AI-based design construction three-dimensional consistency review and collaborative management system

Abstract

The application discloses an AI-based design construction three-dimensional consistency review and collaborative management system and relates to the field of building information.The AI-based design construction three-dimensional consistency review and collaborative management system realizes high-quality acquisition and reliable evaluation of on-site point cloud data through a data acquisition module and a geometric consistency preliminary evaluation module in application. By arranging control sampling points and combining the optimization strategy of point cloud quality data, the effectiveness and integrity of the point cloud data can be significantly improved. On this basis, the system uses 95th percentile directional Hausdorff deviation H95 to perform robust geometric analysis on the registered point cloud set and the three-dimensional drawing BIM model, avoids the distortion of the judgment caused by individual abnormal points, and realizes accurate identification of the overall geometric deviation. This way enables the preliminary evaluation stage to quickly find construction deviations, reduces the links of manual review and repeated collection, and thus improves the review efficiency and data reliability.

Description

Technical Field

[0001] This invention relates to the field of building information technology, specifically to an AI-based design and construction 3D consistency verification and collaborative management system. Background Technology

[0002] With the development of building information modeling (BIM) and intelligent construction technologies, digital management of building projects has gradually become a crucial aspect of engineering construction. Among these technologies, Building Information Modeling (BIM) is widely used in the design, construction, and operation and maintenance phases to achieve 3D modeling of components and data management throughout their entire lifecycle. On construction sites, with the maturity of laser scanning point cloud modeling and digital twin model construction technologies, contractors can quickly generate digital twin models of the site during actual construction and compare them with the 3D drawings and BIM models, thereby achieving refined control and consistency verification of the construction process.

[0003] Currently, although BIM models and construction site models are used in existing construction management systems, most systems only rely on one-way modeling or manual comparison, lacking a real-time consistency verification mechanism between drawings and the actual site. Specifically, existing solutions often involve manual collection of limited measurement data on-site, followed by localized comparison with 3D drawings. This approach has significant drawbacks: first, the comparison scope is limited, easily overlooking hidden works or complex details; second, it requires high manual intervention and is inefficient; and third, it cannot achieve dynamic monitoring of the entire construction process, leading to delayed detection of deviations.

[0004] Due to the lack of an efficient AI-based global comparison mechanism, discrepancies between design and construction often go undetected at construction sites. For example, misalignment of duct and cable tray intersections in the drawings leads to spatial conflicts during installation; deviations between the installation positions of supports and hangers and design benchmarks affect the installation accuracy of subsequent components; and mismatched hole positions and dimensions result in secondary drilling and rework. If these discrepancies are only discovered in the later stages of construction, they can lead to rework, material waste, delays, and significantly increased construction costs, and in severe cases, even pose safety hazards. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides an AI-based design and construction 3D consistency verification and collaborative management system, which solves the problems mentioned in the background technology.

[0006] To achieve the above objectives, the present invention provides the following technical solution: an AI-based design and construction 3D consistency verification and collaborative management system, comprising a data acquisition module, a geometric consistency preliminary assessment module, a topological consistency verification module, and a collaborative correction and reassessment module;

[0007] The data acquisition module acquires point cloud data of the construction site and generates a digital twin model of the construction site. At the same time, it deploys a control sampling point set (CPS) and registers the control sampling point set (CPS) to the coordinate system of the 3D drawing BIM model (ModelB) to obtain the registration point cloud set (PS).

[0008] The geometric consistency preliminary assessment module establishes the correspondence between sampling points and BIM model points in 3D drawings, calculates the 95th percentile orientation Hausdorff deviation H95, performs preliminary assessment level classification, and generates a set of suspected inconsistent areas R1 based on the preliminary assessment level classification results.

[0009] The topology consistency verification module receives a set of suspected inconsistent regions R1, extracts the topology subgraphs of the corresponding regions from the 3D drawing BIM model ModelB and the construction site digital twin model ModelS, and defines them as the 3D drawing subgraph Gb and the construction site subgraph Gs, respectively, and calculates the topology difference rate Rt.

[0010] The collaborative correction and review module calculates the consistency collaboration index Qsync based on the topology difference rate Rt, compares the consistency collaboration index Qsync with the collaboration pass threshold T2, and then executes the review mechanism based on the comparison result.

[0011] Preferably, the data acquisition module includes a point cloud acquisition unit and a control sampling point arrangement unit;

[0012] The point cloud acquisition unit performs a full-range scan of the construction site using a laser scanning device to obtain the raw point cloud dataset RawP of the construction area; and performs noise reduction, outlier removal and downsampling processing on the raw point cloud dataset RawP to obtain the preprocessed point cloud dataset PreP.

[0013] A digital twin model ModelS for the construction site is constructed based on the preprocessed point cloud dataset PreP. A continuous three-dimensional geometric surface is generated using point cloud meshing and surface fitting methods. Then, speech segmentation is used to identify the component categories of the three-dimensional geometric surface. The component categories include classified walls, beams and columns, air ducts, cable trays, supports and hangers, and holes.

[0014] Preferably, the sampling point arrangement unit arranges the control sampling point set CPS by means of the end region, turning radius region and hole edge ring of each identified component category;

[0015] Point cloud quality data is extracted based on the control sampling point set CPS, and then occlusion and incident optimization strategies are set on the point cloud quality data to optimize the point cloud quality.

[0016] The point cloud quality data includes occlusion rate Occ, laser incident angle ainc, and scan overlap rate CoverageCov;

[0017] The occlusion and incident optimization strategy requires an occlusion rate of Occ ≤ 25%, a scan overlap rate of CoverageCov ≥ 60%, and a laser incident angle ainc ∈ [20°, 70°].

[0018] Next, the field coordinates S in the control sampling point set CPS are unified with the reference coordinates b in the 3D drawing BIM model ModelB. An initial registration matrix is ​​generated through the initial registration algorithm of feature points, and then fine registration is performed through the nearest point iteration algorithm to obtain the final registration point cloud set PS. The mapping relationship between the point cloud and the model MapC is output.

[0019] Preferably, the geometric consistency preliminary assessment module includes a deviation calculation unit, a consistency preliminary assessment unit, and a preliminary assessment result execution unit;

[0020] The deviation calculation unit calculates the Euclidean distance between the field coordinates S in the control sampling point set CPS and the reference coordinates b in the three-dimensional drawing BIM model ModelB by using the Euclidean distance calculation formula through the correspondence mapping MapC. It also summarizes the Euclidean distances of the registration points in the correspondence mapping MapC to generate an Euclidean distance set.

