segment is determined, the influence of wrong connection and noise of the line segment is effectively avoided through a series of post-processing, and the extraction of the boundary line segment of the building can be completed in a short time.
(2) Any two line segments may have a parallel or perpendicular relationship, and it is difficult to directly screen unreliable relationships with a fixed threshold value. The main direction of the building is calculated firstly, and the parameters of the line segments are adjusted based on the main direction, so that the regularization efficiency is improved.
(3) The adjacency relation between the line segments is found through the Delaunay triangulation network, and the threshold value does not need to be set manually. Even if the line segments are missing, a closed building contour can be obtained.
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Fig. 1 is a schematic flow chart of a method for extracting rules of an outline of a building in an oblique photography model according to an embodiment of the present invention.
Detailed Description
The following detailed description of embodiments of the present invention is provided in connection with the accompanying drawings and examples. The following examples are intended to illustrate the invention but are not intended to limit the scope of the invention.
As shown in fig. 1, fig. 1 is a schematic flow chart of a method for extracting rules of an outline of a building in an oblique photography model according to an embodiment of the present invention, where the method includes the following steps:
s1: performing straight line fitting on each point on the existing building contour line in the neighborhood of a set range to obtain a plurality of groups of straight line parameters; determining a possible straight line through voting, and determining points belonging to the same straight line; judging the continuity of the points on the same straight line, further dividing the straight line into a plurality of line segments, determining which points form certain line segments, and classifying the points;
specifically, least square fitting is carried out on each point on the existing building contour line in a neighborhood of a certain range, the point is converted into linear parameters rho and theta under polar coordinates, the theta is voted first, the rho is recalculated through a new theta, then the rho is voted, the voting is divided into a plurality of intervals according to the value range of the rho or the theta, each point belongs to a certain interval, the interval with a higher score is subjected to subsequent processing, a voting algorithm obtains a group of straight lines, a threshold is given to judge whether the straight lines are continuous at each point, and the straight lines are divided into a plurality of line segments.
S2: re-evaluating the classified points belonging to certain line segments, further adjusting the belonging relation of the classified points, and re-fitting the line segments; judging whether the unclassified point which belongs to the line segment can not be determined; if some points do not belong to any line segment, clustering the points according to positions, and fitting a new line segment;
specifically, for classified points belonging to some line segments, calculating the distance from the point to the line segment to which the point belongs and the adjacent line segment, and if the distance from the point to the adjacent line segment is smaller, changing the relationship of the point to which the point belongs; for an unclassified point which cannot be determined to which line segment, calculating the distance from the point to an adjacent line segment, and if the distance is smaller than a given threshold value, changing the relationship of the point; a new line segment is re-fitted to a few points that still do not belong to any line segment.
S3: combining two line segments with smaller distance and included angle, weighting each line segment, and setting the point of the line segment with low weight to be competitive with the line segment with high weight;
specifically, if the distance and the included angle between the two line segments are smaller than a given threshold, the two line segments are considered to be combinable, the points of the two line segments are put together, and a new line segment is fit again.
S4: calculating the parallel and vertical relation between the line segments, and finely adjusting the parameters of the line segments to meet the requirements of parallel and vertical;
the stability of the line segment is measured by the length of the line segment, the parallel and vertical relation between the line segments, the fitting accuracy of the line segment and the number of points of the line segment, and for the points of the line segment with low weight, if the line segment with better weight exists in the adjacent line segment, the points are competed by the line segment with high weight.
S5: establishing a Delaunay triangulation network, and reconstructing the adjacency relation among the line segments to ensure that the outline of the polygon in all buildings is a closed and regular building contour line;
the method comprises the following steps:
s51: establishing a Delaunay triangulation network by taking the end points of all the line segments as vertexes, calculating the lengths of all the edges in the Delaunay triangulation network, calculating the number of digits in the Delaunay triangulation network, and deleting all the edges with the lengths smaller than the median;
s52: if the end points of the two line segments are connected by the edge of the triangulation network, the adjacency relation is considered to exist, if the two line segments are parallel, a vertical line segment is generated to connect the parallel line segments, the newly generated line segment can be used for filling the missing line segment in the line segment extraction process, and if the two line segments are not parallel, the line segments are extended to be intersected, so that a closed line segment can be generated;
s53: further splitting the line segments into sub-line segments, namely, each line segment does not have end points of other line segments, searching a closed graph from the sub-line segments to obtain a plurality of sub-polygons and a large polygon containing all the sub-polygons;
s54: calculating the proportion of points inside the building in the internal points of each sub-polygon, and if the proportion is greater than a given threshold value, considering the multi-polygon as the polygon inside the building;
if the area or boundary length of some polygons is small, there may be no points inside them, or there are few points, it is necessary to determine by the length of the common boundary between them and the adjacent polygons, merge all polygons inside the building, calculate their outline to obtain a closed and regular building outline.
