Underwater structure volume measurement method and system based on improved MVSnet

Abstract

This invention belongs to the fields of computer vision, 3D reconstruction, and engineering quantitative assessment, specifically relating to a method and system for underwater structure volume measurement based on an improved MVSNet. It includes: S1, inputting multi-view images of the underwater structure to be measured; S2, performing 3D reconstruction based on the improved MVSNet; S3, volume measurement, constructing a 3D mesh model using the Delaunay triangulation method, and calculating the volume of the underwater structure corresponding to the 3D mesh model using the projected volume method. This invention establishes a complete technical flow from multi-view image input to 3D volume output, improving the accuracy of 3D reconstruction and the stability of volume calculation, while simplifying the volume calculation process and enhancing the convenience of engineering implementation. It is applicable to scenarios such as underwater engineering inspection, structural measurement, cultural relic modeling, and defect volume assessment. This method provides a solution for non-contact 3D volume measurement and can handle targets without a pre-existing 3D model.

Description

Technical Field

[0001] This invention belongs to the fields of computer vision, 3D reconstruction and engineering quantitative evaluation technology, specifically involving an underwater structure volume measurement method and system based on an improved MVSnet. Background Technology

[0002] With the development of 3D vision measurement technology, 3D reconstruction methods based on multi-view images have been widely applied in fields such as engineering inspection, structural measurement, cultural relic modeling, and target surface morphology restoration. Existing 3D reconstruction methods typically recover camera pose by feature matching between multi-view images and further estimate the 3D geometry of the target surface to obtain a point cloud model or mesh model. In volume measurement tasks, the 3D reconstruction results can also be further used for target volume calculation, damage area identification, and volume loss assessment, offering advantages such as non-contact operation, visualization, and adaptability to complex surfaces.

[0003] However, existing technologies still have the following shortcomings when applied to the volume measurement of structural surfaces: First, traditional multi-view stereo matching methods are prone to inaccurate depth estimation and incomplete point clouds in areas with weak texture, complex boundaries, and significant scale changes, thus affecting the accuracy of subsequent volume calculations. Second, dense point clouds typically contain mismatched points, outliers, and local noise points, which can easily lead to surface model distortion if directly used for mesh construction. Third, existing volume calculation methods often suffer from complex calculation processes, sensitivity to mesh quality, or significant engineering implementation difficulties when dealing with irregular 3D surfaces. Therefore, there is an urgent need to propose a volume measurement method that can balance 3D reconstruction accuracy, mesh quality, and volume calculation stability to meet the application requirements for quantitative 3D measurement of structures in engineering scenarios. Summary of the Invention

[0004] To address the problems of insufficient reconstruction accuracy in weak texture regions, significant noise interference from dense point clouds, poor stability of mesh models, and difficulty in calculating the volume of complex surfaces in existing 3D reconstruction volume measurement methods, this paper proposes a high-precision, robust 3D reconstruction and volume measurement method suitable for complex underwater engineering scenarios, enabling complete, accurate, and stable volume quantification calculation of structures.

[0005] The technical solution adopted by this invention to solve its technical problem is based on an improved underwater structure volume measurement method using MVSnet, which includes the following steps: S1. Input a multi-view image of the underwater structure to be measured; S2. 3D reconstruction based on improved MVSNet: First, sparse reconstruction is performed using the incremental SfM method and sparse point cloud is output. Then, dense reconstruction is performed using improved MVSNet and dense point cloud is output. The improved MVSNet network includes a feature pyramid network and a multi-scale convolutional branch module. S3. Volume measurement: A three-dimensional mesh model is constructed using the Delaunay triangulation method, and the volume of the underwater structure corresponding to the three-dimensional mesh model is calculated using the projected volume method.

[0006] Preferably, in step S2, the SIFT algorithm is first used to extract feature points and generate descriptors for the multi-view image; then sparse reconstruction is performed, and the camera intrinsic and extrinsic parameters are recovered through feature matching relationships. The image registration, triangulation and local bundle adjustment are gradually completed, and finally the sparse point cloud and accurate camera pose are output.

[0007] Preferably, in step S2, the feature pyramid network generates three-level multi-scale feature maps P1, P2, and P3 through multi-level feature fusion. The feature maps P1, P2, and P3 are used for depth estimation in order from coarse to fine: P3 is used for coarse-scale depth estimation in the first stage, P2 is used for meso-scale depth refinement in the second stage, and P1 is used for high-resolution fine reconstruction in the third stage.

[0008] Preferably, in step S2, the multi-scale convolution branch module extracts multiple receptive field features through parallel convolution and fuses them to output enhanced features.

[0009] Preferably, in step S2, the multi-scale convolutional branch module performs feature enhancement: the input feature map is convolved with 3×3 and 5×5 respectively to obtain two sets of 64-channel feature maps, and the channel dimension is concatenated to form a 128-channel fused feature map. Then, it is refined by 3×3 convolution, and then concatenated with the feature output of the 7×7 convolution branch to form a 128-channel feature map. After normalization, the number of channels of the concatenated feature map is reduced from 128 to 64 by 1×1 convolution, and the fused feature map is output by the LeakyReLU activation function.

[0010] Preferably, in step S3, the dense point cloud is first filtered to obtain an optimized point cloud, then a three-dimensional mesh model is constructed and optimized, and finally the projected volume method is used for calculation.

[0011] Preferably, step S2 includes: S21. First, perform SIFT feature extraction on the input image sequence and construct feature descriptors. Then, establish the matching relationship between images through SIFT feature matching. S22. Initialize reconstruction: First, construct an image connection graph based on the matching relationship between images. Then, select initial image pairs, perform preliminary camera pose estimation, and restore the relative motion relationship between the two views. Finally, generate initial 3D points through triangulation and perform local bundle adjustment. S23. Incremental reconstruction: First, incremental camera pose estimation is performed and incorporated into the current reconstruction system. Then, triangulation is performed based on the new image observation information to supplement the 3D point cloud. Next, error accumulation is eliminated through local bundle adjustment. Finally, all camera parameters and 3D points are optimized through global bundle adjustment to output sparse point cloud and camera pose. S24. Dense Reconstruction: First, the feature pyramid network extracts multi-scale original feature maps through a bottom-up convolutional encoding process. Then, through lateral connections and top-down progressive upsampling fusion, it merges the high-frequency local details in the shallow layer with the low-frequency global semantic information in the deep layer, outputting a multi-scale pyramid feature map from coarse to fine. Next, the multi-scale convolutional branch module constructs parallel multi-scale feature extraction paths to adaptively extract feature information from different receptive fields. It constructs an aggregate cost body through feature enhancement, and obtains the ground truth depth map of the reference view through regularization and depth regression. Finally, it fuses the data to generate a dense point cloud.

