Automatic room segmentation method based on wall constraints

Abstract

The application discloses a room automatic segmentation method based on wall constraint, which comprises four main steps of wall center line detection, missing wall derivation, initial segmentation and energy optimization, and can effectively solve the problem that the existing room segmentation method is insufficient in segmentation once the point cloud contains more noise or data loss. Meanwhile, the existing method is usually difficult to obtain complete and smooth room boundaries, but when the method is used, even when the point cloud data containing noise, outliers and data loss and other interference is processed, very high segmentation quality can be obtained, and very smooth and complete room boundaries can be segmented, which is of great significance for further processing of the point cloud, such as semantic segmentation in a single room or three-dimensional reconstruction.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of three-dimensional reconstruction and computer graphics, and particularly relates to a room segmentation method for indoor point clouds. BACKGROUND

[0002] How to describe the real world in three dimensions and realize the digitization of the scene is currently in increasing demand for application, for example: with the rapid development of sensor technology and the emergence of a large number of software processing tools, point cloud data has become popular. Point cloud data realizes the digitization of the scene through a large number of three-dimensional point sets, and can densely and accurately represent the three-dimensional geometric shape of objects in the environment.

[0003] Generally, an indoor space is defined as a space enclosed by permanent structural elements (such as floor, ceiling and wall), and the subdivision of indoor space into meaningful subspaces (such as rooms, corridors) has been described in many works, which have applied various methods and have different goals. Since the spatial subdivision provides simpler spatial relationships between subspaces, a detailed and accurate topological map can significantly save the computational effort required to obtain a navigation trajectory. Properly dividing a planar graph into separate room units can be a valuable part of semantic mapping or place classification. Similarly, human-robot communication also greatly benefits from a common concept of room range. In addition, as one of the key steps of indoor three-dimensional reconstruction tasks, room segmentation is also a hot topic of discussion in the AEC (architecture, engineering and construction) industry.

[0004] Existing room segmentation methods often have difficulty obtaining relatively ideal segmentation results when dealing with point clouds containing noise, outliers and data missing, etc. In addition, the room boundaries segmented by existing methods have the problems of being not smooth and not complete. SUMMARY

[0005] The purpose of the present application is to provide a wall-constrained automatic room segmentation method to solve the problems of the current existing room segmentation methods in the background art, which often have difficulty obtaining relatively ideal segmentation results when dealing with point clouds containing noise, outliers and data missing, etc., and the problems of the room boundaries segmented by existing methods being not smooth and not complete.

[0006] To achieve the above purpose, the present application provides the following technical solution: a wall-constrained automatic room segmentation method, comprising the following steps:

[0007] Step 1: Detect the wall center line; extract the wall constraint from the original point cloud to cut off the connection between rooms to complete the initial segmentation, and at the same time use the result as the input for graph construction, which specifically includes:

[0008] A) Detect wall lines. First, traverse the point cloud patches classified as walls and determine whether they are perpendicular to the horizontal plane. For each wall patch that is approximately perpendicular to the horizontal plane, use the least squares method to fit it into a plane. Then, calculate the intersection line formed by the fitted wall plane and the horizontal plane, which is the wall line. This intersection line is the projection of the wall plane onto the horizontal plane. Calculate the set of all wall lines in the point cloud.

[0009] B) Generate double wall centerlines. Search for paired double walls in the set of original wall lines. First, determine whether the two wall lines are parallel. Then, calculate the distance between them. If the distance is less than the given wall thickness threshold, they are paired double walls. Calculate the centerline between the paired double walls and use it as the wall centerline.

[0010] C) Generate the centerline of the outer wall. Given the thickness t of the outer wall, extend the original wall line W to both sides by a distance of t / 2 to determine the positions of the candidate wall centerlines, denoted as L1 and L2. For each candidate wall centerline, calculate the number of non-empty raster cells (SUM1 and SUM2) containing point clouds within the rectangular area enclosed by the candidate wall line and the original wall line. The selection of the outer wall centerline follows these rules:

[0011] Where centerline is the center line of the exterior wall;

[0012] Step Two: Detect the wall centerline; derive the missing wall lines to obtain a robust set of wall lines, specifically including:

[0013] D) Mark the two endpoints of each wall centerline in the set as free endpoints and non-free endpoints. Free endpoints and non-free endpoints are defined according to the following rules: if there are no other wall centerlines within a certain range of the endpoint, that is, it is not adjacent to other wall segments, it is a free endpoint; otherwise, it is called a non-free endpoint.

