Method for reconstructing three-dimensional edge of multi-view picture

Abstract

The invention discloses a method for reconstructing a three-dimensional edge of a multi-view image. The method comprises the following steps: step 1, carrying out two-dimensional image edge detection on the multi-view image to obtain an edge image and calculating to obtain a structural point cloud; 2, initializing a spherical 3D Gaussian primitive based on the structural point cloud; 3, supervising and optimizing the number and attributes of the spherical 3D Gaussian primitives by using the edge graph; step 4, carrying out linear fitting on the optimized spherical 3D Gaussian primitive based on interpolation rough; and step 5, further optimizing a straight line fitting result to a third-order rational Bezier curve to obtain a final multi-view picture three-dimensional edge reconstruction result. According to the method, a spherical 3D Gaussian primitive is introduced as a three-dimensional edge representation medium, and the attribute of the spherical 3D Gaussian primitive is optimized by using edge detection information of a two-dimensional image, so that three-dimensional edge information is extracted from the two-dimensional image; the 3D Gaussian splashing technology is used for monitoring spherical 3D Gaussian attributes, and the consistency of spherical 3D Gaussian primitives in two-dimensional rendering and three-dimensional representation is guaranteed.

Description

Technical Field

[0001] The present invention belongs to the field of artificial intelligence, and particularly relates to a method for reconstructing three-dimensional edges from multi-view images. Background Art

[0002] Edges are the basic structures in three-dimensional objects and provide important geometric information for creating compact model reconstructions. In the process of digitalizing industrial scenarios, completing the three-dimensional edge reconstruction of the scenario can greatly facilitate three-dimensional scene modeling and subsequent digital management. In practical applications, the three-dimensional object edge reconstruction in industrial scenarios is extremely complex. Traditional three-dimensional edge reconstruction methods usually rely on a large amount of three-dimensional point cloud data for model training and feature extraction. However, it is very difficult to obtain such a large-scale and high-quality three-dimensional data. When extracting three-dimensional information data, annotators often need to rely on high-precision spatial scanner devices and frequently carry and move them in the complex industrial scene layout, which further increases the difficulty and cost of data acquisition. For these reasons, traditional three-dimensional edge reconstruction methods are severely restricted in practical industrial applications. Pictures are the most easily obtained form of data in daily life, and can be easily obtained with ordinary shooting devices such as mobile phones or cameras. Therefore, reconstructing parameterized three-dimensional edges from two-dimensional pictures has very important research value.

[0003] With the progress of deep learning technology, the 3D Gaussian splatting technology that has emerged in recent years can perform self-supervised learning from a set of multi-view images and use 3D Gaussian basis elements to real-time render and synthesize new view images. The generation of existing 3D Gaussian basis elements does not have a clear geometric meaning, so it can often only be used for the generation of two-dimensional pictures and cannot perform further three-dimensional reconstruction work. Therefore, there is an urgent need for an innovative method to constrain the attributes of 3D Gaussian basis elements so that they can have good geometric representation significance in three-dimensional space and be utilized, while maintaining the advantages of Gaussian itself in two-dimensional picture rendering. Summary of the Invention

[0004] Object of the Invention: The technical problem to be solved by the present invention is to provide a method for reconstructing three-dimensional edges from multi-view images in view of the deficiencies of the prior art.

[0005] To solve the above technical problem, the present invention discloses a method for reconstructing three-dimensional edges from multi-view images, including the steps of:

[0006] Step 1, performing two-dimensional image edge detection on the multi-view images to obtain an edge map and obtaining a structured point cloud by the COLMAP (Structure-from-Motion pose estimation and Multi-View Stereo multi-view stereo matching) method;

[0007] Step 2: Initialize spherical 3D Gaussian basis elements based on the structural point cloud;

[0008] Step 3: Use the edge map for supervision to optimize the number and properties of the spherical 3D Gaussian basis elements;

[0009] Step 4: Roughly perform linear fitting on the optimized spherical 3D Gaussian basis elements based on interpolation;

[0010] Step 5: Further optimize the linear fitting result to a 3rd-order rational Bezier curve to obtain the final 3D edge reconstruction result of the multi-view image.

[0011] Specifically, Step 1 is as follows:

[0012] Step 1-1: Normalize a set of multi-view input images to a unified resolution size, as the Gaussian optimization process requires the input images to have the same resolution;

[0013] Step 1-2: Use the COLMAP method to estimate the camera pose of each image and obtain the structural point cloud;

[0014] Step 1-3: Use the PiDiNet (Pixel Difference Network) as a detector to perform 2D edge detection on each input image to obtain the edge map of each image.

[0015] Specifically, Step 2 is as follows: The center position and number of the initialized 3D Gaussian basis elements are the same as those of the structural point cloud obtained in Step 1-2 (the position of each point in the point cloud corresponds to the center of a Gaussian, so the number is the same as that of the point cloud). The shape is uniformly set to a sphere with a radius of 0.005. The color attribute only retains the grayscale value, and the rotation, scaling, and spherical harmonic function attributes are removed.