It can be understood that, in the present embodiment, a series of building boundary line segments are obtained by a dense point line extraction algorithm with a certain topological relation, with the existing dense point contour line of the building as an input. And adjusting the angle of the initial boundary line segment according to the internal parallel and vertical relation of the building, establishing the adjacent relation between the line segments, and eliminating uncertain line segments through strategies such as competitive combination and the like, thereby obtaining a closed and regular building contour line.
In one possible implementation, the implementation can be divided into the following three processes:
and (3) line segment extraction process:
(1) and performing least square fitting on each point on the existing building contour line in a neighborhood in a certain range, and converting the least square fitting into linear parameters rho and theta under polar coordinates. Voting theta, recalculating rho through the new theta, and voting rho. Voting is to divide the range into a plurality of intervals according to the value range of rho or theta, each point belongs to a certain interval, and the interval with higher score is subjected to subsequent processing. A group of straight lines can be obtained through the voting algorithm, whether the straight lines are continuous at each point or not is judged by the given threshold value, and the straight lines can be divided into a plurality of line segments.
(2) For classified points belonging to some line segments, the distances from the point to the line segment to which the point belongs and the adjacent line segments are calculated, and if the distance from the point to the adjacent line segments is smaller, the relationship of the point to which the point belongs is changed. And for the unclassified point which cannot be determined to belong to which line segment, calculating the distance from the point to the adjacent line segment, and if the distance is smaller than a given threshold value, changing the relationship of the point. For a small number of points that still do not belong to any line segment, these points either belong to very fine line segments. For these point clusters, a new line segment can be re-fitted for each class.
(3) And if the distance and the included angle of the two line segments are smaller than the given threshold value, the two line segments are considered to be combinable. The points of the two line segments are put together and a new line segment is re-fitted.
(4) With four parameters: the stability of the line segments is measured by the length of the line segments, the parallel and vertical relation among the line segments, the fitting accuracy of the line segments and the number of points of the line segments. For a point of a low-weight line segment, if there is a better-weighted line segment in its neighboring line segments, the point is contended for the past by a high-weight line segment.
And (3) regularization process:
(1) the angles of most of the line segments are parallel or perpendicular to the main direction of the building, in other words, the optimal main direction can be calculated by knowing the angles of all the line segments. The degree of stability of the line segments should also be taken into account when calculating the main direction, i.e. more stable line segments should make a greater contribution to the determination of the main direction.
(2) After the main direction is calculated, a threshold value is given to judge whether each line segment is parallel or vertical to the main direction. And after the line segment related to the main direction is screened out, the main direction is recalculated, and then the parameters of the line segment are adjusted.
And (3) closing process:
(1) and establishing the Delaunay triangulation network by taking the end points of all the line segments as vertexes. And calculating the lengths of all edges in the triangular network, calculating the number of digits in the triangular network, and deleting all edges with the lengths smaller than the median.
(2) If the end points of two segments are connected by an edge of the triangulation network, an adjacency is assumed to exist. If the two line segments are parallel, a vertical line segment is generated to connect the parallel line segments. The newly generated line segments can be used to fill in missing line segments in the line segment extraction process. If the two line segments are not parallel, the line segments are extended to intersect. Thus, a closed line segment may be generated.
(3) And further splitting the line segments into sub-line segments, namely, the end points of other line segments do not exist on each line segment. Searching the closed figure from the sub-line segment can obtain a plurality of sub-polygons and a large polygon containing all the sub-polygons.
(4) And calculating the proportion of points inside the building in the internal points of each sub-polygon. If the multi-polygon is greater than the given threshold, the multi-polygon is considered to be a polygon inside the building. If the area or boundary length of some polygons is small, there may be no points inside, or there are few points, then a decision needs to be made by the length of its common boundary with the adjacent polygons. And combining all polygons in the building, and calculating the outline of the polygons to obtain a closed and regular building outline.
It should be noted that, in the foregoing embodiments, the descriptions of the respective embodiments have respective emphasis, and reference may be made to relevant descriptions of other embodiments for parts that are not described in detail in a certain embodiment.
As will be appreciated by one skilled in the art, embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
While preferred embodiments of the present invention have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. Therefore, it is intended that the appended claims be interpreted as including preferred embodiments and all such alterations and modifications as fall within the scope of the invention.
It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.

Claims (6)

1. A method for extracting rules of an outline of a building of an oblique photography model is characterized by comprising the following steps:
s1: performing straight line fitting on each point on the existing building contour line in the neighborhood of a set range to obtain a plurality of groups of straight line parameters; determining a possible straight line through voting, and determining points belonging to the same straight line; judging the continuity of the points on the same straight line, further dividing the straight line into a plurality of line segments, determining which points form certain line segments, and classifying the points;
s2: re-evaluating the classified points belonging to certain line segments, further adjusting the belonging relation of the classified points, and re-fitting the line segments; judging whether the unclassified point which belongs to the line segment can not be determined; if some points do not belong to any line segment, clustering the points according to positions, and fitting a new line segment;
s3: combining two line segments with smaller distance and included angle, weighting each line segment, and setting the point of the line segment with low weight to be competitive with the line segment with high weight;
s4: calculating the parallel and vertical relation between the line segments, and finely adjusting the parameters of the line segments to meet the requirements of parallel and vertical;
s5: the Delaunay triangulation is established, reconstructing the adjacency between the segments such that the outline of the polygon inside all buildings is a closed and regular building outline.