[0021] Statistical analysis was performed on the Euclidean distance set, and the 95th percentile value was extracted to obtain the 95th percentile orientation Hausdorff bias H95. The geometric bias level of the overall control sampling point set CPS was then analyzed and quantified.

[0022] Preferably, the consistency assessment unit reads the allowable installation deviation value corresponding to the component category through the construction technical specifications, wherein the maximum deviation is set as the upper limit threshold value of the length allowable value Lg1, and the minimum allowable installation deviation value is set as the lower limit threshold value of the length allowable value Lg2.

[0023] The 95th percentile orientation Hausdorff deviation H95 of the registration points in the mapping MapC is traversed and compared with the upper and lower allowable length thresholds Lg1 and Lg2 respectively for preliminary evaluation. Based on the preliminary evaluation comparison results, the deviation level is classified. The specific preliminary evaluation comparison content is as follows:

[0024] When the 95th percentile orientation Hausdorff deviation H95 ≤ the lower limit of the allowable length threshold Lg2, the deviation level is classified as Level A;

[0025] When the lower limit of the length allowable threshold Lg2 < 95th percentile orientation Hausdorff deviation H95 ≤ the upper limit of the length allowable threshold Lg1, the deviation level is classified as level B.

[0026] When the 95th percentile orientation Hausdorff deviation H95 is greater than the upper limit of the length allowable threshold Lg1, the deviation level is classified as level C.

[0027] Preferably, the initial evaluation result execution unit executes a response strategy based on the deviation levels determined by the preliminary comparison results. The specific execution content is as follows:

[0028] When classified as Level A, it passes directly without triggering collaborative correction.

[0029] When classified as Level B, it is added to the watchlist, the data collection quality self-check is initiated, the occlusion and incident radiation optimization strategies are refreshed, and the initial evaluation comparison is re-executed. If it is still classified as Level B, the deviation level is automatically upgraded.

[0030] When classified as Level C, the current registration point is classified as a suspected point, and all suspected points are summarized and output as a suspected inconsistent region set R1, triggering the topology consistency verification module.

[0031] Preferably, the topology consistency verification module includes a topology subgraph definition unit and a topology difference analysis unit;

[0032] The topology subgraph definition unit receives the suspected inconsistent region set R1 and defines the corresponding spatial range in the 3D drawing BIM model ModelB and the construction site digital twin model ModelS respectively, and extracts the 3D drawing subgraph Gb and the construction site subgraph Gs.

[0033] Based on the spatial extent, the edge set E and node set V of the 3D drawing sub-graph Gb and the construction site sub-graph Gs are identified;

[0034] Among them: node set V identifies the characteristic positions of the endpoints, intersections, support points and reserved hole center points of component categories by using geometric feature detection and component semantic parsing according to the spatial range, forming the 3D drawing sub-graph Gb node set Vb and the construction site sub-graph Gs node set Vs;

[0035] Edge set E is associated with the node root in the 3D drawing subgraph Gb node set Vb and the construction site subgraph Gs node set Vs through the geometric continuous edges, physical connection edges, support edges and through edges, generating the edge set Eb of the 3D drawing subgraph Gb and the edge set Es of the construction site subgraph Gs.

[0036] The edge set E and node set V in the 3D drawing subgraph Gb and the construction site subgraph Gs are formatted and standardized.

[0037] Preferably, the topology difference analysis unit performs standardization processing on the node set V and edge set E in the 3D drawing sub-graph Gb and the construction site sub-graph Gs; the standardization processing includes coordinate normalization processing, numbering unification processing, and redundancy elimination processing;

[0038] After standardizing the node set V and edge set E, and calculating the output topology difference rate Rt, the edge set E difference between the 3D drawing subgraph Gb and the construction site subgraph Gs is compared.

[0039] Based on the allowable upper limit of the construction project configuration, a benchmark difference rate R0 is set, and then the topology difference rate Rt is compared with the benchmark difference rate R0 to determine the consistency of the topology relationship. Based on the comparison results, a review unit is triggered. The specific comparison content is as follows.

[0040] When the topological difference rate Rt ≤ the baseline difference rate R0, the topological relationship is determined to be consistent and passes the review;

[0041] When the topology difference rate Rt > the baseline difference rate R0, it is determined that there is a significant deviation in the topology relationship. A serialized correction strategy is then executed. The serialized correction strategy includes process sequence adjustment, support and hanger decoupling correction, hole reset and component posture verification. A topology difference report is generated, and the specific difference edge information in the suspected inconsistent region set R1 is then transmitted to the collaborative correction and review module.

[0042] Preferably, the collaborative correction and re-evaluation module includes a collaborative correction unit and a re-evaluation unit;

[0043] The collaborative correction unit calculates consistency based on the topological difference rate Rt and the 95th percentile orientation Hausdorff deviation H95 after the serialized correction strategy is executed, obtains the consistency coordination index Qsync, and performs quantitative analysis to determine the consistency between the actual construction and the drawings after the serialized correction strategy is executed.

[0044] Preferably, the review unit sets a collaboration pass threshold T2 within the consistency allowable range, and then compares the real-time acquired consistency collaboration index Qsync with the collaboration pass threshold T2 to determine geometric topological consistency. The specific comparison content is as follows:

[0045] When the consistency and coordination index Qsync ≥ coordination passing threshold T2, it means that both geometry and topology are within acceptable ranges and can be directly archived;

[0046] When the consistency and coordination index Qsync < coordination pass threshold T2, it indicates that the overall consistency is insufficient, a deviation anomaly report is generated, staff are prompted to make rectifications, and a re-evaluation is conducted after rectification.

