Multi-view reconstruction method and system based on geometric perception and attention fusion

Abstract

The invention discloses a multi-view reconstruction method and system based on geometric perception and attention fusion. The reconstruction method comprises the following steps: designing a multi-scale feature enhancement network and a geometric perception feature fusion network; the multi-scale feature enhancement network extracts a multi-scale feature map and inputs the multi-scale feature map to a multi-stage depth estimation module to generate a preliminary depth map; inputting the initial depth map into a geometric perception feature fusion network to generate a geometric perception enhanced feature map; inputting the geometric perception enhanced feature map into a multi-stage depth estimation module, and performing iterative optimization to output a refined depth map; and training a model constructed by the network by adopting a joint loss function of a pixel-level cross entropy loss function and a depth distribution similarity loss function. According to the method, the expression ability of image features and the utilization efficiency of geometric information are effectively improved, the problem that depth estimation is difficult in a low-texture area and a structure repeated area in an existing multi-view three-dimensional reconstruction method is mainly solved, and the accuracy and integrity of three-dimensional reconstruction are remarkably improved.

Description

Technical Field

[0001] This invention relates to the field of image processing technology, specifically to a multi-view reconstruction method and system based on geometric perception and attention fusion. Background Technology

[0002] In recent years, with the widespread development of technologies such as autonomous driving, augmented reality (AR), virtual reality (VR), robot navigation, and digital cities, multi-view stereo reconstruction (MVS), as a core problem in 3D reconstruction, has received high attention from researchers in the field of computer vision. Its core objective is to estimate the depth information of each pixel in a scene by analyzing the matching and stereo correspondences between multi-view images, thereby recovering the complete 3D geometric structure. Although existing technologies such as CasMVSNet have made significant progress in this field, the completeness and accuracy of the final point cloud still depend on the accuracy of the depth map, and there is still room for improvement.

[0003] Multi-view stereo reconstruction network (MVSNet), a typical deep learning method, takes a reference image and a source image as input, extracts multi-scale features using a feature pyramid network, constructs a 3D cost volume using a differentiable homography transformation, and finally regresses a high-precision depth map using a 3D convolutional neural network. Subsequent improvements, such as CasMVSNet and UCsNet, propose cascaded cost volumes based on feature pyramids and progressively estimate the depth map in a coarse-to-fine manner. These cost volume pyramid-based methods utilize the depth prediction results from the previous stage to narrow the depth search range in the current stage, optimizing memory and computation time, and providing better reconstruction results in high-resolution image processing. However, these methods still face certain challenges, especially when dealing with regions with low texture and repetitive structures, where details are often overlooked, leading to the loss of fine structures.

[0004] Especially in depth map estimation, existing methods fail to adequately capture the geometric information of low-texture and structurally repetitive regions due to their limited feature extraction and matching capabilities, resulting in insufficient accuracy in these areas. Furthermore, with the continuous improvement of image resolution, the increase in depth search space, and the rise in computational complexity, existing technologies face efficiency bottlenecks while pursuing high accuracy. How to improve feature extraction and geometric modeling capabilities, particularly in detail recovery of low-texture or structurally repetitive regions, while maintaining accuracy remains a significant challenge in the field of multi-view stereo reconstruction.

[0005] In summary, effectively capturing key features of low-texture and structurally repetitive regions in complex environments and combining them with geometric information to enhance the detail recovery capability of depth maps has become a crucial issue for breakthroughs in current multi-view stereo reconstruction methods. This invention aims to enhance the depth recovery capability of these detailed regions and improve the overall accuracy and completeness of 3D reconstruction by introducing innovative geometric perception and attention mechanisms. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention provides a multi-view stereo reconstruction method and system based on geometric perception and attention fusion. This method effectively enhances the expressive power of image features and the utilization efficiency of geometric information by designing a multi-scale feature enhancement network, introducing a geometric perception feature fusion network, and combining an improved loss function. It focuses on solving the problem of depth estimation difficulties in low-texture regions and structurally repetitive regions in existing multi-view stereo reconstruction methods, and significantly improves the accuracy and completeness of 3D reconstruction.

[0007] The technical solution of the present invention is as follows: A multi-view reconstruction method based on geometric perception and attention fusion, comprising the following steps: Step S1: Prepare a multi-view stereo dataset and divide the image pairs in the dataset into reference images and source images; Step S2: Input the reference image and source image from step S1 into the multi-scale feature enhancement network to extract multi-scale feature maps, and input the multi-scale feature maps into the multi-stage depth estimation module to generate a preliminary depth map; Step S3: Perform resolution processing on the reference image in step S1, and perform resolution and normalization processing on the preliminary depth map in step S2 to obtain multi-scale geometric features. Step S4: Input the multi-scale geometric features of the reference image and the initial depth map processed in step S3 into the geometric perception feature fusion network to generate a geometric perception enhanced feature map; Step S5: Input the geometry-aware enhanced feature map into the multi-stage depth estimation module, perform iterative optimization, and output a refined depth map; Step S6: Construct a 3D reconstruction model based on a multi-scale feature enhancement network, a geometric perception feature fusion network, and a multi-stage depth estimation module; train the 3D reconstruction model using a joint loss function of pixel-level cross-entropy loss function and depth distribution similarity loss function.

[0008] Furthermore, the multi-view stereo dataset prepared in step S1 is as follows: The Multi-View Stereo Dataset is an indoor dataset, a publicly available dataset for multi-view stereo reconstruction and 3D modeling. It contains 124 different objects or scenes, each captured from 49 or 64 different viewpoints, with 7 different lighting conditions per viewpoint. The images in the dataset have a resolution of 1600×1200 pixels. The dataset selects one image as the reference image and the remaining images as source images. The dataset provides camera intrinsics, camera extrinsics, high-precision laser point clouds, and true depth map data for mapping pixel coordinates to the camera coordinate system.