[0014] E) The wall centerlines in the set are grouped according to their adjacency to eliminate interference from other wall lines outside the room. The detected wall centerlines were divided into 3 groups;

[0015] F) For combinations with more than 3 wall centerlines, generate virtual wall lines for the free endpoints in the combination according to a certain strategy; assuming that the wall lines are all perpendicular to each other, start from the free endpoint and generate a perpendicular line to the wall centerline where the free endpoint is located. The perpendicular line will intersect with the straight line containing the free endpoint of the wall centerline. Select the intersection point with the nearest straight line containing the free endpoint as the endpoint of the virtual wall line; if there is no such wall centerline, the virtual wall line will not be generated.

[0016] Step 3: Perform initial segmentation of the point cloud using the wall centerline; specifically including:

[0017] G) First, the point cloud is rasterized. Grids that contain the ceiling plane point cloud are marked as occupied, and grids that do not contain it are marked as unoccupied. Point clouds within the offset distance range are selected as the ceiling plane point cloud. The offset distance is set to be within 0.2m of the height of the ceiling point cloud patch with the largest area.

[0018] H) Remove the connecting parts between rooms to make each room an isolated area; using the center line of the wall as the central axis, set the occupied grid within the equidistant range on both sides to be an unoccupied grid. The width of the removed range should not be greater than the thickness of the wall at the corresponding position so that each room area is surrounded by unoccupied grids and becomes an isolated area.

[0019] I) After obtaining the projection of the point cloud onto the two-dimensional plane, it is further identified as different rooms; a label-based watershed algorithm is executed on the generated binary image to segment the binary image into different regions, each region is assigned a unique number, the image segmentation result is assigned to the point cloud to complete the initial labeling of the point cloud, all pixels of the image are traversed, the mapping relationship between image labels and room numbers is established, and then, using the grid corresponding to each pixel as a unit, all points in all grids with the same pixel value are labeled as the same room, until the labeling of the entire point cloud is completed;

[0020] Step 4: Global optimal segmentation based on graph cuts; specifically including:

[0021] J) Constructing a diagram; from the set of wall centerlines, construct an arrangement of infinitely long lines, and generate a plan view by finding the intersections of all candidate wall centerlines on the horizontal plane. ,in, The surface F is the area of ​​the building layout, that is, part of the room or the external area, and the edge It is a possible part of the wall.

[0022] It is the intersection of the center lines of the walls; define the floor plan. The dual graph is Here, each vertex V corresponds to a face F in the graph, denoted by its center, and the edges E represent... The adjacency relationship of each face in the middle, if If two faces are adjacent, there will be an edge between them;

[0023] K) Define a multi-label energy function; the objective function includes two terms: assigning labels to surfaces. The unary cost and the binary cost that assigns labels to adjacent faces; the unary cost provides a hint about the location of a room or external area, and the binary cost guides the selection of appropriate edges to separate faces with different labels; corresponding to the dual graph W, the formulaic form is as follows: Let For a collection of tags, here These are the labels of each marked region in the initial segmentation. Labels for unsegmented regions. Given an external label and a univariate cost function The generation will Assigned to vertices Cost, binary cost function Generate paired tags The cost assigned to a vertex, minimizing the label cost, is expressed as follows:

[0024]

[0025] L) Define a univariate cost function; first, obtain the labels of all points within each grid and save them to an ordered set. Then, select the median of this ordered set as the label of the grid. Next, calculate the proportion of the number of grids with each label within the area to the total number of grids within the area to obtain the probability that each area belongs to each room or external region. The univariate loss function is then defined as:

[0026] ,

[0027] in, As a weighting factor, The label within the unit composite surface is Quantity, This represents the total number of labels within the face. The area of ​​the penalized unit complex is used to influence label assignment;

[0028] M) Define a binary cost function; for a binary loss function, assuming a virtual external vertex is connected to the room vertex to form an edge, then the binary loss function is defined as:

[0029] here As a weighting factor, Centerline of the wall Representing an edge , This is to penalize the effect of different lengths of the common edge between two cells.