[0047] This invention provides an AI-based 3D consistency verification and collaborative management system for design and construction. It offers the following advantages:

[0048] (1) The system, through its AI-powered design and construction 3D consistency verification and collaborative management system, first achieves high-quality acquisition and reliable evaluation of on-site point cloud data via a data acquisition module and a geometric consistency preliminary evaluation module. By arranging control sampling point sets in the end region, turning radius region, and hole edge ring, and combining optimization strategies for occlusion rate Occ, laser incident angle αinc, and scan overlap rate CoverageCov, the effectiveness and completeness of the point cloud data can be significantly improved. On this basis, the system uses the 95th percentile orientation Hausdorff deviation H95 to perform robust geometric analysis on the registration point cloud set and the 3D drawing BIM model, avoiding judgment distortion due to individual anomalies, and achieving accurate identification of overall geometric deviations. This approach enables rapid detection of construction deviations in the preliminary evaluation stage, reduces manual verification and repeated data collection, thereby improving verification efficiency and data reliability.

[0049] (2) Based on the preliminary geometric assessment that generates a set of suspected inconsistencies R1, the system's topology consistency verification module further introduces a method for extracting and analyzing topological subgraphs. This method normalizes the nodes and edges of the 3D drawing subgraphs and the construction site subgraphs under unified semantic rules and calculates the topology difference rate Rt. This mechanism not only reveals structural problems that are difficult to characterize individually due to geometric deviations, but also clarifies the type and location of differences, such as misaligned supports, incomplete holes, or incorrect component connections. Through the quantitative analysis of the topology difference rate Rt, the system can classify and locate deviations, making the causes of problems clearer, the rectification scope more focused, and prioritizing the handling of differences that have the greatest impact on construction feasibility. This reduces the workload of repeated comparisons across the entire scenario and improves the targeted nature and one-time resolution rate of problem handling.

[0050] (3) In the collaborative correction and review process, the system uses the consistency coordination index Qsync to uniformly measure geometric and topological deviations and compares them with the collaborative pass threshold T2. This index exhibits a continuous and sensitive response to deviation changes, which helps to intuitively reflect the improvement effect after correction. When the consistency coordination index Qsync is below the threshold, the system can automatically generate a rectification task list and push it to the responsible professionals, realizing a complete closed loop of deviation discovery, task issuance, rectification execution, and review archiving. When the consistency coordination index Qsync reaches or exceeds the threshold, it can directly output the pass judgment and archive it. This mechanism effectively unifies the cross-professional quality judgment standards, ensures the dynamic consistency between the construction site and the 3D drawings, reduces rework and downtime, shortens the review cycle, and reduces resource waste and cost input during the construction process. Attached Figure Description

[0051] Figure 1 This is a schematic diagram of the steps of the AI-based design and construction three-dimensional consistency verification and collaborative management system of the present invention.

[0052] Figure 2 The graph shows the consistency and synergy index Qsync function curve. Detailed Implementation

[0053] 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.

[0054] Example 1

[0055] This invention provides an AI-based 3D consistency verification and collaborative management system for design and construction. Please refer to [link / reference]. Figure 1 and Figure 2 It includes a data acquisition module, a geometric consistency initial assessment module, a topological consistency verification module, and a collaborative correction and reassessment module;

[0056] The data acquisition module acquires point cloud data of the construction site and generates a digital twin model of the construction site. At the same time, it deploys a control sampling point set (CPS) and registers the control sampling point set (CPS) to the coordinate system of the 3D drawing BIM model (ModelB) to obtain the registration point cloud set (PS).

[0057] The geometric consistency preliminary assessment module establishes the correspondence between sampling points and BIM model points in 3D drawings, calculates the 95th percentile orientation Hausdorff deviation H95, performs preliminary assessment level classification, and generates a set of suspected inconsistent areas R1 based on the preliminary assessment level classification results.

[0058] The topology consistency verification module receives a set of suspected inconsistent regions R1, extracts the topology subgraphs of the corresponding regions from the 3D drawing BIM model ModelB and the construction site digital twin model ModelS, and defines them as the 3D drawing subgraph Gb and the construction site subgraph Gs, respectively, and calculates the topology difference rate Rt.

[0059] The collaborative correction and review module calculates the consistency collaboration index Qsync based on the topology difference rate Rt, compares the consistency collaboration index Qsync with the collaboration pass threshold T2, and then executes the review mechanism based on the comparison result.

[0060] In this embodiment, the design purpose of the system's data acquisition module is to ensure the accuracy and coverage of the input data. Point cloud data from the construction site is acquired through laser scanning. Without sampling points at the ends, turning radii, and hole rings, key locations are often missing or obstructed, leading to distorted subsequent comparison results. For example, insufficient sampling points at the intersection of ducts and cable trays can easily result in missed deviations. By arranging a control sampling point set (CPS) and performing coordinate registration, not only is a one-to-one correspondence between the site data and the 3D drawings / BIM model (Model B) guaranteed, but geometric misjudgments caused by inconsistent coordinate systems are also avoided, ensuring that the registration point cloud set (PS) accurately reflects the spatial position of on-site components. The core of the geometric consistency initial assessment module is to quantify the geometric deviation between the registration points and the drawing points using the 95th percentile orientation Hausdorff deviation (H95). If the traditional Hausdorff "maximum distance" is used, it is easily dominated by single noise points or scanning errors, making the judgment results overly conservative or even invalid. Using the 95th percentile effectively eliminates the impact of the 5% outlier, capturing most of the "tail risks" while avoiding false alarms caused by extreme points. For example, a 5mm overall deviation in the position of a support bracket will be accurately reflected by the H95, rather than being dominated by an isolated 10cm error. The physical significance of this implementation is that it is closer to the actual construction quality, rather than being interfered with by individual errors. The significance of the topology consistency verification module is to further reveal structural problems in scenarios that cannot be explained by geometric deviations. For example, two ducts may be geometrically reasonable, but if the correct connection relationship is not established, installation problems will still occur in actual construction. Therefore, by extracting the edge set and node set of the 3D drawing sub-map Gb and the construction site sub-map Gs, and calculating the topology difference rate Rt, differences in "relationships" can be clearly pointed out, such as holes not being connected or missing support relationships. This implementation method avoids the "false consistency" problem caused by simply relying on geometric distance judgment, ensuring that the results are more usable for construction. The collaborative correction and review module is a closed-loop processing of the aforementioned results. By using the consistency and synergy index Qsync, geometric and topological deviations are unified into a single quantitative indicator and compared with synergy through a threshold T2, ensuring a single and clear standard for judgment. For example, if Qsync is below the threshold, it indicates insufficient overall consistency, triggering a rectification task list, which is then pushed to the responsible personnel to ensure timely handling and re-inspection of the issues. The real significance of this implementation is that it ensures that construction quality evaluation does not stop at the inspection stage, but forms a closed loop of "inspection—rectification—re-evaluation," ultimately keeping the design and the site dynamically synchronized. In summary, the implementation of each module addresses specific pain points in the construction process: data collection avoids the problem of "incomplete understanding," initial geometric evaluation avoids the problem of "inaccurate understanding," topological verification avoids the problem of "not understanding relationships," and synergy re-evaluation avoids the problem of "only discovering but not solving."The resulting benefits include improved overall review efficiency, reduced rework rate, and significantly enhanced controllability of the construction process.