[0009] Furthermore, the reference image and source image from step S1 are input into a multi-scale feature enhancement network to extract multi-scale feature maps. These multi-scale feature maps are then input into a multi-stage depth estimation module to generate a preliminary depth map. Specifically: Step S21: The multi-scale feature enhancement network is divided into a feature selection module and a feature fusion module. The reference image and source image in step S1 are input into the feature selection module of the multi-scale feature enhancement network. Step S22: The reference image and the source image are processed by a preliminary convolution module consisting of two consecutive convolution units to generate an initial feature map of the first layer with a spatial resolution of H×W. Step S23: The feature selection module adopts a top-down downsampling convolution module. The first layer initial feature map is sequentially input into three downsampling convolution modules, and the spatial resolution is gradually reduced to H / 2×W / 2, H / 4×W / 4 and H / 8×W / 8. H / 8×W / 8 is the feature with the highest spatial resolution, and the second, third and fourth layer initial feature maps are obtained. Step S24: The first layer initial feature map, the second layer initial feature map, the third layer initial feature map, and the fourth layer initial feature map are input into the lightweight multi-dimensional fusion attention module, and feature enhancement is performed in the channel-height, channel-width, and spatial dimension directions to obtain the first layer enhanced initial feature map, the second layer enhanced initial feature map, the third layer enhanced initial feature map, and the fourth layer enhanced initial feature map. Step S25: The fourth-layer enhanced initial feature map is input into the multi-scale context aggregation module of the feature fusion module to obtain a deep initial feature map. The feature fusion module uses a bottom-up upsampling module to progressively upsample the deep initial feature map. The progressive upsampling module fuses the deep initial feature map with the first-layer enhanced initial feature map, the second-layer enhanced initial feature map, the third-layer enhanced initial feature map, and the fourth-layer enhanced initial feature map through a channel alignment module, outputting four multi-scale feature maps with different resolutions. The spatial resolution levels are respectively those of the reference image and the source image. ; Step S26: Input four multi-scale feature maps with different resolutions into the multi-stage depth estimation module to generate a preliminary depth map.

[0010] Further, step S3: The reference image from step S1 undergoes resolution processing, and the preliminary depth map from step S2 undergoes resolution and normalization processing to obtain multi-scale geometric features; specifically: Step S31: The reference image and the preliminary depth map are processed for resolution to obtain reference image feature I and preliminary depth map feature D. The preliminary depth map feature is then normalized to obtain a normalized depth map, represented as: ; Where d is the normalized depth map, and D is the preliminary depth map feature. , The maximum and minimum values ​​of the initial depth map features; Step S32: Based on the reference image feature I and the normalized depth map d, multi-scale geometric features with different spatial resolutions are generated according to four modes: std, uv, z, or xyz. The four modes std, uv, z, and xyz represent feature representation methods from no geometric constraints to strong geometric constraints, respectively, providing the geometry-aware convolution module with multi-level geometric information from two-dimensional coordinates to three-dimensional space. In std mode, no geometric features are attached; In UV mode, a two-dimensional coordinate grid covering each pixel of the image is generated based on the size of the input reference image feature I, and the two-dimensional coordinate grid is linearly normalized to the [0,1] interval; the normalized two-dimensional coordinate grid is downsampled step by step through 2×2 average pooling to form a 2-channel feature. In z mode, the normalized depth map d is sparsely pooled and downsampled to form a 1-channel depth feature; In xyz mode, based on the camera intrinsic parameters corresponding to the images in the dataset, the normalized two-dimensional coordinates (u,v) of each pixel in the image are back-projected with the 1-channel depth feature in z mode to the three-dimensional coordinates (x,y,z) in the camera coordinate system, and the 3-channel feature is output. In step S34, the multi-scale geometric features of the four modes are used to generate multi-scale representations according to spatial resolution levels 1, 1 / 2, 1 / 4, and 1 / 8, forming corresponding multi-scale geometric information. The multi-scale geometric features are then input into the geometry-aware convolutional module as multi-scale geometric feature information.

[0011] Further, in step S4, the multi-scale geometric features of the reference image and the initial depth map processed in step S3 are input into the geometric perception feature fusion network to generate a geometric perception enhanced feature map; the geometric perception feature fusion network is divided into a first branch decoding module, a second branch decoding module, and a final fusion module; specifically: Step S41: The reference image and the initial depth map processed in step S3 are stitched together and input into the preliminary convolution module of the first branch decoding module to generate the first fusion feature map. The first fusion feature map is input into the five-level geometric perception convolution module. Each level of the geometric perception convolution module simultaneously fuses the multi-scale geometric feature information of the reference image and the initial depth map to obtain the second, third, fourth, fifth and sixth fusion feature maps, respectively. In step S42, the first branch decoding module performs progressive upsampling of the fused feature map through the deconvolution module. During the progressive upsampling process, the deconvolution module performs residual connection with the fused feature map output by the initial convolution module and the geometric perception convolution module; and generates a second initial depth map with the same resolution as the input reference image. Step S421: After the deconvolution module performs the first-level upsampling, it is connected with the residual of the fifth fusion feature map of the fourth-level geometric perception convolution module to obtain a spatial resolution of H / 8xW / 8. Step S422: After the deconvolution module performs the second-level upsampling, it is connected with the third fusion feature map residual of the second-level geometric perception convolution module to obtain a spatial resolution of H / 4xW / 4. Step S423: After the deconvolution module performs the third-level upsampling, it is connected with the second fusion feature map residual of the first-level geometric perception convolution module to obtain a spatial resolution of H / 4xW / 4. Step S424: After the deconvolution module performs the fourth level of upsampling, it is connected with the first fused feature map residual of the initial convolution module to obtain a spatial resolution of H / 2XW / 2. Step S425: After the deconvolution module performs the fifth level of upsampling, a spatial resolution of H×W is obtained; a second initial depth map is generated. Step S43: The normalized depth map d channel and the second initial depth map channel are concatenated and input into the preliminary convolution module of the second branch decoding module to generate the seventh fusion feature map. The seventh fusion feature map is input into the five-level geometric perception convolution module of the second branch decoding module. Each level of fusion simultaneously fuses the corresponding multi-scale geometric feature information of the reference image and the initial depth map. Step S44: The seventh fused feature map is input into the first and second geometric perception convolutional modules to obtain the eighth fused feature map. The eighth fused feature map is concatenated with the features output from the residual connection in step S424 to obtain the first joint feature. The first joint feature is input into the third and fourth geometric perception convolutional modules to obtain the ninth fused feature map. The ninth fused feature map is concatenated with the features output from the residual connection in step S421 to obtain the second joint feature. The second joint feature is input into the fifth geometric perception convolutional module to generate the third initial depth map. Step S45: The final fusion module consists of a five-level deconvolution module and five fusion processes. The five-level deconvolution module is divided into a first-level deconvolution module, a second-level deconvolution module, a third-level deconvolution module, a fourth-level deconvolution module, and a fifth-level deconvolution module. The third deconvolution module processes the first stage to output the first-level geometric perception enhanced feature map. The fourth deconvolution module processes the second stage to output the second-level geometric perception enhanced feature map. The fifth deconvolution module processes the third stage to output the third-level geometric perception enhanced feature map. Step S46, the first fusion process, the features of the sixth fusion feature map of the first branch decoding module and the third initial depth map of the second branch decoding module are added element by element and input into the first-level deconvolution module of the final fusion module to generate the first-level fusion feature; Step S47, the second fusion process: the fourth-level geometric perception module of the second branch decoding module adds the first-level fusion features element by element and inputs them into the second-level deconvolution module of the final fusion module to generate the second-level fusion features; Step S48, the third fusion process: the second-level geometric perception module of the second branch decoding module adds the second-level fusion features element-wise to the second-level fusion features, and inputs them into the third-level deconvolution module of the final fusion module to generate third-level fusion features. If it belongs to the first stage, the third-level fusion features are input into the first-level RGB deconvolution module, and the output is then combined with the output of the multi-scale feature enhancement network. Residual connections are made between multi-scale feature maps of different resolutions to obtain the first-stage geometric perception enhancement feature map. Step S49, the fourth fusion process: The first-level geometric perception module of the second branch decoding module adds the third-level fusion features element-wise, and inputs them into the fourth-level deconvolution module of the final fusion module to generate fourth-level fusion features. If it belongs to the second stage, the fourth-level fusion features are input into the second-level RGB deconvolution module, and the output is then combined with the output of the multi-scale feature enhancement network. Residual connections are performed on the multi-scale feature maps to obtain the second-stage geometric perception enhancement feature maps. Step S50, the fifth fusion process: the initial convolution module of the second branch decoding module adds the fourth-level fusion feature element by element and inputs it into the fifth-level deconvolution module of the final fusion module to generate the fifth-level fusion feature. If it belongs to the third stage, the fifth-level fusion feature is input into the third-level RGB deconvolution module. After output, it is residually connected with the 1 / 1 resolution multi-scale feature map output by the multi-scale feature enhancement network to obtain the third-stage geometric perception enhancement feature map. Geometric perception-enhanced feature maps, expressed by the formula: ; Where Y is the geometry-aware enhanced feature map. These are features in multi-scale feature enhancement networks. It is a fusion feature of the first branch decoding module and the second branch decoding module. The final fusion module enhances the network's features by combining the fusion features of the first branch decoding module and the second branch decoding module, along with multi-scale features. Perform element-by-element fusion. and These represent the first branch decoding module and the second branch decoding module, respectively. I is the reference image feature, and d is the normalized depth map. It is a depth map guided by a reference image.