[0030] Compared with the prior art, the beneficial effects of the present invention are:

[0031] The automatic room segmentation method based on wall constraints includes four main steps: wall centerline detection, missing wall derivation, initial segmentation, and energy optimization. It effectively overcomes noise between walls and obtains accurate segmentation results. Furthermore, based on the Manhattan world hypothesis, it derives the missing walls to improve the algorithm's robustness. Finally, it describes room segmentation as an effectively solvable Markov random field optimization problem, thus obtaining complete and smooth room edges. Compared with existing methods, this method demonstrates significant advantages when dealing with point clouds containing significant noise or missing data, and when handling point cloud data with interference such as noise, outliers, and missing data. Attached Figure Description

[0032] Figure 1 This is a flowchart of the overall segmentation method of the present invention;

[0033] Figure 2 To extract the schematic diagram of the wall lines;

[0034] Figure 3 This is a schematic diagram illustrating the generation of the center lines of the double walls;

[0035] Figure 4 To select an appropriate wall centerline based on the number of non-empty grid cells within the rectangular area;

[0036] Figure 5 This is a schematic diagram of virtual wall line generation;

[0037] Figure 6 This is a schematic diagram of point cloud rasterization;

[0038] Figure 7 This is a schematic diagram showing the point cloud around the center line of the wall after removal;

[0039] Figure 8 It is the two-dimensional projection in the step of removing the point cloud around the center line of the wall;

[0040] Figure 9 This is a schematic diagram of rasterizing the point cloud within the selected offset distance;

[0041] Figure 10 A schematic diagram illustrating image segmentation using the watershed algorithm;

[0042] Figure 11 This is to obtain the initial room marking results;

[0043] Figure 12 Diagram of the wall centerline;

[0044] Figure 13 Construct a unit composite shape from the centerline of the wall;

[0045] Figure 14 Topological diagram of a single-unit complex;

[0046] Figure 15 Overlay display of wall centerline and topology map;

[0047] Figure 16 The optimal labeling result is mapped to the point cloud;

[0048] Figure 17 The segmentation results are from a publicly available dataset;

[0049] Figure 18 To compare the IoU metric before and after adding virtual wall lines using the proposed method;

[0050] Figure 19 This is a quantitative evaluation diagram of the initial and final segmentation results of the present invention;

[0051] Figure 20 This invention compares various evaluation metrics with existing methods on the ISPRS dataset and local dataset. Detailed Implementation

[0052] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0053] This invention proposes an automatic room segmentation method based on wall constraints, which can effectively overcome noise between walls and obtain accurate segmentation results. The overall idea is: based on the Manhattan world hypothesis, the missing walls are deduced to improve the robustness of the algorithm. The room segmentation is described as a Markov random field optimization problem that can be effectively solved, thereby obtaining complete and smooth room boundaries.

[0054] This method takes a pre-classified 3D point cloud of an interior room (the point cloud is classified into architectural elements such as walls, ceilings, and floors, and may contain noise, incompleteness, and outliers) as input and outputs a 3D point cloud with fine room segmentation. Figure 1 As shown. This method mainly consists of four parts.

[0055] Step 1: Detect wall centerlines. Extract wall constraints from the original point cloud to cut off connections between rooms, completing the initial segmentation, and also serving as input for subsequent graph construction. The specific steps are as follows:

[0056] Step 1.1: Detect wall lines. First, traverse the point cloud patches classified as walls and determine if they are perpendicular to the horizontal plane. For each wall patch approximately perpendicular to the horizontal plane, use the least squares method to fit it into a plane, as shown by the rectangle in Figure 2. Then, calculate the intersection line formed by the fitted wall plane and the horizontal plane. This intersection line is the projection of the wall plane onto the horizontal plane, which we call the wall line. Figure 2 As shown by the midline segment, the set of all wall lines in the point cloud is calculated, and its visualization result is as follows. Figure 2 As shown in the shaded diagram on the right side of the middle.

[0057] Step 1.2: Generate the centerline of the double wall. Search for paired double walls in the set of original wall lines. First, determine whether the two wall lines are parallel, and then calculate the distance between them. If the distance is less than a given wall thickness threshold, they are paired double walls. The centerline between the paired double walls is then calculated as the wall centerline. Figure 3 An example of generating the center line of a double wall is given in the document.