2. The oblique photography model building outer contour rule extraction method as claimed in claim 1, wherein the step S1 comprises: performing least square fitting on each point on the existing building contour line in a neighborhood in a certain range, converting the point into linear parameters rho and theta under polar coordinates, voting theta, recalculating rho through new theta, voting rho, dividing the voting into a plurality of intervals according to the value range of rho or theta, wherein each point belongs to a certain interval, the interval with higher score is subjected to subsequent processing, a voting algorithm obtains a group of straight lines, a threshold is given to judge whether the straight lines are continuous at each point, and the straight lines are divided into a plurality of line segments.
3. The oblique photography model building outer contour rule extraction method as claimed in claim 1, wherein the step S2 comprises: for classified points belonging to some line segments, calculating the distances from the points to the line segments to which the points belong and the adjacent line segments, and if the distances from the points to the adjacent line segments are smaller, changing the belonging relation of the points; for an unclassified point which cannot be determined to which line segment, calculating the distance from the point to an adjacent line segment, and if the distance is smaller than a given threshold value, changing the relationship of the point; a new line segment is re-fitted to a few points that still do not belong to any line segment.
4. The method for extracting rules of an outline of a building under oblique photography of claim 1, wherein in step S3, if the distance and the included angle between two segments are less than a predetermined threshold, the two segments are considered to be merged, and points of the two segments are put together to re-fit a new segment.
5. The method of claim 4, wherein the stability of the line segment is measured by the length of the line segment, the parallel and vertical relationship between the line segments, the fitting accuracy of the line segment, and the number of points of the line segment, and for a point of a line segment with low weight, if a line segment with better weight exists in its neighboring line segments, the point is competed by a line segment with high weight.
6. The oblique photography model building outer contour rule extraction method as claimed in claim 1, wherein the step S5 comprises:
s51: establishing a Delaunay triangulation network by taking the end points of all the line segments as vertexes, calculating the lengths of all the edges in the Delaunay triangulation network, calculating the number of digits in the Delaunay triangulation network, and deleting all the edges with the lengths smaller than the median;
s52: if the end points of the two line segments are connected by the edge of the triangulation network, the adjacency relation is considered to exist, if the two line segments are parallel, a vertical line segment is generated to connect the parallel line segments, the newly generated line segment can be used for filling the missing line segment in the line segment extraction process, and if the two line segments are not parallel, the line segments are extended to be intersected, so that a closed line segment can be generated;
s53: further splitting the line segments into sub-line segments, namely, each line segment does not have end points of other line segments, searching a closed graph from the sub-line segments to obtain a plurality of sub-polygons and a large polygon containing all the sub-polygons;
s54: calculating the proportion of points inside the building in the internal points of each sub-polygon, and if the proportion is greater than a given threshold value, considering the multi-polygon as the polygon inside the building;
if the area or boundary length of some polygons is small, there may be no points inside them, or there are few points, it is necessary to determine by the length of the common boundary between them and the adjacent polygons, merge all polygons inside the building, calculate their outline to obtain a closed and regular building outline.
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Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115600307A (en) * 2022-12-01 2023-01-13 北京飞渡科技有限公司(Cn) Method for generating single building from Mesh model of urban scene
CN115631307A (en) * 2022-11-17 2023-01-20 北京飞渡科技有限公司 Building segmented contour extraction and vertical face three-dimensional reconstruction method
CN116129076A (en) * 2023-04-17 2023-05-16 深圳大学 Building Mesh model simplification method with rule feature maintained
CN116580048A (en) * 2023-07-12 2023-08-11 武汉峰岭科技有限公司 Method and system for extracting contour line of right-angle house on house inclination model

Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115631307A (en) * 2022-11-17 2023-01-20 北京飞渡科技有限公司 Building segmented contour extraction and vertical face three-dimensional reconstruction method
CN115631307B (en) * 2022-11-17 2023-03-21 北京飞渡科技有限公司 Building segmented contour extraction and vertical face three-dimensional reconstruction method
CN115600307A (en) * 2022-12-01 2023-01-13 北京飞渡科技有限公司(Cn) Method for generating single building from Mesh model of urban scene
CN116129076A (en) * 2023-04-17 2023-05-16 深圳大学 Building Mesh model simplification method with rule feature maintained
CN116580048A (en) * 2023-07-12 2023-08-11 武汉峰岭科技有限公司 Method and system for extracting contour line of right-angle house on house inclination model
CN116580048B (en) * 2023-07-12 2023-09-26 武汉峰岭科技有限公司 Method and system for extracting contour line of right-angle house on house inclination model

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