[0012] Further, step S5: Input the geometry-aware enhanced feature map into the multi-stage depth estimation module for iterative optimization, and output a refined depth map; specifically: Step S51: Input the geometric perception enhancement feature map, which contains reference image features and source image features. Using the camera intrinsic and extrinsic parameters provided in the dataset, the source image features are projected onto the reference viewpoint according to the depth assumption of each pixel to achieve feature alignment. Step S52: Calculate the correlation between the features of the reference image and the aligned features of the source image by grouping them. Step S53: The correlation of all source image features is weighted and averaged to construct a preliminary cost volume. The preliminary cost volume is regularized by deep learning to perform three-dimensional spatial consistency modeling. Step S54: The initial cost volume for regularization is normalized by an exponential function to form the probability distribution of each pixel of the image under the depth hypothesis set; Step S55: Obtain the final depth value of each pixel in the image based on probability distribution regression, and combine the final depth values ​​of all pixels in the image to obtain a complete depth map. Step S56: Based on the final depth value of the current stage, generate a more refined set of depth hypotheses for the next stage by performing inverse depth resampling in the inverse depth domain of each pixel of the image. Step S57 involves multiple stages of processing, ultimately outputting the final depth map.

[0013] Furthermore, a multi-view reconstruction system based on geometric perception and attention fusion constructs a 3D reconstruction model based on a multi-scale feature enhancement network, a geometric perception feature fusion network, and a multi-stage depth estimation module. A 3D reconstruction model is constructed based on a multi-scale feature enhancement network, a geometric perception feature fusion network, and a multi-stage depth estimation module. The multi-scale feature enhancement network includes a feature selection module and a feature fusion module; The feature selection module includes a preliminary convolution module, a downsampling convolution module, and a lightweight multi-dimensional fusion attention module; The feature fusion module consists of a channel alignment module, an upsampling module, and a multi-scale context aggregation module; Among them, the geometric perception feature fusion network mainly includes a first branch coding module, a second branch coding module and a final fusion module; The first branch encoding module includes an initial convolution module, a geometry-aware convolution module, and a deconvolution module; The second branch encoding module includes an initial convolution module and a geometry-aware convolution module; The final fusion module receives the outputs of the first branch coding module and the second branch coding module, and performs scale fusion of the first branch coding module and the second branch coding module accordingly. The multi-stage depth estimation module consists of feature alignment, correlation calculation, regularization, normalization, depth regression, and inverse depth resampling.

[0014] Compared with existing technologies, the present invention has the following advantages: This invention designs a multi-scale feature enhancement network, employing an innovative structure that combines bottom-up feature extraction with top-down feature fusion. In each processing stage, upsampling effectively fuses deep, high-level semantic features with shallow, high-resolution features, achieving efficient integration of multi-scale features. A lightweight multi-dimensional fusion attention module is introduced into each layer of the bottom-up feature extraction to fully exploit spatial, channel, and directional information interactions, enhancing the network's ability to focus on targets or boundary regions. In the top-down feature fusion stage, a multi-scale context aggregation module is applied to the highest-level features for feature enhancement, strengthening the consistency and stability of semantic features, thereby improving the feature fusion effect.

[0015] This invention designs a geometric-aware feature fusion network that integrates geometric perception and attention mechanisms. The aim is to fuse reference images, depth maps, and geometric guidance information to generate enhanced feature maps with stronger spatial perception and structural representation capabilities. The geometric-aware feature fusion network adopts a dual-branch structure, performing guided injection and multi-scale fusion of semantic and geometric information respectively, thereby synergistically improving depth estimation accuracy. A geometric-aware convolutional module is introduced at each encoding stage to provide structural guidance and saliency enhancement for features at each scale, effectively improving the spatial discriminative ability and structural consistency of the feature maps. The attention-enhanced feature maps output by the multi-scale feature enhancement network are superimposed on the final result through residual connections, thus balancing detail restoration and overall consistency.