[0061] Real-time Example 2

[0062] Please see Figure 1 Specifically: the data acquisition module includes a point cloud acquisition unit and a control sampling point layout unit;

[0063] The point cloud acquisition unit performs a full-range scan of the construction site using a laser scanning device to obtain the raw point cloud dataset RawP of the construction area; and performs noise reduction, outlier removal and downsampling on the raw point cloud dataset RawP to obtain the preprocessed point cloud dataset PreP.

[0064] A digital twin model ModelS for the construction site is constructed based on the preprocessed point cloud dataset PreP. Continuous three-dimensional geometric surfaces are generated using point cloud meshing and surface fitting methods. Then, speech segmentation is used to identify the component categories of the three-dimensional geometric surfaces, including classified walls, beams and columns, air ducts, cable trays, supports and hangers, and holes. This achieves a component-level semantic correspondence between the construction site digital twin model ModelS and the three-dimensional drawing BIM model ModelB.

[0065] The sampling point arrangement unit arranges the control sampling point set CPS by using the end region, turning radius region and hole edge ring of each identified component category;

[0066] Point cloud quality data is extracted based on the control sampling point set CPS, and then occlusion and incident optimization strategies are set on the point cloud quality data to optimize the point cloud quality.

[0067] Point cloud quality data includes occlusion rate Occ, laser incident angle ainc, and scan overlap rate CoverageCov;

[0068] The occlusion and incident light optimization strategy requires an occlusion rate of Occ ≤ 25%, a scan overlap rate of CoverageCov ≥ 60%, and a laser incident angle ainc ∈ [20°, 70°].

[0069] Next, the field coordinates S in the control sampling point set CPS are unified with the reference coordinates b in the 3D drawing BIM model ModelB. An initial registration matrix is ​​generated through the initial registration algorithm of feature points, and then fine registration is performed through the nearest point iteration algorithm to obtain the final registration point cloud set PS. The mapping relationship between the point cloud and the model MapC is output to provide input data for the subsequent geometric consistency initial evaluation module.

[0070] In this embodiment, the system's point cloud acquisition unit must denoise and remove outliers from the raw point cloud dataset RawP. This is to avoid false points caused by temporary debris or personnel movement at the construction site. Without processing, these points would be identified as walls or beams, leading to "false deviations" in subsequent geometric comparisons. Downsampling also ensures a uniform distribution of the point cloud, improving processing efficiency. For example, in areas with stacked rebar, unprocessed RawP might mistake the rebar for wall structures, resulting in significant false deviations. Preprocessed PreP, on the other hand, can remove these interfering points, maintaining data accuracy. When controlling the sampling point layout, ends, turning radius areas, and hole rings are specifically selected to identify the most error-prone critical areas. Without sampling at these locations, situations may arise where the overall error is small, but local functionality cannot be met. For example, a duct port deviation of only 5mm might be completely ignored without end sampling points, but could actually prevent flange connection. By strategically deploying the Control Point Set (CPS), similar problems can be detected and avoided in advance. The introduction of three metrics—Occ (occlusion rate), laser incident angle (ainc), and CoverageCov (scan overlap rate)—in point cloud quality optimization ensures the geometric reliability of the sampling points. Excessive occlusion rate leads to key areas being "unseen"; insufficient incident angle causes point cloud stretching and deformation; and insufficient overlap rate results in sparse data and unstable registration. For example, in a densely piped server room, if the scan overlap rate is below 60%, the registration algorithm may experience overall misalignment, while meeting certain conditions ensures stable point cloud alignment. During registration, initial feature point registration is performed first, followed by iterative fine registration using the nearest point. This aims to avoid the accumulation of errors from a single algorithm. Initial registration quickly determines the approximate location but may have centimeter-level errors; iterative optimization further converges the error to the millimeter level. For example, if a cable tray is misaligned by 3cm, initial registration alone might misjudge it as a serious deviation. However, through refined iterative convergence, the error can be reduced to 2mm, accurately reflecting the consistency between the site and the design. Through these implementation methods, the system ensures "data authenticity" during data acquisition, "critical location" during data point placement, "geometric reliability" during quality optimization, and "precise alignment" during registration. The ultimate goal is to avoid false deviations, reduce missed detections, improve comparison accuracy, and ensure that subsequent geometric initial assessments and topology verifications are based on reliable data.

[0071] Real-time Example 3

[0072] Please see Figure 1 Specifically: the geometric consistency preliminary assessment module includes a deviation calculation unit, a consistency preliminary assessment unit, and a preliminary assessment result execution unit;

[0073] The deviation calculation unit calculates the Euclidean distance between the field coordinates S in the control sampling point set CPS and the reference coordinates b in the 3D drawing BIM model ModelB by using the Euclidean distance calculation formula through the correspondence mapping MapC. It also summarizes the Euclidean distances of the registration points in the correspondence mapping MapC to generate a set of Euclidean distances.

[0074] Statistical analysis was performed on the Euclidean distance set, and the 95th percentile value was extracted to obtain the 95th percentile orientation Hausdorff bias H95. The geometric bias level of the overall control sampling point set CPS was then analyzed and analyzed.

[0075] The 95th percentile orientation Hausdorff deviation H95 is calculated and output using the following algorithm formula;

[0076] ;

[0077] In the formula, Quantile 0.95 (·) represents the 95th percentile operator; This represents the Euclidean distance, and min means minimizing it.

[0078] Initial Source (Theory and Classic Algorithm): The 95th percentile orientation Hausdorff bias H95 originates from the orientation Hausdorff distance concept in the fields of metric geometry and computer vision. The classic orientation Hausdorff distance is defined as "the supremum of the minimum distance from a point in one set to another set". It is widely used in scenarios such as target matching, shape comparison, and edge detection evaluation (a common-sense basic concept in mathematics and computer vision). The classic form uses the "maximum value (supremum)" to represent the worst point at the tail. However, in engineering scenarios such as noise, occlusion, and local missing sampling, it is easily dominated by individual outliers.