[0012] Preferably, in step S3, the optimization of the three-dimensional mesh model includes: mesh smoothing, edge flipping optimization, hole repair, texture mapping, and mesh refinement.

[0013] Preferably, step S3 includes: S31. Divide the surface of the three-dimensional mesh model into several local triangular patches, and treat each triangular patch as a tiny volume unit; S32. Set a certain reference plane as the projection plane, and project the triangular facets of the three-dimensional mesh model onto the projection plane to form several triangles on the projection plane; S33. Divide the triangle on the projection plane into triangular units, and calculate the volume of each triangular unit by combining the area of ​​the triangle and the height information of its corresponding vertices. S34. The overall volume is obtained by summing the volumes of all triangular units.

[0014] An underwater structure volume measurement system based on an improved MVSNet, applied to the above method, includes: The feature extraction and matching module is used to perform SIFT feature point extraction, descriptor generation and matching, and remove mismatches to obtain high-quality matching results; The sparse reconstruction module is used to perform incremental SfM reconstruction and output sparse point cloud and camera pose. The dense reconstruction module incorporates an improved MVSNet network with a feature pyramid network and multi-scale convolutional branch modules to generate dense point clouds. The point cloud optimization module is used to perform statistical outlier filtering to remove noise points and obtain an optimized point cloud. The volume calculation module is used to perform Delaunay triangulation, mesh optimization, and projected volume calculation to output the volume of the underwater structure.

[0015] Compared with the prior art, the present invention has the following beneficial effects: 1. This invention achieves accurate volume measurement after 3D reconstruction, using multi-view images as input and ultimately outputting the target volume, focusing on a "complete measurement process from image to volume." Based on improved MVSNet multi-view stereo matching, it combines point cloud filtering, Delaunay triangulation, and projected volume methods to achieve a complete calculation process from image to point cloud, mesh, and finally volume. This process overcomes the limitations of traditional methods that only focus on 3D reconstruction, realizing quantitative engineering from image to volume calculation. The entire technology chain is seamlessly integrated, from image data preparation to final loss quantization, requiring no manual intervention and possessing feasibility for engineering applications.

[0016] 2. This invention introduces the FPN feature pyramid network and the MSDB multi-scale convolution branch module on the basis of the MVSNet network, which enhances the network's ability to express features in weak texture regions, complex boundary regions and scale-changing regions, thereby improving the completeness of dense reconstruction results and the accuracy of depth estimation.

[0017] 3. Before volume measurement, this invention performs optimization processing such as statistical outlier filtering on dense point clouds, which can effectively remove outlier noise points, improve point cloud quality, and enhance the continuity and stability of point cloud distribution, providing a more reliable data foundation for subsequent 3D mesh construction.

[0018] 4. This invention uses the Delaunay triangulation method to construct a three-dimensional mesh model, which can avoid the generation of slender triangles or distorted elements as much as possible, improve the geometric quality and topological stability of the mesh, and thus reduce the volume calculation error caused by mesh degradation.

[0019] 5. This invention combines Delaunay triangulation with the projected volume method, transforming the complex three-dimensional volume problem into an area integration problem on the projection plane. The calculation process is clear, the implementation method is simple, and the calculation efficiency is high. It is particularly suitable for volume measurement of irregular structures in engineering scenarios.

[0020] In summary, this invention constructs a complete technical process from multi-view image input to 3D volume output, improving the accuracy of 3D reconstruction and the stability of volume calculation, especially in image degradation datasets. It also simplifies the volume calculation process, enhancing the convenience of engineering implementation, and is applicable to scenarios such as underwater engineering inspection, structural measurement, cultural relic modeling, and defect volume assessment. This method provides a solution for non-contact 3D volume measurement, adapting to fields such as underwater concrete structures, cultural relics, and industrial parts that require rapid volume acquisition from images, and can handle targets without pre-existing 3D models. Attached Figure Description

[0021] Figure 1 This is a flowchart of the SfM sparse reconstruction process in this invention.

[0022] Figure 2 This is a diagram showing the reconstruction results of the SfM coefficients.

[0023] Figure 3 This is an improved MVSNet dense reconstruction network diagram.

[0024] Figure 4 This is a diagram of the feature pyramid network structure.

[0025] Figure 5 This is a block diagram of the MSDB module.

[0026] Figure 6 This is a schematic diagram of the dense reconstruction effect. The left image is a real picture of the structure, and the right image is a dense point cloud model after dense reconstruction.

[0027] Figure 7 This is a flowchart of point cloud filtering.

[0028] Figure 8 These are mesh model diagrams of a concrete structure. The left image is the point cloud model after statistical outlier filtering, and the right image is the 3D mesh model.

[0029] Figure 9 This is a schematic diagram of mesh repair. The left image is the 3D model before repair, the middle image shows the target area to be repaired and filled, and the right image is the 3D model after repair.

[0030] Figure 10 It is a schematic diagram of the geometric structure of a columnar body. Detailed Implementation

[0031] To facilitate understanding of the present invention, it will be described in more detail below with reference to the accompanying drawings and specific embodiments. However, the present invention can be implemented in many different forms and is not limited to the embodiments described in this specification. Rather, these embodiments are provided to provide a more thorough and complete understanding of the disclosure of the present invention.

[0032] This invention relates to computer vision, 3D reconstruction, and engineering quantitative evaluation technologies, specifically to a multi-view structure suitable for underwater scenarios. Figure 3 The reconstruction and volume loss assessment methods are particularly suitable for morphological restoration, volume measurement and quantitative loss analysis of underwater engineering structures, cultural relics and biological habitats, and can be applied to scenarios such as marine engineering monitoring, cultural relic protection and marine disaster loss assessment.