[0016] This invention employs a pixel-level cross-entropy loss function and a depth distribution similarity loss function. The pixel-level cross-entropy loss function supervises the prediction of each pixel category in the model's output, enhancing the classification ability for detailed regions and boundary objects, and effectively improving the accuracy of overall semantic segmentation or depth estimation. The depth distribution similarity loss function measures the similarity between the model's predicted depth map and the true depth map in terms of overall distribution; this loss function enhances the network's ability to model structural consistency and geometric continuity, thereby improving the stability of overall depth perception while maintaining local accuracy. The joint optimization of these two loss functions achieves a good balance between spatial perception and semantic understanding, ultimately outputting prediction results with higher accuracy and structural integrity. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of the three-dimensional reconstruction model framework of the present invention.

[0018] Figure 2 This is a schematic diagram of the multi-scale feature enhancement network framework of the present invention.

[0019] Figure 3 This is a schematic diagram of the geometric perception fusion network framework of the present invention.

[0020] Figure 4 This is a schematic diagram of the multi-stage depth estimation module framework of the present invention. Detailed Implementation

[0021] like Figure 1 The diagram shown is a schematic of the 3D reconstruction model framework of the present invention. A multi-view reconstruction method based on geometric perception and attention fusion includes the following steps: Step S1: Prepare a multi-view stereo dataset and divide the image pairs in the dataset into reference images and source images; Step S2: Input the reference image and source image from step S1 into the multi-scale feature enhancement network to extract multi-scale feature maps, and input the multi-scale feature maps into the multi-stage depth estimation module to generate a preliminary depth map; Step S3: Perform resolution processing on the reference image in step S1, and perform resolution and normalization processing on the preliminary depth map in step S2 to obtain multi-scale geometric features. Step S4: Input the multi-scale geometric features of the reference image and the initial depth map processed in step S3 into the geometric perception feature fusion network to generate a geometric perception enhanced feature map; Step S5: Input the geometry-aware enhanced feature map into the multi-stage depth estimation module, perform iterative optimization, and output a refined depth map; Step S6: Construct a 3D reconstruction model based on a multi-scale feature enhancement network, a geometric perception feature fusion network, and a multi-stage depth estimation module; train the 3D reconstruction model using a joint loss function of pixel-level cross-entropy loss function and depth distribution similarity loss function.

[0022] Furthermore, in step S1, this invention uses a multi-view stereo dataset, which is an indoor dataset consisting of 124 different scenes. Each scene is recorded from 49 views, with 7 different lighting conditions and 7 brightness levels per viewpoint. It includes ground point clouds collected under well-controlled laboratory conditions and can be used to evaluate the accuracy and completeness of 3D reconstruction methods. The multi-view stereo dataset is an open dataset for multi-view stereo reconstruction and 3D modeling released by the Computer Vision Laboratory of the Technical University of Denmark (DTU). The images in the dataset have a resolution of 1600×1200 pixels, and each image contains detailed depth information, along with camera intrinsic and extrinsic parameters to map pixel coordinates to the camera coordinate system and provide geometric constraints in multi-view reconstruction. It is suitable for research in computer vision, 3D reconstruction, and other fields. In addition, each image is accompanied by a source image and a reference image, facilitating the application and testing of multi-view reconstruction algorithms. The image pairs in the dataset are divided into source images and reference images: the source image serves as the target image for current depth estimation, while the reference image is used to provide geometric constraints and texture supplementation information across views.

[0023] Further, in step S2: the multi-scale feature enhancement network extracts feature maps of the source and reference images at multiple scales. Unlike the traditional multi-scale feature extraction structure, the multi-scale feature enhancement network introduces a multi-stage feature fusion mechanism, which can effectively alleviate the problems of feature weakening and semantic expression instability caused by downsampling in low-texture regions or regions with repetitive structures.

[0024] To further enhance the discriminative power of feature representations, a lightweight multi-dimensional fusion attention module is introduced in each feature fusion stage. This module, based on a triple attention mechanism combined with lightweight convolutional layers, further strengthens the features. Finally, residual connections are used to fuse the original input and the enhanced features, enhancing the expressive power of the feature maps, particularly across different spatial and channel dimensions. A multi-scale context aggregation module is introduced into the high-level output of the network to further optimize the representation of high-level semantic information and enhance the network's understanding of global structure and semantics. The image features extracted in the first stage are then input into a multi-stage depth estimation network to obtain the depth estimation results for the first stage.

[0025] Furthermore, in step S4, the geometrically aware feature fusion network performs joint feature extraction on the initial depth result and the reference image. The network achieves deep coupling between features and geometric information through embedded geometrically aware convolutional modules. The fused features are then upsampled via deconvolution to restore spatial details and further jointly constructed with the output of the multi-scale feature enhancement network to form a geometrically consistent feature representation, which guides the depth estimation and refinement processes in subsequent stages. After forming this geometrically consistent feature representation, these features guide the depth estimation and refinement processes in subsequent stages, thereby further improving the accuracy of depth prediction.

[0026] Furthermore, in step S5, the features output from the geometric perception feature fusion network are input into the multi-stage depth estimation network to calculate the final depth map. The multi-stage depth estimation module refines and optimizes the accuracy of the depth map through progressive feature updates and depth prediction. Each stage utilizes the depth estimation results from the previous stage to further adjust and improve the quality of the depth map, ensuring that the final output depth map achieves higher precision features in terms of spatial and geometric consistency.