[0079] The improved formula (engineering quantile improvement) replaces "maximum value" with "95th percentile", resulting in the 95th percentile orientation Hausdorff deviation H95. This improvement balances "tail risk concern" and "robustness to outliers", that is, it retains the overall level of the worst 5% of points, but avoids being infinitely amplified by a very small number of outliers. At the same time, it limits the "direction" to "from the control sampling point set CPS to the 3D drawing BIM model ModelB", which is in line with the engineering semantics of "on-site verification aligned with design benchmarks".

[0080] The initial consistency assessment unit reads the allowable installation deviation value corresponding to the component category through the construction technical specifications. The maximum deviation is set as the upper limit threshold value of the length allowable value Lg1, and the minimum allowable installation deviation value is set as the lower limit threshold value of the length allowable value Lg2.

[0081] The 95th percentile orientation Hausdorff deviation H95 of the registration points in the mapping MapC is traversed and compared with the upper and lower allowable length thresholds Lg1 and Lg2 respectively for preliminary evaluation. Based on the preliminary evaluation comparison results, the deviation level is classified. The specific preliminary evaluation comparison content is as follows:

[0082] When the 95th percentile orientation Hausdorff deviation H95 ≤ the lower limit of the allowable length threshold Lg2, the deviation level is classified as Level A;

[0083] When the lower limit of the length allowable threshold Lg2 < 95th percentile orientation Hausdorff deviation H95 ≤ the upper limit of the length allowable threshold Lg1, the deviation level is classified as level B.

[0084] When the 95th percentile orientation Hausdorff deviation H95 is greater than the upper limit of the length allowable threshold Lg1, the deviation level is classified as level C.

[0085] The initial evaluation results execution unit will implement a response strategy based on the deviation levels identified in the preliminary comparison results. The specific implementation details are as follows:

[0086] When classified as Level A, it passes directly without triggering collaborative correction.

[0087] When classified as Level B, it is added to the watchlist, the data collection quality self-check is initiated, the occlusion and incident radiation optimization strategies are refreshed, and the initial evaluation comparison is re-executed. If it is still classified as Level B, the deviation level is automatically upgraded to Level C.

[0088] When classified as Level C, the current registration point is classified as a suspected point, and all suspected points are summarized and output as a suspected inconsistent region set R1, triggering the topology consistency verification module.

[0089] In this embodiment, the system deviation calculation unit uses the 95th percentile Hausdorff deviation H95 instead of the classic Hausdorff maximum distance to avoid individual noise points dominating the overall result. If the maximum value is directly taken, an isolated outlier may amplify the overall deviation tenfold, leading to misjudgment. The choice of the 95th percentile can take into account the worst 5% of points while maintaining robustness to outliers. For example, points lost due to obstruction at duct corners will not affect the overall assessment, thus truly reflecting the installation accuracy of most components. The consistency initial assessment unit defines the maximum and minimum values ​​of the allowable installation deviation as the upper limit threshold Lg1 and the lower limit threshold Lg2, respectively. The purpose is to transform the vague provisions of industry standards into quantitative and comparable level judgments. Without this grading, all deviations are treated equally, which is not conducive to screening out "critical risk points". Grading allows for differentiated processing: for example, the allowable deviation for beams and columns is more stringent, while that for supports and hangers can be slightly more lenient, avoiding unnecessary rework caused by a one-size-fits-all approach in engineering. The initial assessment result execution unit is configured with a "level B automatically upgraded to level C" logic to prevent risk points that remain in a borderline state for extended periods from repeatedly consuming resources. If a point remains at level B after two self-checks, it indicates a persistent deviation risk and should be directly upgraded to level C for subsequent topology review. For example, if a cable tray location is detected at the deviation boundary twice consecutively, it is likely to cause larger problems during subsequent cable installation. The automatic upgrade mechanism can preemptively classify it into the suspected inconsistency area set R1, avoiding rework in subsequent construction phases. Through this implementation, the geometric consistency initial assessment module achieves a balance between accuracy and risk classification while ensuring robustness. The ultimate effect is reduced false alarms and false negatives, improved detection rate of hidden risk points, and allows subsequent topology reviews to focus only on areas that truly require attention, thus improving detection efficiency and reducing the overall construction rework rate.

[0090] Real-time Example 4

[0091] Please see Figure 1 Specifically: the topology consistency verification module includes a topology subgraph definition unit and a topology difference analysis unit;

[0092] The topology subgraph definition unit receives the suspected inconsistent region set R1 and defines the corresponding spatial range in the 3D drawing BIM model ModelB and the construction site digital twin model ModelS respectively, and extracts the 3D drawing subgraph Gb and the construction site subgraph Gs.

[0093] Based on the spatial extent, the edge set E and node set V of the 3D drawing sub-graph Gb and the construction site sub-graph Gs are identified;

[0094] Among them: node set V identifies the characteristic positions of the endpoints, intersections, support points and reserved hole center points of component categories by using geometric feature detection and component semantic parsing according to the spatial range, forming the 3D drawing sub-graph Gb node set Vb and the construction site sub-graph Gs node set Vs;

[0095] Edge set E is associated with the node root in the 3D drawing subgraph Gb node set Vb and the construction site subgraph Gs node set Vs through the geometric continuous edges, physical connection edges, support edges and through edges, generating the edge set Eb of the 3D drawing subgraph Gb and the edge set Es of the construction site subgraph Gs.

[0096] When two nodes exist continuously in the direction of the geometric center line of the same component, a "geometric continuous edge" is established;

[0097] When two nodes are located on different interconnected components and the endpoint-to-endpoint distance is less than a set threshold, a "physical connection edge" is established.

[0098] When there is a contact relationship between the supporting node and the node of the supported component, a "support edge" is established;

[0099] When a hole node intersects with a component node that passes through the hole, a "through edge" is established.

[0100] Finally, the edge set Eb of the 3D drawing subgraph and the edge set Es of the construction site subgraph are formed, and the semantic classification of the edges is kept consistent in the two types of subgraphs.