[0033] In summary, this invention achieves accurate volume measurement after 3D reconstruction, using multi-view images as input and ultimately outputting the target volume, focusing on a "complete measurement process from image to volume." It utilizes an improved MVSNet multi-view stereo matching network as its core, combined with point cloud filtering, Delaunay triangulation, and projected volume methods to achieve a complete calculation process from image to point cloud, mesh, and finally volume. This process overcomes the limitations of traditional methods that only focus on 3D reconstruction, realizing quantitative engineering from image to volume calculation. The entire technology chain is seamlessly integrated, from image data preparation to final loss quantization, requiring no manual intervention and possessing feasibility for engineering applications. A detailed introduction follows.

[0034] This application involves 3D reconstruction and volume measurement. First, an image dataset is created. Then, dense reconstruction is performed based on an improved MVSNet to obtain the target 3D point cloud. Subsequently, point cloud filtering, Delaunay triangulation, and projective volume method are combined to achieve accurate estimation of the structure's volume.

[0035] I. Construction of Multi-Type Underwater Image Datasets The dataset used in this experiment comes from a 3D concrete mesh model with volume loss created using 3ds Max 2022 software. The three-axis dimensions of this 3D mesh model in the spatial coordinate system are 7.1, 6.9, and 50, corresponding to a model volume of 1455. To obtain a realistic model suitable for experimental measurement, this application uses 3D printing to scale it proportionally, controlling the longest side (corresponding to the Z-axis direction) to 20 cm. Since the geometric proportions of the model remain unchanged during printing, its linear scaling factor can be obtained from the ratio of the longest side after printing to the longest side of the original model, which is approximately 0.4. Under the condition of scaling the linear scale by a factor of 0.4, the dimensions of the model in all three directions are correspondingly reduced to 0.4 times the original size. Therefore, the length, width, and height of the printed model are approximately 2.84 cm, 2.76 cm, and 20 cm, respectively. Furthermore, since volume is a three-dimensional quantity, its change is proportional to the cube of the linear scaling factor; therefore, the corresponding volume scaling factor is approximately 0.064. Finally, multiplying the original model volume of 1455 by this scaling factor, the volume of the printed model is approximately 93.12 cm³. 3 Therefore, while maintaining geometric similarity, by scaling down the original 3D mesh model and printing it as a solid model with a longest side of 20cm, its corresponding volume can be determined to be 93.12cm². 3 This value can be used as a true reference value in subsequent volume measurement experiments.

[0036] The shooting equipment was set to 1080P@30fps video recording mode, with each frame being 720×1280 pixels. During the data preprocessing stage, distortion correction was performed on all images. Intrinsic calibration parameters were used to correct radial and tangential distortion, mitigating the potential impact of this issue on the accuracy of 3D modeling at its source. Operators walked at a natural speed, shooting in a 50cm radius circle to ensure that the viewing angle difference between adjacent video frames remained between 8° and 15°. After three cyclical shooting angles from top to bottom and filtering, a total of 94 valid images were obtained. The original dataset was named "Origin," meeting the basic requirements for 3D reconstruction.

[0037] First, using a computer equipped with a processor, the acquired images of structures in the air are input into the WaterGAN style transfer network. The network extracts color attenuation and light scattering features from real underwater images to perform style rendering on the air images, generating synthetic images with underwater optical properties.

[0038] Secondly, combined with histogram equalization, basic color space conversion and data preprocessing are performed on the image. Channel-level adjustments are then made using a color attenuation simulation module. This process enhances the blue channel and suppresses the intensity of the red and green channels, simulating the differences in water absorption of different wavelengths of light, resulting in an overall blue-green hue common in underwater environments. This achieves a preliminary color mapping from air images to underwater images.

[0039] After simulating color distortion, the model further incorporates contrast adjustment and brightness redistribution operations to simulate the impact of water scattering on the image. In an underwater environment, suspended particles cause light scattering, resulting in a fog-like effect and reduced overall contrast. Therefore, traditional methods typically employ histogram equalization enhancement algorithms to adjust the image's brightness channels, preserving underwater visual characteristics while maintaining a certain level of recognizability, thus making the generated image closer to realistic underwater imaging.

[0040] After completing the color distortion and scattering simulations, the system finally outputs images with underwater visual characteristics. This not only provides a large number of training samples for underwater image processing algorithms, but also provides an important experimental basis for studying the mechanism of underwater visual degradation.

[0041] II. 3D Reconstruction Based on Improved MVSNet In the surface reconstruction section, this method constructs a complete multi-view structure. Figure 3 The 3D reconstruction process includes feature point extraction, feature point matching, SfM sparse reconstruction, and improved MVSNet dense reconstruction.

[0042] First, in the feature processing stage, the SIFT (Scale Invariant Feature Transform) algorithm is used for keypoint detection and descriptor extraction.

[0043] An incremental SfM (Structure of Motion) method is employed for sparse reconstruction. This process recovers camera intrinsic and extrinsic parameters through feature matching, progressively completing image registration, triangulation, and local bundle adjustment, ultimately outputting a sparse point cloud and accurate camera pose, providing geometric priors for subsequent dense reconstruction.

[0044] like Figure 3 As shown, to address the shortcomings of traditional MVSNet in feature matching for weak underwater textures and complex boundary regions, this application makes a deep innovation to the original network architecture in the dense reconstruction stage. The core innovation lies in the coupling of FPN (Feature Pyramid Network) with an innovatively designed MSDB (Multi-Scale Convolutional Branch Module). This improvement significantly enhances the network's feature representation capability under harsh imaging conditions, and its innovative significance is specifically reflected in the following two dimensions: First, the introduction of the FPN module enables deep fusion of semantics and details across layers. Traditional networks often struggle to balance receptive field size and feature resolution, while FPN, through bottom-up feature encoding and top-down semantic propagation, combined with lateral connection mechanisms, successfully fuses shallow high-frequency local details (such as structure edges and micro-textures) with deep low-frequency global semantic information. The multi-scale hierarchical features output by this structure, from coarse to fine, provide accurate geometric priors for subsequent cascaded deep inference, effectively overcoming the problem of feature recognition difficulties caused by low contrast in underwater images.

[0045] Secondly, the cascaded MSDB module enables parallel perception across multiple receptive fields at the same level. Addressing the issues of drastic scale changes and local distortions in underwater structures, the MSDB module innovatively constructs parallel multi-scale feature extraction paths. It uses 3×3 convolutions to finely capture local micro-textures, 5×5 convolutions to transition between mesoscale structures, and independent 7×7 large-size convolutional kernels to force the acquisition of a wide range of global context and overall contour information. Subsequently, dimensionality reduction and recombination are performed through cross-channel stitching, batch normalization, and 1×1 convolutions. This multi-path parallel design endows the network with extremely strong scale adaptability, compensating for the limitations of a single convolutional kernel in terms of field of view.