[0027] By inputting higher-precision features into the multi-stage depth estimation module, and through a multi-stage iterative process, the module can gradually eliminate errors and inaccurate estimates at each step, ultimately obtaining an accurate and detailed depth map. These steps ensure that global and local information are fully integrated and optimized during the depth estimation process, thereby improving the overall quality of depth prediction. Specific Implementation

[0028] like Figure 2As shown, in the designed multi-scale feature enhancement network, the first, second, third, and fourth initial feature maps are input into a lightweight multi-dimensional fusion attention module. Feature enhancement is performed in the channel-height, channel-width, and spatial dimension directions to obtain the first, second, third, and fourth enhanced initial feature maps. The lightweight multi-dimensional fusion attention module is represented as follows: ; in, Feature maps from a lightweight, multi-dimensional fusion attention module It is the input feature map after being processed by the preliminary convolution module or the downsampling convolution module. R represents the set of real numbers, B represents the batch size of the input feature maps, and C represents the number of channels in the input feature maps. and These represent the height and width of the input feature map, respectively. Let S denote a light convolution, and let S denote a direction-aware spatial attention generation module. Indicates channel pooling, , These represent substitution operations between the channel and its height and width, respectively. , It is the inverse operation of permuting between channel and height / width; This represents element-wise multiplication; The fourth-layer enhanced initial feature map is input into the multi-scale context aggregation module to obtain the deep initial feature map. The feature fusion module uses a bottom-up upsampling module to progressively upsample the deep initial feature map. The progressive upsampling module then fuses the deep initial feature map with the first, second, third, and fourth-layer enhanced initial feature maps through a channel alignment module, outputting four multi-scale feature maps with different resolutions. The spatial resolutions are 1 / 3 of the reference image and 1 / 3 of the source image, respectively. The formula is expressed as: ; ; in, For the i-th multi-scale feature map, For the (i+1)th multi-scale feature map, For multi-scale semantic features, x represents the reference image and the source image. For the generated i-th initial feature map, For the i-th lightweight multi-dimensional fusion attention module, This is a multi-scale context aggregation module. For upsampling module, For channel alignment module, For i+1 channel alignment modules.

[0029] like Figure 3 As shown, in the design of the geometry-aware feature fusion network, the geometry-aware convolutional module incorporates a geometric convolutional attention module (Geo) and channel attention (SE) to enhance the response of input features to key geometric information, thereby improving feature fusion and depth perception capabilities. The specific process for improving the geometry-aware convolutional module is as follows: The input features x (reference image and source image) and the first geometric information g1 are fused through the geometric convolutional attention module Geo. The fused features are then processed by convolution Conv, normalization BN, and activation function ReLU. Then it enters the geometric convolutional attention module Geo and is fused with the corresponding second geometric information g2 as input. After convolution, normalization, and ReLU activation, it enters the squeeze-excitation attention enhancement feature. The squeeze-enhanced attention module strengthens the features and outputs the final features, represented as follows: ; in, A feature map representing a series of operations. This represents the activation function. Indicates channel attention, Indicates normalization operation, This represents the convolution operation. This represents geometric convolutional attention, where g1 and g2 are the first and second geometric information, respectively. In step S32, two feature patterns corresponding to the current resolution are selected from the multi-scale geometric information as convolution inputs, referred to as the first geometric information g1 and the second geometric information g2. At the low-resolution level, z-mode and uv-mode features can be selected as the first geometric information g1 and the second geometric information g2, and at the high-resolution level, z-mode and xyz-mode features can be selected as the first geometric information g1 and the second geometric information g2.

[0030] The geometric convolutional attention module takes the input feature x and the corresponding geometric information at the specified resolution and feeds them into channel attention (CA) and spatial attention (SA) for weighting. It then concatenates the input feature x and the geometric information g using concat to output the feature, represented as: ; Here, `final` represents the output feature, and `concat` represents concatenation. SA represents channel attention.

[0031] like Figure 4As shown, the geometric perception-enhanced feature map is input into the multi-stage depth estimation module for iterative optimization, and a refined depth map is output. Multi-stage depth estimation module: Initializes a set of depth hypotheses for the first stage. , where n is the number of depth hypotheses; the depth hypothesis set for the first stage is determined by the minimum and maximum depths of the high-precision laser point cloud in the dataset, and the depth hypothesis set is generated within the sampling interval using equal-interval or inverse-proportional sampling; the depth hypothesis set for subsequent stages is provided by the depth from the previous stage; specifically: Step S51: Input the geometrically aware enhanced feature map, which contains features from the reference image and the source image. Using the camera intrinsic and extrinsic parameters provided in the dataset, the source image features are projected onto the reference viewpoint according to the depth assumption of each pixel, achieving feature alignment; as shown in the formula: ; ; Where p represents the pixel coordinates (spatial location) in the feature map of the reference image. This represents the pixel coordinate p in the feature map of the reference image at the j-th depth hypothesis. The pixel coordinates of the i-th source image below; It is the intrinsic parameter of the i-th source image. , The rotation and translation matrices (external parameters) between the reference image and the i-th source image; It is a depth hypothesis. This represents the pixel coordinate p in the feature map of the reference image at the j-th depth hypothesis. The feature map below shows the pixel coordinates corresponding to the i-th source image. `warp` represents a bilinear sampling operation, and it is assumed that the pixel coordinates `p` in the feature map of the reference image are at the j-th depth. The pixel coordinates of the i-th source image below From source image feature map The alignment feature is obtained; The reference image feature map is The source image feature map is Let i = 1, 2, ..., N−1, where N is the total number of feature maps from the reference image plus all feature maps from the source images, and the intrinsic parameter of the reference image is... ; Step S52: Calculate the correlation between the features of the reference image and the aligned features of the source image by grouping them. The number of channels in the geometrically aware enhanced feature map is divided into G groups, with the number of channels in each group being Cg = C / G. The correlation between the reference features and the aligned source features in each group is calculated as shown in the formula: ; in, Indicating in depth hypothesis Pixel coordinates in the feature map of the reference image below The correlation value of the g-th group; This represents the g-th feature group in the feature map of the reference image at pixel coordinate p. It's an inner product operation. ; For all groups The correlations are averaged and summed to obtain the results under the deep hypothesis. Correlation between pixel coordinate p in the lower reference feature map and the feature map of the i-th source image (Integrating all channels), as shown in the formula: ; The overall correlation is normalized using an exponential function, as shown in the formula: ; in, Indicating in depth hypothesis The matching probability of pixel coordinate p in the feature map of the reference image with the feature map of the i-th source image, where k refers to the traversal depth hypothesis set. ; Take the pixel coordinates p of the feature map of the reference image under the depth assumption The maximum probability of the i-th source image is the weight. As shown in the formula: =max ; The relevance of all source images is weighted and averaged, as shown in the formula: ; in, Indicating in depth hypothesis The correlation of pixel coordinates p in the feature map of the reference image is calculated; the preliminary cost volume is obtained by batch calculation of pixel coordinates p in the feature map of the reference image. ); Step S53: The correlation of all source image features is weighted and averaged to construct a preliminary cost volume. The preliminary cost volume is regularized by deep learning to perform three-dimensional spatial consistency modeling. The initial cost body The input to a 3D convolutional neural network (RegNet) is regularized to obtain a smoother and more accurate cost volume. As shown in the formula: ; in, Indicating in depth hypothesis The regularized cost volume of all pixel coordinates p in the feature map of the lower reference image; Step S54: The initial cost volume for regularization is normalized by an exponential function to form the probability distribution of each pixel of the image under the depth hypothesis set; The regularized cost body is then processed through... The operation is normalized along the depth dimension to obtain hypotheses at different depths. The probability volume of pixel coordinate p in the feature map of the reference image below Also called a probability distribution; for a probability body Depth regression yields the final depth of each pixel, as shown in the formula: ; in, This represents the final regression depth value in all pixel coordinates p in the feature map of the reference image, and the combination of all pixel depth values ​​forms the complete normalized depth map d; Step S55: The final depth value of each pixel in the image is obtained by regression based on the probability distribution. The final depth values ​​of all pixels in the image are combined to obtain a complete depth map. The regularized cost body is then processed through... The operation is normalized along the depth dimension to obtain hypotheses at different depths. The probability volume of pixel coordinate p in the feature map of the reference image below This is also called a probability distribution. Then, regarding the probability volume... Depth regression yields the final depth of each pixel, as shown in the formula: ; in, This represents the final regression depth value in all pixel coordinates p in the feature map of the reference image, and the combination of all pixel depth values ​​forms the complete depth map d.