[0058] Step 1.3: Generate the center line of the exterior wall. Figure 4 The diagram illustrates the calculation of the exterior wall centerline. Given a wall thickness of t, the original wall line W is extended to both sides by a distance of t / 2 to determine the candidate wall centerlines, denoted as L1 and L2. For each candidate wall centerline, we calculate the number of non-empty raster cells (SUM1 and SUM2) containing point clouds within the rectangular area enclosed by the candidate wall line and the original wall line. The selection of the exterior wall centerline follows these rules:

[0059]

[0060] Step 2: Derive the missing walls. This step aims to obtain a robust set of wall lines. Specifically, it involves first marking the two endpoints of the centerline of each wall in the set as free endpoints and non-free endpoints. For example... Figure 5 As shown, the definitions of a free endpoint and a non-free endpoint are as follows: if there are no other wall centerlines within a certain range of the endpoint, i.e., it is not adjacent to other wall segments, we call it a free endpoint; otherwise, it is called a non-free endpoint. We analyze two cases based on the difference in the position of the intersection of the two wall centerlines. Let the intersection of the wall centerlines be p. When p is located within a wall segment, we directly determine whether the distance from the endpoint to the wall segment meets a given threshold to determine if the endpoint is a free endpoint. When p is located outside a wall segment, it is a non-free endpoint only if the distances from both the endpoint of the wall segment and the endpoint to p are less than the threshold; otherwise, it is a free endpoint.

[0061] The second step is to group the wall centerlines in the set according to the adjacency relationship between the wall centerlines. This is done in order to eliminate the interference of other wall lines outside the room. Figure 5The detected wall centerlines were divided into three groups. Finally, for combinations with more than three wall centerlines, virtual wall lines were generated for the free endpoints within the combination according to a specific strategy. Our method is based on the Manhattan hypothesis: wall lines are perpendicular to each other. Starting from a free endpoint, a perpendicular line to the wall centerline containing that free endpoint is generated. This perpendicular line intersects with other lines containing wall centerlines that also contain free endpoints. We select the intersection point with the nearest line containing a free endpoint as the endpoint of the virtual wall line. If no such wall centerline exists, this virtual wall line will not be generated.

[0062] Step 3: Perform initial segmentation of the point cloud using the wall centerline. First, rasterize the point cloud, marking the grid containing the ceiling plane point cloud as occupied ( Figure 6 (White area in the middle) Grids not included are marked as unoccupied ( Figure 6 (The black area in the middle) Note that, in order to obtain a complete ceiling plane while filtering out indoor environmental noise, the point cloud within the offset distance range is selected as the ceiling plane point cloud, such as... Figure 7 As shown in the box, the offset distance is set to be within 0.2m of the height of the largest ceiling point cloud panel. This is because measurements have shown that the distance between the ceiling and the beam is generally around 0.2m, and this height filters out noise from flat surfaces such as tables and wardrobes in the room.

[0063] To isolate each room from the others, it's necessary to further remove the connecting parts between rooms. Walls, as room boundaries, are natural constraints that separate rooms. Using the wall's centerline as the central axis, the occupied grid cells (white pixels) within an equidistant range on both sides are set to unoccupied grid cells (black pixels), as follows: Figure 7 The gray area is shown. Note that the width of the removed area should not exceed the thickness of the wall at the corresponding location. This way, each room area is surrounded by an unoccupied grid, becoming an isolated region, resulting in the final binary image as shown. Figure 10 As shown.

[0064] After obtaining the projection of the point cloud onto a two-dimensional plane, it needs to be further identified as different rooms, each with a unique identifier. We perform a label-based watershed algorithm on the generated binary image to segment the binary image into different regions, such as... Figure 8 As shown, each region has a unique number. Next, the image segmentation results need to be assigned to the point cloud to complete the initial labeling of the point cloud. Figure 10 We first iterate through all the pixels of the image to establish a mapping relationship between image labels and room numbers. Then, using the raster corresponding to each pixel as a unit, we mark the points in all raster cells with the same pixel value as the same room, until the labeling of the entire point cloud is completed.

[0065] Step 4: Global optimal segmentation based on graph cuts. The specific steps are as follows:

[0066] Step 4.1: Constructing the Graph. We construct an arrangement of infinitely long lines from the set of wall centerlines, and then we consider the intersections of all candidate wall centerlines on the horizontal plane, which produces the plan view. ,like Figure 13 As shown, The surface F is the area of ​​the building layout (i.e., part of the room or the exterior area), and the edge... It is a possible part of the wall. It is the intersection of the centerlines of the walls. Define the floor plan. The dual graph is Each vertex V here corresponds to a graph Let F be the face of a plane, denoted by its center, and E be the edge of the plane. The adjacency relationship of each face in the middle, if If two faces are adjacent, then there will be an edge between them. The corresponding result is as follows: Figure 14 As shown, W can perfectly represent... The topological relationships between the various faces are crucial information.