[0046] The synergy between FPN and MSDB breaks through the bottleneck of feature extraction based on a single scale and receptive field. This dual enhancement mechanism enables it to extract more discriminative and robust fused features when facing typical underwater weak-texture regions, complex boundary regions, and regions with drastic scale changes. This not only fundamentally improves the construction quality of the 3D cost volume but also significantly enhances the accuracy of depth regression, laying a solid algorithmic foundation for the final output of a high-fidelity dense point cloud.

[0047] III. Volume Measurement and Quantitative Assessment of Structural Loss After obtaining the dense point cloud, this application further conducts volume measurement research to achieve quantitative analysis of the three-dimensional morphology and volume changes of the target structure. Since dense reconstruction results typically contain a small number of mismatched points, isolated noise points, and locally discrete points, directly using them for subsequent mesh construction and volume calculation can easily cause surface distortion and boundary deviations, thus affecting measurement accuracy. Therefore, the point cloud is first processed using Statistical Outlier Removal (SOR). This method calculates the average distance between each point and its neighboring points and combines this with the overall distribution characteristics to determine whether a point is an outlier, removing noise points that significantly deviate from the point cloud distribution. After filtering, the continuity and stability of the point cloud are improved, providing a more reliable data foundation for subsequent three-dimensional model reconstruction.

[0048] After point cloud denoising, this application employs the Delaunay triangulation method to construct a 3D mesh model. This method generates a relatively regular triangular mesh based on the discrete distribution of point sets, minimizing the occurrence of slender triangles or distorted units, thereby improving the geometric quality and structural stability of the mesh. For complex structures, a high-quality mesh not only helps to realistically reflect the spatial contour of the target but also reduces the adverse effects of local reconstruction errors on volume estimation. After the initial mesh generation, this application further improves the model through operations such as mesh smoothing, edge flipping optimization, hole repair, texture mapping, and mesh refinement. Among these, mesh smoothing enhances surface continuity, hole repair improves model integrity, and mesh refinement helps to enhance the ability to express local details, thus obtaining a more accurate and complete 3D model.

[0049] In the volume calculation stage, this application combines Delaunay triangulation with the projected volume method to estimate the target volume. The basic idea is to first project a 3D point cloud or mesh model onto a reference plane, forming several triangular elements on the projection plane. Then, the local volume is calculated by combining the area of ​​the triangles and the height information of their corresponding vertices. Specifically, the volume of a local element can be approximated by the product of the projected area of ​​each triangle and the average height of its three vertices. Finally, the overall volume is obtained by summing the volumes of all triangular elements.

[0050] First, this invention introduces the Feature Pyramid Network (FPN) and the MSDB multi-scale convolutional branch module into the MVSNet network, enhancing the network's ability to represent features in weakly textured regions, complex boundary regions, and regions with scale variations, thereby improving the completeness of dense reconstruction results and the accuracy of depth estimation. Second, before volume measurement, this invention performs optimization processing on the dense point cloud, such as statistical outlier filtering, which effectively removes outlier noise points, improves point cloud quality, and enhances the continuity and stability of the point cloud distribution, providing a more reliable data foundation for subsequent 3D mesh construction. Furthermore, this invention uses the Delaunay triangulation method to construct the 3D mesh model, which can minimize the generation of slender triangles or distorted units, improve the geometric quality and topological stability of the mesh, and thus reduce volume calculation errors caused by mesh degradation. Simultaneously, this invention combines Delaunay triangulation with the projected volume method, transforming the complex 3D volume problem into an area integration problem on the projection plane. The calculation process is clear, the implementation method is simple, and the computational efficiency is high, making it particularly suitable for volume measurement of irregular structures in engineering scenarios. This invention establishes a complete technical workflow from multi-view image input to 3D volume output, applicable to scenarios such as underwater engineering inspection, structural measurement, cultural relic modeling, and defect volume assessment. It provides a solution for non-contact 3D volume measurement, suitable for fields requiring rapid volume acquisition from images, such as underwater concrete structures, cultural relics, and industrial parts. It can handle targets without pre-existing 3D models. It improves 3D reconstruction accuracy (enhancing weak textures) and volume calculation stability (reducing volume errors through filtering and high-quality meshes), while simplifying the volume calculation process and enhancing the ease of engineering implementation.

[0051] Example: An underwater structure volume measurement method and system based on an improved MVSnet, the specific implementation steps are as follows: I. 3D Volume Reconstruction Based on Improved MVSNet 1. Feature point extraction and matching In the 3D reconstruction process, feature point extraction and descriptor generation are first performed on the multi-view images. In a preferred embodiment, the SIFT algorithm is used to detect key points and describe features in each view image. The SIFT algorithm has good robustness to scale changes, rotation changes, and a certain degree of brightness change, and is therefore suitable for front-end feature extraction in multi-view reconstruction.

[0052] After obtaining the feature points and descriptors of each image, the descriptor, a digital vector used in computer vision to represent local image features, encodes specific regions (such as keypoints) in the image, giving these features a stable and easily comparable representation. It typically possesses scale invariance, rotation invariance, and illumination adaptability, ensuring that the descriptor remains effective under image scaling, rotation, and illumination changes, allowing for feature matching between different views. During the matching process, the nearest neighbor to second nearest neighbor distance ratio criterion can be used to filter candidate matching point pairs, and further, geometric consistency constraints can be combined to remove mismatched points. To improve matching reliability, a random sampling consensus algorithm can be used to divide candidate matches into inside and outside points, eliminating erroneous correspondences that do not meet geometric constraints, thereby obtaining high-quality matching results.

[0053] 2. Sparse Reconstruction Based on Incremental SfM like Figure 1 As shown, this application adopts an incremental Structure from Motion (SfM) 3D reconstruction method based on SIFT features. The overall process follows the steps of "feature processing - initial reconstruction - incremental reconstruction - global optimization", which aims to gradually restore the camera pose and the 3D structure of the scene, and has high stability and scalability.

[0054] In the initial stage of the process, SIFT feature extraction is first performed on the input image sequence. This process detects scale- and rotation-invariant keypoints in each image and constructs a feature descriptor for each keypoint to provide a robust local representation for cross-viewpoint matching. Next, correspondences between images are established through SIFT feature matching, and mismatched points are effectively removed by combining a distance ratio criterion, thus providing a reliable foundation for subsequent geometric estimation.