[0032] Step S56: Based on the final depth value of the current stage, generate a more refined set of depth hypotheses for the next stage by performing inverse depth resampling in the inverse depth domain of each pixel of the image. Step S57 involves multiple processing stages, ultimately outputting the final depth map.

[0033] To enable the next stage to sample a more precise depth range, it is necessary to use the final regressed depth values ​​from all pixel coordinates p in the feature map of the reference image output from the current stage. The new depth sampling interval is redefined, so the inverse depth of the predicted depth of each pixel is first calculated, and then resampled at small intervals in the inverse depth domain; finally, the inverse depth is reversed back to the positive depth; as shown in the formula. ; ; in, It is the upper and lower bounds of the resampling of all pixel coordinates p in the inverse depth domain of the reference image feature map. It is the scaling factor. This is the current depth sampling interval; within this new range, c depth values ​​are uniformly sampled to form the refined depth hypothesis set for the next stage. .

[0034] A 3D reconstruction model is trained using a joint loss function combining pixel-level cross-entropy loss and depth distribution similarity loss. The model incorporates both pixel-level cross-entropy loss and depth distribution similarity loss. Loss Function: In multi-view stereo reconstruction tasks, the design of the loss function plays a crucial role in the performance of the depth estimation network. Traditional multi-view stereo networks do not directly predict depth values, but rather predict a depth probability volume, that is, predicting the probability distribution of each pixel across a series of candidate depth values, and finally regressing the depth using a weighted average. To effectively guide the network in learning spatial geometry, two complementary loss functions are introduced during the training phase: pixel-level cross-entropy loss and depth distribution similarity loss. The former focuses on improving the discriminative ability of each pixel in predicting depth, while the latter focuses on the consistency between the statistical structure of the predicted depth distribution and the true depth.

[0035] Pixel cross-entropy loss is used to train the network to predict the depth probability distribution of each pixel, making its probability in the depth dimension as concentrated as possible at the true depth value. This strategy can better guide the network to learn depth distribution features, improving the accuracy and stability of matching. Specifically, it matches the true depth with the predicted depth value to obtain the minimum difference index for each pixel, and then uses the cross-entropy formula to calculate the loss for each pixel. Depth distribution similarity loss, on the other hand, aims to make the distribution of the predicted depth map as close as possible to the distribution of the true depth map.

[0036] Therefore, KL divergence is used to measure the difference between the predicted depth distribution and the true depth distribution. As shown in the formula: ; Where n is the number of deep hypothesis sets, and z is the index for traversing the deep hypothesis sets. This represents the true probability distribution of each pixel within the depth hypothesis set, generated by mapping the true depth map in the dataset to the depth hypothesis set. This represents the depth assumption of each pixel. The probability distribution is provided by the multi-stage depth estimation module. It is the pixel-level cross-entropy loss value.

[0037] ; Where KL represents the KL divergence between the predicted distribution and the true distribution for each pixel. This represents the depth distribution similarity loss value.

[0038] The comprehensive loss function combines pixel-level cross-entropy loss and depth distribution similarity loss, and progressively optimizes the depth estimation at each stage through a weighted average. As shown in the formula: ; in , These are weighting coefficients used to balance the effects of pixel-level loss and depth distribution similarity loss. The total loss function, where m represents different stages.

[0039] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A multi-view reconstruction method based on geometric perception and attention fusion, characterized in that, Includes the following steps: Step S1: Prepare a multi-view stereo dataset and divide the image pairs in the dataset into reference images and source images; Step S2: Input the reference image and source image from step S1 into the multi-scale feature enhancement network to extract multi-scale feature maps, and input the multi-scale feature maps into the multi-stage depth estimation module to generate a preliminary depth map; Step S3: Perform resolution processing on the reference image in step S1, and perform resolution and normalization processing on the preliminary depth map in step S2 to obtain multi-scale geometric features. Step S4: Input the multi-scale geometric features of the reference image and the initial depth map processed in step S3 into the geometric perception feature fusion network to generate a geometric perception enhanced feature map; Step S5: Input the geometry-aware enhanced feature map into the multi-stage depth estimation module, perform iterative optimization, and output a refined depth map; Step S6: Construct a 3D reconstruction model based on a multi-scale feature enhancement network, a geometric perception feature fusion network, and a multi-stage depth estimation module; train the 3D reconstruction model using a joint loss function of pixel-level cross-entropy loss function and depth distribution similarity loss function.