[0101] Furthermore, the edge set E and node set V in the 3D drawing subgraph Gb and the construction site subgraph Gs are formatted and standardized to eliminate inconsistencies caused by differences in coordinate systems, data sampling methods, or component numbering, thereby ensuring that the calculation of the topology difference rate Rt is based on unified topological semantic rules.

[0102] The Topology Difference Analysis Unit standardizes the node set V and edge set E in the 3D drawing sub-map Gb and the construction site sub-map Gs. The standardization process includes coordinate normalization, numbering unification, and redundancy resolution.

[0103] Coordinate normalization process unifies the node coordinates of the 3D drawing sub-map Gb and the construction site sub-map Gs to the same reference coordinate system, eliminating deviations caused by differences in coordinate systems.

[0104] The unified numbering process renumbers nodes and edges by using component ID, node type, and spatial adjacency to ensure a one-to-one semantic correspondence between the 3D drawing sub-graph Gb and the construction site sub-graph Gs.

[0105] Redundancy elimination removes isolated nodes, duplicate edges, and abnormally short edges, ensuring the simplicity and comparability of the topological subgraph structure.

[0106] After standardizing the node set V and edge set E, and calculating the output topology difference rate Rt, the edge set E difference between the 3D drawing subgraph Gb and the construction site subgraph Gs is compared.

[0107] Based on the allowable upper limit of the construction project configuration, a benchmark difference rate R0 is set, and then the topology difference rate Rt is compared with the benchmark difference rate R0 to determine the consistency of the topology relationship. Based on the comparison results, a review unit is triggered. The specific comparison content is as follows.

[0108] When the topological difference rate Rt ≤ the baseline difference rate R0, the topological relationship is determined to be consistent and passes the review;

[0109] When the topology difference rate Rt > the baseline difference rate R0, it is determined that there is a significant deviation in the topology relationship. The serialized correction strategy is executed. The serialized correction strategy includes process sequence adjustment, support and hanger decoupling correction, hole resetting and component posture verification, and generates a topology difference report. Then, the specific difference edge information in the suspected inconsistent area set R1 is transmitted to the collaborative correction and review module as the input basis for subsequent process adjustment, local decoupling or component correction.

[0110] The topological difference rate Rt is calculated and output using the following algorithm formula;

[0111] ;

[0112] In the formula, Represents the cardinality of a set;

[0113] Initial Source: The topological difference rate Rt adopts the Jaccard distance concept from the field of set similarity to quantify the degree of difference between two sets. Jaccard similarity comes from classical mathematics and computer science fields such as set theory and information retrieval, and measures the ratio of the intersection of two sets to their union.

[0114] In engineering practice, the elements of the set are defined as "topological edges," that is, the edge set E in the BIM model subgraph Gb of the 3D drawing and the digital twin model subgraph Gs of the construction site are used as the comparison object. The semantics of the edges are limited to one of three categories: "adjacency relationship," "support relationship," and "through relationship," so that the topological difference rate Rt can intuitively reflect "whether the relationship is missing, redundant, or mismatched."

[0115] In this embodiment, the key to implementing the topology consistency verification module is to accurately expose the hidden danger of "geometric approximation is correct but relationship mismatch": First, based on the suspected inconsistent region set R1, a local range is defined within the 3D drawing BIM model ModelB and the construction site digital twin model ModelS, and the 3D drawing sub-map Gb and the construction site sub-map Gs are extracted. The reason for only doing local extraction is to reduce noise and false alarms and concentrate the calculation on high-risk areas; then, the node sets Vb and Vs are constructed using endpoints, intersections, support points, and reserved hole centers, because these locations bear the "constructability" constraints such as installation continuity and force transmission, and can directly reflect the real physical reality. The relationship is not purely geometric distance; then, edge sets Eb and Es are generated using geometrically continuous edges, physically connected edges, supporting edges, and penetrating edges. The purpose is to explicitly encode the engineering semantics of "whether it can be installed, whether it can be supported, and whether it can pass through," avoiding false consistency such as "very close distance but not connected." Next, coordinate normalization, numbering unification, and redundancy resolution are performed to eliminate false differences caused by differences in coordinate systems and IDs, and to clean up the virtual height of the union caused by abnormal short edges, ensuring that the topological difference rate Rt is based on the same semantic caliber. Finally, the topological difference rate Rt is compared with the benchmark difference rate R0 to directly quantify the relationship deviation and trigger the serialization correction strategy (penetrating first, then supporting, then adjacent). For example, if a cable tray needs to cross a duct, the 3D drawing sub-drawing Gb has a continuous edge connecting the "hole node to the cable tray node," but the construction site sub-drawing Gs lacks this edge. In reality, the hole is not drilled or it is misaligned by 15mm. Even if the Euclidean distance is very small, it will be judged as a difference edge, causing the topology difference rate Rt to increase and triggering hole resetting first. By following this path, the problem of "geometrically correct but actually cannot be installed" can be effectively avoided. The direct effect is more accurate difference positioning, smaller rectification scope, shorter review cycle, and a significant reduction in rework rate.

[0116] Real-time Example 5

[0117] Please see Figure 1 and Figure 2 Specifically: the collaborative correction and review module includes a collaborative correction unit and a review unit;

[0118] The collaborative correction unit calculates consistency based on the topological difference rate Rt and the 95th percentile orientation Hausdorff deviation H95 after the serialized correction strategy is executed, obtains the consistency coordination index Qsync, and performs quantitative analysis to determine the consistency between the design, actual construction, and drawings after the serialized correction strategy is executed.

[0119] The consistency and synergy index Qsync is calculated and output using the following algorithm formula;

[0120] ;

[0121] In the formula, exp represents an exponential function;

[0122] The consistency and synergy index Qsync adopts the idea of ​​"multi-index normalization and synthesis": geometric deviation and topological deviation are dimensionless respectively, synthesized in the same scale space, and obtained as a similarity index in the (0,1] interval through exponential mapping. This idea comes from the "Euclidean synthesis + exponential similarity mapping" approach commonly used in mathematical and engineering evaluation. It has the characteristics of continuity, monotonicity and easy interpretation. The exponential function exp is used because it is derived from the classical kernel function in mathematics, can keenly reflect deviation and provide smooth continuity in engineering, and conforms to the actual law that "the greater the deviation, the exponentially increase the risk" in quality management. Therefore, it is the optimal choice for synthesizing geometric deviation and topological deviation.