[0055] During the initial reconstruction phase, the system constructs an image connectivity graph based on the matching relationships between images, reflecting the degree of overlap between them. Based on this, initial image pairs with sufficient disparity and matching points are selected for preliminary camera pose estimation, and the relative motion relationship between the two views is recovered. Subsequently, initial 3D points are generated through triangulation, and local bundle adjustment is performed to optimize camera parameters and 3D point positions, thereby obtaining a stable initial reconstruction model.

[0056] After entering the incremental reconstruction phase, the system progressively expands the 3D reconstruction model according to the steps of "registering new views—triangulation—local optimization". For each unregistered image, its camera pose is first estimated and incorporated into the current reconstruction system; then, triangulation is performed based on the new image observation information to supplement the 3D point cloud; finally, local bundle adjustment is used to eliminate error accumulation and improve overall consistency. By determining whether there are unregistered images, the iteration of the process is controlled, making the entire reconstruction process highly adaptive.

[0057] Once all images are registered, the global optimization phase begins. Through global bundle adjustment, all camera parameters and 3D points are uniformly optimized, further reducing error accumulation and improving the model's global consistency and accuracy. Ultimately, high-quality sparse point clouds and accurate camera poses are output, providing reliable input data for subsequent dense reconstruction.

[0058] Overall, the incremental SfM method employed in this application is a mature and highly robust technique, generating results such as... Figure 2 The sparse image shown. The sparse point cloud model constructed in the SfM sparse reconstruction process is gradually improved as images from different angles are added. Figure 2 This is a picture taken from a specific angle; different angles will produce different images.

[0059] 3. Dense Reconstruction Based on Improved MVSNet like Figure 3 As shown, based on sparse reconstruction, an improved MVSNet network is further used for dense reconstruction. While traditional MVSNet can perform multi-view depth estimation well, it still suffers from insufficient feature representation in weakly textured regions, edge regions, and regions with significant scale changes. Therefore, this application introduces an FPN feature pyramid network and an MSDB multi-scale convolutional branch module into MVSNet to form a feature enhancement module, reconstructing and fusing multi-scale features. The core objective is to enhance the discriminativeness, robustness, and scale adaptability of features while preserving the hierarchical information of the pyramid features, thereby providing a more reliable feature representation for subsequent cost volume construction and depth estimation.

[0060] Among them, such as Figure 4As shown, in the FPN (Feature Pyramid Network) structure, features at different levels are organized and fused. The entire network consists of multiple stages designed to progressively extract features from the input image and ultimately fuse information at different scales to generate the final feature map. The image first undergoes multiple feature extraction stages (F1, F2, F3). Each stage extracts image features through convolution operations and progressively reduces the image's spatial size while increasing or adjusting the number of channels. In the first stage (F1), the input image size is H / 4 x W / 4 x C1. A 3×3 convolutional layer is first used to extract local features, followed by a 1×1 convolutional layer to adjust the number of channels to C1. The second stage (F2) then performs similar processing on the feature map with an input size of H / 8 x W / 8 x C2, again using a 3×3 convolutional layer and a 1×1 convolutional layer. In the third stage (F3), the input feature map size is further reduced to H / 16 x W / 16 x C3, and then convolution operations are used to extract higher-level abstract features. In these stages, the ReLU activation function is applied after each convolutional layer to increase the network's non-linear expressive power, enabling it to learn more complex features. After feature extraction, these features at different scales are fused through their respective channels (P1, P2, P3). Each channel uses a 1×1 convolutional layer to further adjust the number of channels and integrate features from different levels, ultimately generating a rich output feature map. This process helps the network capture both the details and global information of the image, enhancing the model's performance. This network architecture extracts image features layer by layer from low to high levels by progressively reducing the spatial size and increasing the number of channels, and generates the final output feature map through feature fusion. The use of the ReLU activation function gives the network non-linear mapping capabilities, enhancing the learning of complex image patterns. This architecture is widely used in computer vision tasks such as image classification and object detection, and can efficiently process and extract image information at different scales. A key feature of this network architecture is weight sharing, that is, the same convolutional kernel weights are used in the convolutional operations. The convolutional kernel (Conv 3×3) in the figure slides across the entire input feature map, extracting local features of the image by applying the same weights. Regardless of where the convolution kernel is computed in the image, the weights it uses remain constant; this is the embodiment of weight sharing. By sharing weights, the same convolution kernel can be used repeatedly in different regions of the input, thereby extracting similar features from different locations, rather than setting independent weights for each local region.

[0061] Building upon this foundation, FPN further generates multi-scale pyramid feature maps, P1, P2, and P3, through lateral connections and top-down, progressive upsampling fusion. P3 is typically obtained by 1×1 convolution of the deepest F3 feature, representing the coarsest scale feature. P2 is obtained by fusing the mid-level feature F2 with the upsampled P3, preserving some detail while introducing higher-level semantic information. P1 is obtained by fusing the shallow feature F1 with the upsampled P2, possessing the highest spatial resolution and the richest local structural information. Through this multi-level feature fusion, the network can simultaneously process deep semantic information and shallow details, thereby enhancing feature representation capabilities in multi-view stereo matching.

[0062] P1, P2, and P3 are not only multi-scale feature maps output by the FPN, but also serve as different stages in the cascaded depth estimation process for feature fusion computation. Typically, P3 is used for the first stage of coarse-scale depth estimation, aiming to quickly obtain the overall depth distribution of the scene at lower resolution; P2 is used for the second stage of meso-scale depth refinement, further narrowing the depth search range and improving prediction accuracy; and P1 is used for the final stage of high-resolution fine reconstruction, focusing on restoring object edges, textures, and subtle geometric structures. Therefore, P3→P2→P1 actually represents a progressively optimized depth inference process from coarse to fine.

[0063] Functionally, P1, P2, and P3 can be understood as three sets of feature representations tailored to different resolution reconstruction tasks. P3 focuses on perceiving the overall structure and modeling the global context, while P2 takes into account both structural outlines and supplementing local details, and P1 emphasizes detail recovery and boundary delineation at high resolution. It is precisely because of this multi-scale pyramid feature design that FPN can achieve high-precision depth estimation and 3D reconstruction in dense multi-view reconstruction while controlling computational complexity.