2. The multi-view reconstruction method based on geometric perception and attention fusion according to claim 1, characterized in that: The multi-view stereo dataset prepared in step S1 is as follows: The Multi-View Stereo Dataset is an indoor dataset that is a public dataset for multi-view stereo reconstruction and 3D modeling. It contains 124 different objects or scenes, each scene is taken from 49 or 64 different viewpoints, and each viewpoint has 7 different lighting conditions. The images in the dataset have a resolution of 1600×1200 pixels. The dataset selects one image as the reference image and the rest as source images. The dataset provides camera intrinsics, camera extrinsics, high-precision laser point clouds, and real depth map data for mapping pixel coordinates to the camera coordinate system.

3. The multi-view reconstruction method based on geometric perception and attention fusion according to claim 2, characterized in that: The reference image and source image from step S1 are input into a multi-scale feature enhancement network to extract multi-scale feature maps. These multi-scale feature maps are then input into a multi-stage depth estimation module to generate a preliminary depth map. Specifically: Step S21: The multi-scale feature enhancement network is divided into a feature selection module and a feature fusion module. The reference image and source image in step S1 are input into the feature selection module of the multi-scale feature enhancement network. Step S22: The reference image and the source image are processed by a preliminary convolution module consisting of two consecutive convolution units to generate an initial feature map of the first layer with a spatial resolution of H×W. Step S23: The feature selection module adopts a top-down downsampling convolution module. The first layer initial feature map is sequentially input into three downsampling convolution modules, and the spatial resolution is gradually reduced to H / 2×W / 2, H / 4×W / 4 and H / 8×W / 8. H / 8×W / 8 is the feature with the highest spatial resolution, and the second, third and fourth layer initial feature maps are obtained. Step S24: The first layer initial feature map, the second layer initial feature map, the third layer initial feature map, and the fourth layer initial feature map are input into the lightweight multi-dimensional fusion attention module, and feature enhancement is performed in the channel-height, channel-width, and spatial dimension directions to obtain the first layer enhanced initial feature map, the second layer enhanced initial feature map, the third layer enhanced initial feature map, and the fourth layer enhanced initial feature map. Step S25: The fourth-layer enhanced initial feature map is input into the multi-scale context aggregation module of the feature fusion module to obtain a deep initial feature map. The feature fusion module uses a bottom-up upsampling module to progressively upsample the deep initial feature map. The progressive upsampling module fuses the deep initial feature map with the first-layer enhanced initial feature map, the second-layer enhanced initial feature map, the third-layer enhanced initial feature map, and the fourth-layer enhanced initial feature map through a channel alignment module, outputting four multi-scale feature maps with different resolutions. The spatial resolution levels are respectively those of the reference image and the source image. ; Step S26: Input four multi-scale feature maps with different resolutions into the multi-stage depth estimation module to generate a preliminary depth map.

4. The multi-view reconstruction method based on geometric perception and attention fusion according to claim 3, characterized in that: Step S3: Perform resolution processing on the reference image in step S1, and perform resolution and normalization processing on the preliminary depth map in step S2 to obtain multi-scale geometric features. Specifically: Step S31: The reference image and the preliminary depth map are processed for resolution to obtain reference image feature I and preliminary depth map feature D. The preliminary depth map feature is then normalized to obtain a normalized depth map, represented as: ； Where d is the normalized depth map, and D is the preliminary depth map feature. , The maximum and minimum values ​​of the initial depth map features; Step S32: Based on the reference image feature I and the normalized depth map d, multi-scale geometric features with different spatial resolutions are generated according to four modes: std, uv, z, or xyz. The four modes std, uv, z, and xyz represent feature representation methods from no geometric constraints to strong geometric constraints, respectively, providing the geometry-aware convolution module with multi-level geometric information from two-dimensional coordinates to three-dimensional space. In std mode, no geometric features are attached; In UV mode, a two-dimensional coordinate grid covering each pixel of the image is generated based on the size of the input reference image feature I, and the two-dimensional coordinate grid is linearly normalized to the [0,1] interval; the normalized two-dimensional coordinate grid is downsampled step by step through 2×2 average pooling to form a 2-channel feature. In z mode, the normalized depth map d is sparsely pooled and downsampled to form a 1-channel depth feature; In xyz mode, based on the camera intrinsic parameters corresponding to the images in the dataset, the normalized two-dimensional coordinates (u,v) of each pixel in the image are back-projected with the 1-channel depth feature in z mode to the three-dimensional coordinates (x,y,z) in the camera coordinate system, and the 3-channel feature is output. In step S34, the multi-scale geometric features of the four modes are used to generate multi-scale representations according to spatial resolution levels 1, 1 / 2, 1 / 4, and 1 / 8, forming corresponding multi-scale geometric information. The multi-scale geometric features are then input into the geometry-aware convolutional module as multi-scale geometric feature information.