[0123] The review unit sets a collaboration pass threshold T2 within the consistency allowable range, and then compares the real-time acquired consistency collaboration index Qsync with the collaboration pass threshold T2 to determine geometric topological consistency. The specific comparison content is as follows:

[0124] When the consistency and coordination index Qsync ≥ coordination passing threshold T2, it means that both geometry and topology are within acceptable ranges and can be directly archived;

[0125] When the consistency and coordination index Qsync < coordination pass threshold T2, it indicates that the overall consistency is insufficient, a deviation anomaly report is generated, staff are prompted to make rectifications, and a re-evaluation is conducted after rectification.

[0126] In this embodiment, the key to implementing the system's collaborative correction and review module lies in integrating geometric and topological deviation results into a quantifiable comprehensive index. The design intent of the consistency coordination index Qsync is to avoid misleading judgments based on a single dimension: if only the geometric deviation H95 is considered, a deviation less than 10mm might be considered acceptable, but if there are topological misalignments in the pipeline (e.g., the cable tray and supports lack effective support edges), it will still prevent actual construction. By normalizing H95 and the topological difference rate Rt and then using the exponential function exp for nonlinear mapping, the impact of high-risk deviations can be visually amplified in the consistency coordination index Qsync value. For example, when the ratio of H95 to Lg is only 0.2, while Rt exceeds twice R0, the consistency coordination index Qsync will quickly drop below 0.3, clearly indicating that although the dimensions of the area match, the relationship is invalid, thus triggering rectification. The review unit sets a coordination threshold T2 to provide a clear boundary for engineering decisions. A threshold that is too low will lead to a large number of meaningless rectifications, increasing costs; a threshold that is too high will overlook key risk points. In practice, the importance of component categories is considered. For example, a coordination threshold T2 ≥ 0.85 may be required for main beam and column joints, while a coordination threshold T2 ≥ 0.75 is acceptable for secondary pipelines. This approach aims to balance construction costs and structural safety. For instance, when the consistency coordination index Qsync = 0.8 and the coordination threshold T2 = 0.75 for duct supports and hangers, it can be directly archived. However, if misalignment of cable tray holes leads to a consistency coordination index Qsync = 0.7 while the coordination threshold T2 is set to 0.85, a deviation report will inevitably be triggered, and a re-evaluation will be arranged. Overall, this implementation method achieves a closed-loop logic of "correcting deviations first, then quantifying, then making decisions," ensuring dual consistency between the construction site and 3D drawings in terms of geometric accuracy and structural relationships. The ultimate effect is a significant reduction in rework rates and delay risks, improved coordination management capabilities, and clear definition of responsibility and risk levels for each re-evaluation, thereby achieving efficient and controllable construction consistency management.