[0064] Other examples Figure 5 As shown, the feature enhancement module structurally consists of three main feature extraction and fusion paths. First, the input image (feature map) is processed using 3×3 and 5×5 convolutional kernels respectively, resulting in two sets of 64-channel feature maps. The 3×3 convolution focuses on extracting local texture, edge, and detail information, while the 5×5 convolution has a larger receptive field, capturing broader contextual information. These two paths are responsible for modeling detail information and mesoscale structures, respectively. Next, the module concatenates these two sets of features along the channel dimension to form a 128-channel fused feature map, and further refines the features through a 3×3 convolution, enhancing the interaction and fusion effect between multi-scale features.

[0065] Meanwhile, the module also includes a separate 7×7 convolutional branch that directly processes the original input image (feature map). Because the 7×7 convolution has a larger receptive field, this branch can extract broader structural information and global contextual features, helping to improve the network's ability to perceive overall contours, regional distributions, and low-frequency information.

[0066] In the feature fusion stage, the module concatenates the features obtained from the fusion of 3×3 and 5×5 convolutions with the output of the 7×7 branch to form a new 128-channel feature map. Then, Batch Normalization is used to normalize the concatenated features, ensuring a more stable training process and accelerating convergence. Finally, a 1×1 convolution reduces the number of channels in the concatenated feature map from 128 to 64, reducing the number of parameters while achieving feature recombination. The LeakyReLU activation function is then used to enhance the network's non-linear expressive power, ultimately outputting the fused feature map.

[0067] The feature enhancement module not only supplements the shortcomings of single-layer features but also improves the adaptability of the overall feature representation space to complex scenes through multi-scale convolution and cross-layer information fusion. Enhanced features can more accurately describe details in texture-rich regions and maintain stability in sparsely textured or illumination-varying regions, making them suitable for cost volume construction and depth regression. For depth estimation, enhanced features improve multi-view matching consistency, enhance the separability of the cost volume, and effectively suppress noise and redundant information, thus improving the network's robustness to complex scenes. This enhancement mechanism provides high-quality feature input for subsequent depth estimation and fine-grained recovery.

[0068] In the specific reconstruction process, one image is selected as the reference view, and several other images are used as source views. Combining the camera parameters recovered by SfM, the features of the source views are mapped onto different depth hypothesis planes corresponding to the reference view, constructing a 3D cost volume. This process occurs during the depth map initialization stage. Specifically, by projecting the features of the source views onto multiple depth hypothesis planes of the reference view, a cost volume containing different depth hypotheses and corresponding cost values ​​can be generated. This cost volume provides preliminary depth information for subsequent depth map estimation. Next, in the depth map refinement stage, a convolutional neural network is used to optimize the initialized depth map. By further adjusting the depth hypotheses in the cost volume, a more accurate depth estimate is obtained.

[0069] Repeating the above process for all reference views yields multiple refined depth maps. Further combining camera parameters and depth consistency constraints, the refined depth maps from each view are fused to generate a dense point cloud model of the target region. Compared to traditional methods, the improved MVSNet described in this application exhibits better reconstruction capabilities for complex boundaries, local details, and weakly textured regions, effectively improving the integrity and accuracy of dense point clouds.

[0070] II. Underwater Structure Volume Measurement 1. Point cloud filtering processing like Figure 7 As shown, Statistical Outlier Removal (SOR) is a point cloud denoising method based on statistical analysis, primarily used to remove outlier noise points from point clouds, thereby improving the quality of point cloud data. This method identifies and removes outliers by analyzing the distance distribution of local neighborhoods in the point cloud and combining it with global statistical modeling. First, the original point cloud data is input, and a KD-Tree spatial index structure is constructed to improve neighborhood search efficiency. For each point in the point cloud, the k-nearest neighbor algorithm is used to calculate its Euclidean distance to its neighboring points, and the average neighborhood distance of that point is obtained. After traversing all points, the average neighborhood distance distribution of the entire point cloud is obtained. Next, these average neighborhood distances are statistically analyzed to calculate the global mean and standard deviation, and a discrimination threshold is set accordingly. This threshold controls the filtering intensity based on a multiple of the standard deviation. Finally, if the average neighborhood distance of a point exceeds the set threshold, the point is determined to be an outlier and deleted; if its average neighborhood distance is less than the threshold, the point is considered a valid point and retained.

[0071] 2. Delaunay triangulation to construct a mesh model like Figure 8 As shown, in Figure 8 The optimized point cloud model shown in the middle left figure is used to construct a 3D mesh model using the Delaunay triangulation method, as follows. Figure 8 As shown in the right-middle figure, Delaunay triangulation has good geometric properties, which can avoid generating slender triangles or distorted mesh elements as much as possible under discrete point set distribution conditions, thereby improving the stability of the mesh structure and the quality of surface reconstruction.

[0072] For the surface of a target structure, a more regular triangular mesh can more accurately represent the spatial contour and local morphology of the target, reducing geometric errors introduced by mesh distortion. After generating an initial mesh through Delaunay triangulation, a three-dimensional surface model of the target region can be obtained.

[0073] 3. Mesh Model Optimization like Figure 9As shown, the repair effect on the holes at the bottom of the columnar structure is illustrated from left to right. The left image is the 3D model before repair, the middle image (marked in red) shows the target area for repair and filling, and the right image is the 3D model after repair. To further improve the quality of the 3D model, the following optimization steps were performed after the initial mesh generation: Mesh smoothing: By locally adjusting the vertex positions, the jagged edges on the surface are reduced, making the model surface more continuous and natural; Edge flipping optimization: Improves mesh cell quality by adjusting local triangulation topology; Hole repair: Fills in local discontinuous areas caused by occlusion, missing viewpoints, or matching failures to improve the model's closure. Mesh refinement: Increase the density of triangular units in areas with significant changes in detail to improve the accuracy of local morphological representation; Texture mapping: Mapping the texture of the original image onto a 3D surface to enhance the visual expressiveness of the model.

[0074] 4. Implementation method of volume measurement using the projected volume method In the process of volume measurement of 3D reconstructed models, Delaunay triangulation and projective volume methods can be combined quite naturally. Delaunay triangulation is mainly used to organize discrete point cloud data into a continuous, regular triangular mesh structure, while projective volume methods are used to transform complex 3D volume problems into area integration problems on a projection plane. In simple terms, after triangulation, the surface of the target object is divided into several local triangular patches, each of which can be considered a tiny volume unit. Then, by calculating the area and corresponding average height of this unit on the projection plane, its contribution to the overall volume can be estimated. Finally, the total volume of the target model is obtained by summing the volumes of all units.