[0067] Step 4.2: Define the multi-label energy function. The objective function consists of two terms: assigning labels to... The univariate cost of a face and the binary cost of assigning labels to adjacent faces. The univariate cost provides a hint about the location of a room (or exterior area), while the binary cost guides the selection of appropriate edges to separate faces with different labels. Corresponding to the dual graph W, the formulaic form is as follows: Let For a collection of tags, here These are the labels of each marked region in the initial segmentation. Labels for unsegmented regions (yellow areas in the point cloud). External label. Given a univariate cost function. The generation will Assigned to vertices Cost, binary cost function Generate paired tags Assigned to vertices The cost of minimizing the label cost is expressed as follows:

[0068]

[0069] Step 4.3: Define the univariate cost function. First, obtain the labels of all points within each grid cell and save them to an ordered set. Then, select the median of the ordered set as the label of the grid cell. Finally, calculate the cost function based on the surface area. The number of grid cells occupied by each label within the area The ratio of all grid numbers within the surface is used to obtain the number of each face. The probability of belonging to each room or external area. Then the univariate loss function is defined as:

[0070]

[0071] here As a weighting factor, The label within the unit composite surface is Quantity, This represents the total number of labels within the face. The area of ​​the unit complex is used to penalize the effect of label assignment.

[0072] Step 4.4: Define the bivariate cost function. For the bivariate loss function... Our intuition is that walls separate different areas, either adjacent rooms or a room from the outside world. Observe the topological diagram of the wall centerline and the corresponding unit complex. Overlay display ( Figure 15 ),consider edge We can easily see that if the edge Intersects with the center line of the wall ( Figure 15 (As shown), vertex They should belong to different rooms, then for the vertices Assign tags Cost It should be lower, conversely, if the edge It does not intersect with any wall centerline. Figure 15 (As shown), vertex Assigning different labels to vertices belonging to the same room would be very costly. Specifically, for the case where a room region is adjacent to the outside world, we assume a virtual external vertex connected to the room vertex to form an edge. Therefore, the binary loss function is defined as:

[0073]

[0074] here As a weighting factor, Centerline of the wall Representing an edge , This is to penalize the effect of different lengths of the common edge between two cells.

[0075] We use the algorithm of Boykov et al. to minimize the energy solution formula (2). The optimal labeling results of the unit complex are as follows: Figure 16 As shown.

[0076] like Figures 17 to 20As shown, compared to existing technologies, the advantages of this solution are as follows: Existing room segmentation methods can achieve relatively good segmentation quality when the point cloud is free of noise and the scan is complete. However, when the point cloud contains a lot of noise or has missing data, existing methods often suffer from insufficient segmentation. Furthermore, existing methods typically struggle to obtain complete and smooth room boundaries. This invention effectively solves these problems, achieving very high segmentation quality even when processing point cloud data containing noise, outliers, and missing data. It can also segment very smooth and complete room boundaries, which is of great significance for further point cloud processing, such as semantic segmentation within a single room or 3D reconstruction.