[0127] 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. An AI-based design and construction three-dimensional consistency review and collaborative management system, characterized in that: The method comprises a data acquisition module, a geometric consistency preliminary evaluation module, a topological consistency review module, and a collaborative correction and reevaluation module. The data acquisition module acquires point cloud data of the construction site and generates a digital twin model of the construction site, arranges a control sampling point set CPS, and registers the control sampling point set CPS to a three-dimensional drawing BIM model ModelB coordinate system to obtain a registration point cloud set PS. The geometric consistency preliminary evaluation module establishes a correspondence between the sampling points and the three-dimensional drawing BIM model points, calculates a 95th percentile directional Hausdorff deviation H95, and performs preliminary grade division, and generates a suspected inconsistent region set R1 based on the preliminary grade division result. The topological consistency review module receives the suspected inconsistent region set R1, extracts the topological subgraph of the corresponding region from the three-dimensional drawing BIM model ModelB and the digital twin model of the construction site ModelS, respectively defines the three-dimensional drawing subgraph Gb and the construction site subgraph Gs, and calculates the topological difference rate Rt. The collaborative correction and reevaluation module calculates a consistency collaboration index Qsync according to the topological difference rate Rt, compares the consistency collaboration index Qsync with a collaborative passing threshold T2, and executes a reinspection mechanism based on the comparison result. The consistency collaboration index Qsync is calculated by the following algorithm formula: ； In the formula, exp represents an exponential function, H95 represents a 95th percentile directional Hausdorff deviation, Rt represents a topological difference rate, and R0 represents a reference difference rate. 2.The AI-based design and construction three-dimensional consistency review and collaborative management system according to claim 1, characterized in that: The data acquisition module comprises a point cloud acquisition unit and a control sampling point arrangement unit. The point cloud acquisition unit performs omnidirectional scanning on the construction site by a laser scanning device to obtain an original point cloud data set RawP of the construction area, and performs denoising, outlier removal, and downsampling processing on the original point cloud data set RawP to obtain a preprocessed point cloud data set PreP. Based on the preprocessed point cloud data set PreP, a digital twin model of the construction site ModelS is constructed, and a continuous three-dimensional geometric surface is generated by using point cloud gridding and surface fitting methods, and the component categories of the three-dimensional geometric surface are identified by using voice segmentation, wherein the component categories include classified walls, beams and columns, air pipes, bridge frames, support hangers, and holes. 3.The AI-based design and construction three-dimensional consistency review and collaborative management system according to claim 2, characterized in that: The sampling point arrangement unit arranges the control sampling point set CPS based on the end region, the turning radius zone, and the hole edge ring of each identified component category. Point cloud quality data is extracted based on the control sampling point set CPS, and the point cloud quality data is subjected to a shielding and incidence optimization strategy for point cloud quality optimization. The point cloud quality data includes an occlusion rate Occ, a laser incidence angle ainC, and a scanning overlap rate CoverageCov. The shielding and incidence optimization strategy requires that the occlusion rate Occ≤25%, the scanning overlap rate CoverageCov≥60%, and the laser incidence angle ainC∈[20°, 70°]. Then, the field coordinates S in the control sampling point set CPS are aligned with the reference coordinates b in the three-dimensional drawing BIM model ModelB, an initial registration matrix is generated through a feature point initial registration algorithm, and a final registration point cloud set PS is obtained through a nearest point iteration algorithm, and a corresponding relationship mapping MapC between the point cloud and the model is output. 4.The AI-based design and construction three-dimensional consistency review and collaborative management system according to claim 1, characterized in that: The geometric consistency preliminary evaluation module comprises a deviation calculation unit, a consistency preliminary evaluation unit and a preliminary evaluation result execution unit; The deviation calculation unit calculates the Euclidean distance between the field coordinates S in the control sampling point set CPS and the reference coordinates b in the three-dimensional drawing BIM model ModelB using the Euclidean distance calculation formula based on the corresponding relationship mapping MapC, and the Euclidean distances of the registration points in the corresponding relationship mapping MapC are summarized to generate a Euclidean distance set. The Euclidean distance set is statistically analyzed, and the 95% quantile value is extracted to obtain the 95 quantile directional Hausdorff deviation H95, which quantitatively analyzes the geometric deviation level of the control sampling point set CPS as a whole. 5.The AI-based design and construction three-dimensional consistency review and collaborative management system according to claim 4, characterized in that: The consistency preliminary evaluation unit reads the installation allowed deviation value corresponding to the component category from the construction technical specification, wherein the maximum deviation value is set as the length allowed upper limit value threshold Lg1, and the minimum installation allowed deviation value is set as the length allowed lower limit value threshold Lg2. The 95 quantile directional Hausdorff deviation H95 of the registration points in the corresponding relationship mapping MapC is traversed, and is compared with the length allowed upper limit value threshold Lg1 and the length allowed lower limit value threshold Lg2 respectively, and the deviation level is divided based on the preliminary evaluation comparison result; the specific preliminary evaluation comparison content is as follows: When the 95 quantile directional Hausdorff deviation H95 is less than or equal to the length allowed lower limit value threshold Lg2, the deviation level is divided into level A; When the length allowed lower limit value threshold Lg2 is less than the 95 quantile directional Hausdorff deviation H95 and the 95 quantile directional Hausdorff deviation H95 is less than or equal to the length allowed upper limit value threshold Lg1, the deviation level is divided into level B; When the 95 quantile directional Hausdorff deviation H95 is greater than the length allowed upper limit value threshold Lg1, the deviation level is divided into level C. 6.The AI-based design and construction three-dimensional consistency review and collaborative management system according to claim 5, characterized in that: The preliminary evaluation result execution unit executes the response strategy according to the deviation level divided by the preliminary comparison result, and the specific execution content is as follows: When it is divided into level A, it is directly passed without triggering the collaborative correction; When it is divided into level B, it is listed in the attention list at this time, the acquisition quality self-check is started, the occlusion and incidence optimization strategy is refreshed, the preliminary evaluation comparison is re-executed, and if it still belongs to level B, the deviation level is automatically upgraded at this time; When it is divided into level C, the current registration point is divided into a suspected point at this time, all suspected points are summarized to output a suspected inconsistent area set R1, and the topological consistency review module is triggered. 7.The AI-based design and construction three-dimensional consistency review and collaborative management system according to claim 6, characterized in that: The topological consistency review module comprises a topological subgraph definition unit and a topological difference analysis unit; The topology subgraph definition unit extracts the three-dimensional drawing subgraph Gb and the construction site subgraph Gs by receiving the suspected inconsistent region set R1 and defining the corresponding spatial range in the three-dimensional drawing BIM model ModelB and the construction site digital twin model ModelS respectively; Then the edge set E and the node set V of the three-dimensional drawing subgraph Gb and the construction site subgraph Gs are identified according to the spatial range; Wherein: the node set V is identified by using geometric feature detection and component semantic analysis according to the spatial range to identify the feature positions of the end points, intersection points, support points and reserved hole center points of the component category, forming the node set Vb of the three-dimensional drawing subgraph Gb and the node set Vs of the construction site subgraph Gs; The edge set E is generated by associating the geometric continuous edges, physical connection edges, support edges and through edges between the nodes in the node set Vb of the three-dimensional drawing subgraph Gb and the node set Vs of the construction site subgraph Gs. And the edge set E and the node set V in the three-dimensional drawing subgraph Gb and the construction site subgraph Gs are formatted and standardized. 8.The AI-based design and construction three-dimensional consistency review and collaborative management system according to claim 7, characterized in that: The topology difference analysis unit performs standardization processing on the node set V and the edge set E in the three-dimensional drawing subgraph Gb and the construction site subgraph Gs; the standardization processing includes coordinate normalization processing, number unification processing and redundancy elimination processing; Then the node set V and the edge set E after standardization processing are calculated to output the topology difference rate Rt, and the edge set E difference between the three-dimensional drawing subgraph Gb and the construction site subgraph Gs is compared; Based on the allowed upper limit of the construction project configuration, the reference difference rate R0 is set, and then the topology difference rate Rt and the reference difference rate R0 are compared for topology relationship consistency, and based on the comparison result, the reevaluation unit is triggered, and the specific comparison content is as follows: When the topology difference rate Rt is less than or equal to the reference difference rate R0, it is determined that the topology relationship is consistent and is reviewed; When the topology difference rate Rt is greater than the reference difference rate R0, it is determined that there is a significant deviation in the topology relationship, and a serialized correction strategy is executed, which includes process sequence adjustment, support and hanger decoupling correction, hole resetting and component posture review, and a topology difference report is generated, and the specific difference edge information in the suspected inconsistent region set R1 is transmitted to the collaborative correction and reevaluation module. 9.The AI-based design and construction three-dimensional consistency review and collaborative management system according to claim 8, characterized in that: The collaborative correction and reevaluation module includes a collaborative correction unit and a reevaluation unit. The collaborative correction unit calculates the consistency based on the topology difference rate Rt and the 95th quantile oriented Hausdorff deviation H95 after the serialized correction strategy is executed, obtains the consistency collaborative index Qsync, and quantitatively analyzes the consistency between the actual construction and the drawing after the serialized correction strategy is executed. 10.The AI-based design and construction three-dimensional consistency review and collaborative management system according to claim 9, characterized in that: The reevaluation unit sets the collaborative passing threshold T2 through the consistency allowed range, compares the real-time obtained consistency collaborative index Qsync with the collaborative passing threshold T2, judges the geometric topology consistency, and the specific comparison content is as follows: When the consistency collaborative index Qsync is greater than or equal to the collaborative passing threshold T2, it means that both the geometry and the topology are within the acceptable range, and it is directly archived. When the consistency coordination index Qsync is less than the coordination passing threshold T2, it indicates that the overall consistency is insufficient, a deviation anomaly report is generated, the staff is prompted to make rectification, and reevaluation is performed after rectification.

Images