[0075] like Figure 10 As shown, for a local triangular prism bounded by base triangle A`B`C` and top triangle ABC, if the height of the top face varies linearly within the triangular region, then the average height of this region can be represented by the average of the heights of the three vertices. Since the triangular facets themselves can be considered as planes, this assumption holds. Based on this, the volume of a single triangular element can be expressed as: ; in, Indicates the first The projection area of ​​the triangles on the projection plane (XOY plane) Represent the area of ​​the projected triangle, ( , (), , )and( , Let ) represent the two-dimensional coordinates of the three vertices of the triangle on the projection plane. , , These represent the height values ​​of the three vertices of the triangle relative to the projection plane, where M is the total number of triangles. Furthermore, by summing the volumes of all triangular units, the overall volume can be obtained. .

[0076] Therefore, it can be seen that this method essentially discretizes the projected region using triangulation, and then performs analytical integration on each triangular unit and sums the results to calculate the overall volume.

[0077] In the specific implementation process, the 3D point cloud first needs to be preprocessed, including denoising, downsampling, and normalization, to reduce the impact of outliers and local anomalies on the subsequent subdivision quality. Then, the point cloud is projected onto a reference plane according to the selected projection direction. For example, it can be projected onto the XOY plane along a principal direction; for structures with obvious axial features, coordinate alignment can be completed first through cylinder fitting or principal axis estimation before projection to improve the stability of volume estimation. After projection, the corresponding point set can be obtained on the 2D plane, and Delaunay triangulation can be performed on it to construct the 2D triangle connection relationship.

[0078] For each two-dimensional triangle, its area can be expressed as: ; Then, extract the height value corresponding to the vertex of the triangle from the original 3D points or the coordinate-aligned point set, and substitute it into the element volume formula: ; Finally, by summing the volume results of all triangular elements, the total volume of the target model can be obtained.

[0079] Delaunay triangulation offers good triangle quality and topological stability, reducing numerical errors caused by triangle degeneration. Meanwhile, the analytical volume formula based on the average vertex height avoids further slice integration or complex surface integration processes, allowing each triangular element to directly participate in volume calculations. Therefore, it exhibits high computational efficiency and good result stability. In summary, Delaunay triangulation solves the problem of discrete representation of the projected region, while the projected volume method solves the problem of volume integral calculation. Combining the two forms a volume measurement method with a clear structure, simple implementation, and applicability to engineering scenarios.

[0080] III. Experimental Verification To verify the effectiveness of the proposed method in 3D reconstruction and volume measurement of underwater structures, this application conducted experimental analyses from two aspects: first, the changes in volume measurement results before and after image processing; and second, the volume error performance of different 3D reconstruction methods on various datasets (Origin, Water1, and Water2). Origin is the original dataset without special degradation processing, while Water1 and Water2 are two datasets with more severe degradation, with Water1 showing less degradation than Water2. Table 1 shows the volume measurement results of the proposed method (Ours) under different image processing conditions, while Table 2 further compares the volume errors of the proposed method (Ours) with other typical 3D reconstruction methods (MVSNet, Fast-MVSNet, PatchmatchNet, ET-MVSNet, and ACMP) on different datasets.

[0081] Table 1. Volume measurement results of the method in this application under different image processing conditions. Table 2. Statistical table of volumetric errors of the method in this application and other typical 3D reconstruction methods on different datasets. First, as can be seen from Table 1, different image conditions have a significant impact on the volume measurement results. The actual volume is 93.12 cm³. 3 The volume measured by the method in this application was 85.21 cm³ under different datasets. 3 79.12cm 3 and 79.43cm 3 The corresponding errors are 8.5%, 15.0%, and 14.7%, respectively. In the original Origin dataset, the volume error is 8.5%, indicating that the proposed method can perform 3D reconstruction and volume estimation tasks well under conditions without special degradation processing. However, on the Water1 and Water2 datasets, which suffer from more severe degradation, the errors increase to 15.0% and 14.7%, respectively. This is because color distortion, decreased contrast, and loss of texture details in underwater images significantly interfere with feature matching, depth estimation, and point cloud restoration, leading to a greater deviation between the reconstructed volume and the true value.

[0082] Furthermore, Table 2 analyzes the performance differences of different 3D reconstruction methods on various datasets. On the Origin dataset, the volume error of our proposed method is 8.5%, which is better than MVSNet and ACMP, but slightly worse than Fast-MVSNet, PatchmatchNet, and ET-MVSNet. This indicates that our proposed method is competitive under the original image conditions, but there is still room for further improvement. Overall, the volume errors of all methods on the Origin dataset are generally lower than those on the Water1 and Water2 datasets, indicating a strong correlation between image degradation and volume measurement error. In other words, the worse the image quality, the more likely the subsequent 3D reconstruction results are to suffer from surface detail loss, geometric distortion, and incomplete point clouds, ultimately leading to increased volume measurement deviation. Specifically, on the Water1 dataset, the error of our proposed method is 15.0%, placing it in the upper-middle range overall, lower than MVSNet, Fast-MVSNet, PatchmatchNet, and ET-MVSNet, but slightly higher than ACMP. On the Water2 dataset, the proposed method achieves an error of 14.7%, outperforming MVSNet, Fast-MVSNet, PatchmatchNet, ET-MVSNet, and ACMP. This demonstrates that in underwater scenes with severe image degradation, the performance of various methods generally declines, indicating that image degradation remains a major factor affecting the accuracy of 3D reconstruction. However, the proposed method maintains superior error control in most cases.

[0083] In summary, experimental results demonstrate that the proposed method can achieve relatively stable 3D reconstruction and volume measurement under different underwater image conditions. On the restored dataset, the proposed method exhibits stable error control. The improved 3D reconstruction network further enhances depth estimation and geometric reconstruction capabilities, making the volume measurement results closer to the true values. The experimental results fully validate the effectiveness and application potential of the proposed method in underwater structure 3D reconstruction and loss assessment tasks, indicating that the method has good synergy between image enhancement and 3D reconstruction modules, providing a new technical path for accurate modeling and volume measurement of underwater structures.