5. The multi-view reconstruction method based on geometric perception and attention fusion according to claim 4, characterized in that: Step S4: Input the multi-scale geometric features of the reference image and the initial depth map processed in step S3 into the geometric perception feature fusion network to generate a geometric perception enhanced feature map; the geometric perception feature fusion network is divided into a first branch decoding module, a second branch decoding module and a final fusion module; Specifically: Step S41: The reference image and the initial depth map processed in step S3 are stitched together and input into the preliminary convolution module of the first branch decoding module to generate the first fusion feature map. The first fusion feature map is input into the five-level geometric perception convolution module. Each level of the geometric perception convolution module simultaneously fuses the multi-scale geometric feature information of the reference image and the initial depth map to obtain the second, third, fourth, fifth and sixth fusion feature maps, respectively. In step S42, the first branch decoding module performs progressive upsampling of the fused feature map through the deconvolution module. During the progressive upsampling process, the deconvolution module performs residual connection with the fused feature map output by the initial convolution module and the geometric perception convolution module; and generates a second initial depth map with the same resolution as the input reference image. Step S421: After the deconvolution module performs the first-level upsampling, it is connected with the residual of the fifth fusion feature map of the fourth-level geometric perception convolution module to obtain a spatial resolution of H / 8xW / 8. Step S422: After the deconvolution module performs the second-level upsampling, it is connected with the third fusion feature map residual of the second-level geometric perception convolution module to obtain a spatial resolution of H / 4xW / 4. Step S423: After the deconvolution module performs the third-level upsampling, it is connected with the second fusion feature map residual of the first-level geometric perception convolution module to obtain a spatial resolution of H / 4xW / 4. Step S424: After the deconvolution module performs the fourth level of upsampling, it is connected with the first fused feature map residual of the initial convolution module to obtain a spatial resolution of H / 2XW / 2. Step S425: After the deconvolution module performs the fifth level of upsampling, a spatial resolution of H×W is obtained; a second initial depth map is generated. Step S43: The normalized depth map d channel and the second initial depth map channel are concatenated and input into the preliminary convolution module of the second branch decoding module to generate the seventh fusion feature map. The seventh fusion feature map is input into the five-level geometric perception convolution module of the second branch decoding module. Each level of fusion simultaneously fuses the corresponding multi-scale geometric feature information of the reference image and the initial depth map. Step S44: The seventh fused feature map is input into the first and second geometric perception convolutional modules to obtain the eighth fused feature map. The eighth fused feature map is concatenated with the features output from the residual connection in step S424 to obtain the first joint feature. The first joint feature is input into the third and fourth geometric perception convolutional modules to obtain the ninth fused feature map. The ninth fused feature map is concatenated with the features output from the residual connection in step S421 to obtain the second joint feature. The second joint feature is input into the fifth geometric perception convolutional module to generate the third initial depth map. Step S45: The final fusion module consists of a five-level deconvolution module and five fusion processes. The five-level deconvolution module is divided into a first-level deconvolution module, a second-level deconvolution module, a third-level deconvolution module, a fourth-level deconvolution module, and a fifth-level deconvolution module. The third deconvolution module processes the first stage to output the first-level geometric perception enhanced feature map. The fourth deconvolution module processes the second stage to output the second-level geometric perception enhanced feature map. The fifth deconvolution module processes the third stage to output the third-level geometric perception enhanced feature map. Step S46, the first fusion process, the features of the sixth fusion feature map of the first branch decoding module and the third initial depth map of the second branch decoding module are added element by element and input into the first-level deconvolution module of the final fusion module to generate the first-level fusion feature; Step S47, the second fusion process: the fourth-level geometric perception module of the second branch decoding module adds the first-level fusion features element by element and inputs them into the second-level deconvolution module of the final fusion module to generate the second-level fusion features; Step S48, the third fusion process: the second-level geometric perception module of the second branch decoding module adds the second-level fusion features element-wise to the second-level fusion features, and inputs them into the third-level deconvolution module of the final fusion module to generate third-level fusion features. If it belongs to the first stage, the third-level fusion features are input into the first-level RGB deconvolution module, and the output is then combined with the output of the multi-scale feature enhancement network. Residual connections are made between multi-scale feature maps of different resolutions to obtain the first-stage geometric perception enhancement feature map. Step S49, the fourth fusion process: The first-level geometric perception module of the second branch decoding module adds the third-level fusion features element-wise, and inputs them into the fourth-level deconvolution module of the final fusion module to generate fourth-level fusion features. If it belongs to the second stage, the fourth-level fusion features are input into the second-level RGB deconvolution module, and the output is then combined with the output of the multi-scale feature enhancement network. Residual connections are performed on the multi-scale feature maps to obtain the second-stage geometric perception enhancement feature maps. Step S50, the fifth fusion process: the initial convolution module of the second branch decoding module adds the fourth-level fusion feature element by element and inputs it into the fifth-level deconvolution module of the final fusion module to generate the fifth-level fusion feature. If it belongs to the third stage, the fifth-level fusion feature is input into the third-level RGB deconvolution module. After output, it is residually connected with the 1 / 1 resolution multi-scale feature map output by the multi-scale feature enhancement network to obtain the third-stage geometric perception enhancement feature map. Geometric perception-enhanced feature maps, expressed by the formula: ； Where Y is the geometry-aware enhanced feature map. These are features in multi-scale feature enhancement networks. It is a fusion feature of the first branch decoding module and the second branch decoding module. The final fusion module enhances the network's features by combining the fusion features of the first branch decoding module and the second branch decoding module, along with multi-scale features. Perform element-by-element fusion. and These represent the first branch decoding module and the second branch decoding module, respectively. I is the reference image feature, and d is the normalized depth map. It is a depth map guided by a reference image.

6. The multi-view reconstruction method based on geometric perception and attention fusion according to claim 5, characterized in that: Step S5: Input the geometry-aware enhanced feature map into the multi-stage depth estimation module for iterative optimization, and output a refined depth map; specifically: Step S51: Input the geometric perception enhancement feature map, which contains reference image features and source image features. Using the camera intrinsic and extrinsic parameters provided in the dataset, the source image features are projected onto the reference viewpoint according to the depth assumption of each pixel to achieve feature alignment. Step S52: Calculate the correlation between the features of the reference image and the aligned features of the source image by grouping them. Step S53: The correlation of all source image features is weighted and averaged to construct a preliminary cost volume. The preliminary cost volume is regularized by deep learning to perform three-dimensional spatial consistency modeling. Step S54: The initial cost volume for regularization is normalized by an exponential function to form the probability distribution of each pixel of the image under the depth hypothesis set; Step S55: Obtain the final depth value of each pixel in the image based on probability distribution regression, and combine the final depth values ​​of all pixels in the image to obtain a complete depth map. Step S56: Based on the final depth value of the current stage, generate a more refined set of depth hypotheses for the next stage by performing inverse depth resampling in the inverse depth domain of each pixel of the image. Step S57 involves multiple stages of processing, ultimately outputting the final depth map.

7. A multi-view reconstruction system based on geometric perception and attention fusion, applied to the multi-view reconstruction method based on geometric perception and attention fusion as described in claim 6, characterized in that: A 3D reconstruction model is constructed based on a multi-scale feature enhancement network, a geometric perception feature fusion network, and a multi-stage depth estimation module. The multi-scale feature enhancement network includes a feature selection module and a feature fusion module; The feature selection module includes a preliminary convolution module, a downsampling convolution module, and a lightweight multi-dimensional fusion attention module; The feature fusion module consists of a channel alignment module, an upsampling module, and a multi-scale context aggregation module; Among them, the geometric perception feature fusion network mainly includes a first branch coding module, a second branch coding module and a final fusion module; The first branch encoding module includes an initial convolution module, a geometry-aware convolution module, and a deconvolution module; The second branch encoding module includes an initial convolution module and a geometry-aware convolution module; The final fusion module receives the outputs of the first branch coding module and the second branch coding module, and performs scale fusion of the first branch coding module and the second branch coding module accordingly. The multi-stage depth estimation module consists of feature alignment, correlation calculation, regularization, normalization, depth regression, and inverse depth resampling.

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