[0077] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for automatic room partitioning based on wall constraints, characterized in that, Includes the following steps: Step 1: Detect wall centerlines; extract wall constraints from the original point cloud to cut off connections between rooms to complete the initial segmentation, and use the results as input for the construction graph, specifically including: A) Detect wall lines. First, traverse the point cloud patches classified as walls and determine whether they are perpendicular to the horizontal plane. For each wall patch that is approximately perpendicular to the horizontal plane, use the least squares method to fit it into a plane. Then, calculate the intersection line formed by the fitted wall plane and the horizontal plane, which is the wall line. This intersection line is the projection of the wall plane onto the horizontal plane. Calculate the set of all wall lines in the point cloud. B) Generate double wall centerlines. Search for paired double walls in the set of original wall lines. First, determine whether the two wall lines are parallel. Then, calculate the distance between them. If the distance is less than the given wall thickness threshold, they are paired double walls. Calculate the centerline between the paired double walls and use it as the wall centerline. C) Generate the centerline of the outer wall. Given the thickness t of the outer wall, extend the original wall line W to both sides by a distance of t / 2 to determine the positions of the candidate wall centerlines, denoted as L1 and L2. For the two candidate wall centerlines, calculate the number of non-empty raster cells containing the point cloud within the rectangular area enclosed by them and the original wall line, SUM1 and SUM2 respectively. The selection of the outer wall centerline follows these rules: Where centerline is the center line of the exterior wall; Step Two: Detect the wall centerline; derive the missing wall lines to obtain a robust set of wall lines, specifically including: D) Mark the two endpoints of each wall centerline in the set as free endpoints and non-free endpoints. Free endpoints and non-free endpoints are defined according to the following rules: if there are no other wall centerlines within a certain range of the endpoint, that is, it is not adjacent to other wall segments, it is a free endpoint; otherwise, it is called a non-free endpoint. E) The wall centerlines in the set are grouped according to the adjacency relationship between the wall centerlines to eliminate the interference of other wall lines outside the room. The detected wall centerline set is divided into 3 groups. F) For combinations with more than 3 wall centerlines, generate virtual wall lines for the free endpoints in the combination according to a certain strategy; assuming that the wall lines are all perpendicular to each other, start from the free endpoint and generate a perpendicular line to the wall centerline where the free endpoint is located. The perpendicular line will intersect with the straight line containing the free endpoint of the other wall centerline. Select the intersection point with the nearest straight line containing the free endpoint as the endpoint of the virtual wall line; if there is no such wall centerline, then do not generate this virtual wall line. Step 3: Perform initial segmentation of the point cloud using the wall centerline; specifically including: G) Rasterize the point cloud, mark the grid containing the ceiling plane point cloud as occupied, and mark the grid not containing it as unoccupied. Select the point cloud within the offset distance range as the ceiling plane point cloud. The offset distance is set to a range of 0.2m below the height of the ceiling point cloud patch with the largest area. H) Remove the connecting parts between rooms to make each room an isolated area; using the center line of the wall as the central axis, set the occupied grid within the equidistant range on both sides to be an unoccupied grid, and the width of the removed range is no greater than the thickness of the wall at the corresponding position so that each room area is surrounded by unoccupied grids and becomes an isolated area. I) After obtaining the projection of the point cloud onto the two-dimensional plane, it is further identified as different rooms; a label-based watershed algorithm is executed on the generated binary image to segment the binary image into different regions, each region is assigned a unique number, the image segmentation result is assigned to the point cloud to complete the initial labeling of the point cloud, all pixels of the image are traversed, the mapping relationship between image labels and room numbers is established, and then, using the grid corresponding to each pixel as a unit, all points in all grids with the same pixel value are labeled as the same room, until the labeling of the entire point cloud is completed; Step 4: Global optimal segmentation based on graph cuts; specifically including: J) Constructing a diagram; from the set of wall centerlines, construct an arrangement of infinitely long lines, and generate a plan view by finding the intersections of all candidate wall centerlines on the horizontal plane. ,in, The surface F is the area of ​​the building layout, that is, part of the room or the external area, and the edge It is a possible part of the wall. It is the intersection of the center lines of the walls; define the floor plan. The dual graph is Each vertex V here corresponds to a graph Let F be the face of a plane, denoted by its center, and E be the edge of the plane. The adjacency relationship of each face in the middle, if If two faces are adjacent, there will be an edge between them; K) Define a multi-label energy function; the objective function includes two terms: assigning labels to... The unary cost of a face and the binary cost of assigning labels to adjacent faces; the unary cost provides a hint about the location of a room or external area, and the binary cost guides the selection of appropriate edges to separate faces with different labels; corresponding to the dual graph W, the formulaic form is as follows: Let For a collection of tags, here These are the labels of each marked region in the initial segmentation. Labels for unsegmented regions. Given a univariate cost function for external labels. The generation will Assigned to vertices Cost, binary cost function Generate paired tags Assigned to vertices The cost of minimizing the label cost is expressed as follows: L) Define a univariate cost function; first, obtain the labels of all points within each grid and save them to an ordered set, then select the median of the ordered set as the label of the grid, and then calculate the cost function based on the surface cost. The number of grid cells occupied by each label within the area The ratio of all grid numbers within the surface is used to obtain the number of each face. Given the probability of belonging to each room or external area, the univariate loss function is defined as: ， in, As a weighting factor, The label within the unit composite surface is Quantity, This represents the total number of labels within the face. The area of ​​the penalized unit complex is used to influence label assignment; M) Define a binary cost function; for a binary loss function Assuming a virtual external vertex is connected to the room vertex to form an edge, then the binary loss function is defined as: ， here As a weighting factor, Centerline of the wall Representing an edge , This is to penalize the effect of different lengths of the common edge between two cells.

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