[0084] This invention establishes a complete technical workflow from multi-view image input to 3D volume output, applicable to scenarios such as underwater engineering inspection, structural measurement, cultural relic modeling, and defect volume assessment. It provides a solution for non-contact 3D volume measurement, suitable for fields requiring rapid volume acquisition from images, such as underwater concrete structures, cultural relics, and industrial parts. It can handle targets without pre-existing 3D models. It improves 3D reconstruction accuracy (enhancing weak textures) and volume calculation stability (reducing volume errors through filtering and high-quality meshes), while simplifying the volume calculation process and enhancing the ease of engineering implementation.

[0085] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

Claims

1. An underwater structure volume measurement method based on an improved MVSnet, characterized in that, Includes the following steps: S1. Input a multi-view image of the underwater structure to be measured; S2. 3D reconstruction based on improved MVSNet: First, sparse reconstruction is performed using the incremental SfM method and sparse point cloud is output. Then, dense reconstruction is performed using improved MVSNet and dense point cloud is output. The improved MVSNet network includes a feature pyramid network and a multi-scale convolutional branch module. S3. Volume measurement: A three-dimensional mesh model is constructed using the Delaunay triangulation method, and the volume of the underwater structure corresponding to the three-dimensional mesh model is calculated using the projected volume method.

2. The underwater structure volume measurement method based on the improved MVSnet according to claim 1, characterized in that, In step S2, the SIFT algorithm is first used to extract feature points and generate descriptors for the multi-view image; then sparse reconstruction is performed, and the camera intrinsic and extrinsic parameters are recovered through feature matching relationships. The image registration, triangulation and local bundle adjustment are gradually completed, and finally the sparse point cloud and accurate camera pose are output.

3. The underwater structure volume measurement method based on the improved MVSnet according to claim 1, characterized in that, In step S2, the feature pyramid network generates three-level multi-scale feature maps P1, P2, and P3 through multi-level feature fusion. The feature maps P1, P2, and P3 are used for depth estimation in order from coarse to fine: P3 is used for coarse-scale depth estimation in the first stage, P2 is used for meso-scale depth refinement in the second stage, and P1 is used for high-resolution fine reconstruction in the third stage.

4. The underwater structure volume measurement method based on the improved MVSnet according to claim 1, characterized in that, In step S2, the multi-scale convolution branch module extracts multiple receptive field features through parallel convolution and fuses them to output enhanced features.

5. The underwater structure volume measurement method based on the improved MVSnet according to claim 1, characterized in that, In step S2, the multi-scale convolutional branch module performs feature enhancement: the input feature map is convolved with 3×3 and 5×5 to obtain two sets of 64-channel feature maps, and the channel dimension is concatenated to form a 128-channel fused feature map. Then, it is refined by 3×3 convolution, and then concatenated with the feature output from the 7×7 convolution branch to form a 128-channel feature map. After normalization, the number of channels of the concatenated feature map is reduced from 128 to 64 by 1×1 convolution. Finally, the fused feature map is output by the LeakyReLU activation function.

6. The underwater structure volume measurement method based on the improved MVSnet according to claim 1, characterized in that, Step S3: First, perform point cloud filtering on the dense point cloud to obtain an optimized point cloud. Then, construct a three-dimensional mesh model and optimize the three-dimensional mesh model. Finally, use the projected volume method to calculate.

7. The underwater structure volume measurement method based on the improved MVSnet according to any one of claims 1-6, characterized in that, Step S2 includes: S21. First, perform SIFT feature extraction on the input image sequence and construct feature descriptors. Then, establish the matching relationship between images through SIFT feature matching. S22. Initialize reconstruction: First, construct an image connection graph based on the matching relationship between images. Then, select initial image pairs, perform preliminary camera pose estimation, and restore the relative motion relationship between the two views. Finally, generate initial 3D points through triangulation and perform local bundle adjustment. S23. Incremental reconstruction: First, incremental camera pose estimation is performed and incorporated into the current reconstruction system. Then, triangulation is performed based on the new image observation information to supplement the 3D point cloud. Next, error accumulation is eliminated through local bundle adjustment. Finally, all camera parameters and 3D points are optimized through global bundle adjustment to output sparse point cloud and camera pose. S24. Dense Reconstruction: First, the feature pyramid network extracts multi-scale original feature maps through a bottom-up convolutional encoding process. Then, through lateral connections and top-down progressive upsampling fusion, it merges the high-frequency local details in the shallow layer with the low-frequency global semantic information in the deep layer, outputting a multi-scale pyramid feature map from coarse to fine. Next, the multi-scale convolutional branch module constructs parallel multi-scale feature extraction paths to adaptively extract feature information from different receptive fields. It constructs an aggregate cost body through feature enhancement, and obtains the ground truth depth map of the reference view through regularization and depth regression. Finally, it fuses the data to generate a dense point cloud.

8. The underwater structure volume measurement method based on the improved MVSnet according to claim 6, characterized in that, In step S3, the optimization of the 3D mesh model includes: mesh smoothing, edge flipping optimization, hole repair, texture mapping, and mesh refinement.

9. The underwater structure volume measurement method based on the improved MVSnet according to claim 1, characterized in that, Step S3 includes: S31. Divide the surface of the three-dimensional mesh model into several local triangular patches, and treat each triangular patch as a tiny volume unit; S32. Set a certain reference plane as the projection plane, and project the triangular facets of the three-dimensional mesh model onto the projection plane to form several triangles on the projection plane; S33. Divide the triangle on the projection plane into triangular units, and calculate the volume of each triangular unit by combining the area of ​​the triangle and the height information of its corresponding vertices. S34. The overall volume is obtained by summing the volumes of all triangular units.

10. An underwater structure volume measurement system based on an improved MVSNet, applied to the method described in claim 1, characterized in that, include: The feature extraction and matching module is used to perform SIFT feature point extraction, descriptor generation and matching, and remove mismatches to obtain high-quality matching results; The sparse reconstruction module is used to perform incremental SfM reconstruction and output sparse point cloud and camera pose. The dense reconstruction module incorporates an improved MVSNet network with a feature pyramid network and multi-scale convolutional branch modules to generate dense point clouds. The point cloud optimization module is used to perform statistical outlier filtering, remove noise points, and obtain an optimized point cloud. The volume calculation module is used to perform Delaunay triangulation, mesh optimization, and projective volume calculation to output the volume of the underwater structure.

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