[0016] Specifically, Step 3 includes the following steps:

[0017] Step 3-1: Use the edge map in the edge detection result for supervision, use the 3D Gaussian splashing technique to render the Gaussian image, and calculate the edge pixel loss L edge , and the calculation formula is as follows:

[0018]

[0019] where N I represents the total number of pixels in the image, E I represents the number of edge pixels (grayscale value greater than 0.3) in the edge map, I i and respectively represent the corresponding pixels in the edge map and the Gaussian rendering result map, represents the L2 loss function, that is, the square of the absolute value difference; this loss makes the rendering results of the spherical Gaussian basis elements in multiple views as close as possible to the real edge map;

[0020] Step 3-2: Calculate the color opacity consistency loss L of the spherical Gaussian basis elements, and the calculation formula is as follows; oc , and the calculation formula is as follows;

[0021]

[0022] where N SG represents the number of current spherical Gaussian basis elements, o i and the opacity attribute of each spherical Gaussian basis element, c i represents the color grayscale value attribute of each spherical Gaussian basis element; this loss enables the spherical Gaussian to render an edge result map without perspective occlusion;

[0023] Step 3-3: Calculate the regularization loss L of the spherical Gaussian basis elements, and the calculation formula is as follows; reg , and the calculation formula is as follows;

[0024]

[0025] where N SG represents the number of current spherical Gaussian basis elements, o i represents the opacity attribute of each spherical Gaussian basis element; this loss enables the overall opacity of the 3D spherical Gaussian basis elements to be minimized as much as possible, so as to remove redundant basis elements subsequently and streamline the final result;

[0026] Step 3-4: Jointly optimize all spherical Gaussian basis elements with the edge pixel loss L edge , the color opacity consistency loss L oc and the regularization loss L reg ; during the Gaussian optimization iteration process, remove the Gaussian basis elements with opacity and color grayscale values less than a certain threshold.

[0027] In Step 3-4, specifically: use the total loss function L = 0.8L edge +2L oc +0.01L reg to perform 6000 rounds of iterative optimization on all spherical Gaussian basis elements. Split and clone the Gaussian basis elements every 200 rounds, reset the opacity attributes of all Gaussians to 0.1 every 1000 rounds, and remove all Gaussian basis elements with opacity less than 0.5 and color grayscale value less than 0.1 every 3000 rounds; the remaining spherical Gaussian basis elements after the final iteration will be used for 3D edge reconstruction, and the iteration is consistent with the iteration process of the D Gaussian splash in Step 3-13.

[0028] Step 4 is specifically as follows:

[0029] Step 4-1: In the optimized spherical Gaussian basis elements in Step 3, randomly select the centers of two Gaussian basis elements as the endpoints to initialize a straight line. Interpolate N points evenly on this line, and add Gaussian noise with a standard deviation of 0.005 to these interpolated points; s Step 4-2: Calculate the average chamfer distance between these N interpolated points and the centers of all spherical Gaussian basis elements within a distance of δ1 around them. Iteratively optimize the endpoint positions of this straight line several times to minimize this average chamfer distance;

[0030] Step 4-3: Record the optimized endpoints of the straight line, and temporarily delete all spherical Gaussian basis elements within a distance of δ1 around the straight line; s Step 4-4: Repeat the above steps several times until the number of remaining spherical Gaussian basis elements is less than the threshold N0.

[0031] In Step 4-2, to calculate the average chamfer distance between the interpolated points on the straight line and the centers of all spherical Gaussian basis elements within a distance of δ1 around them, the following formula is specifically used:

[0032] where p and q represent the two endpoints of the current straight line, l represents all the interpolated points on the straight line, x represents an interpolated point on l, P(G) represents the centers of all spherical Gaussian basis elements within a distance of δ1 from the current straight line, y represents the center of a spherical Gaussian basis element in P(G). By optimizing the positions of p and q, the calculated average chamfer distance is minimized. At this time, the straight line represented by p and q fits the spherical Gaussians within a distance of δ1 around it.

[0033] Step 5 includes the following steps:

[0034]

[0035] Step 5-1: Add 2 control points to all the straight lines fitted in Step 4, and combine with the endpoints to transform them into the form of a 3rd-order rational B-spline curve. Each curve is determined by 4 control points; Interpolate N points on each B-spline curve, and add Gaussian noise with a standard deviation of 0.005; p,q Step 5-2: Restore all the spherical Gaussian basis elements deleted in Step 4-3, calculate the weighted chamfer distance between all B-spline curves and the centers of all spherical Gaussian basis elements, and iteratively optimize the control points on all B-spline curves several times to minimize this weighted chamfer distance; p,q where p and q represent the two endpoints of the current straight line, l represents all the interpolated points on the straight line, x represents an interpolated point on l, P(G) represents the centers of all spherical Gaussian basis elements within a distance of δ1 from the current straight line, y represents the center of a spherical Gaussian basis element in P(G). By optimizing the positions of p and q, the calculated average chamfer distance is minimized. At this time, the straight line represented by p and q fits the spherical Gaussians within a distance of δ1 around it. i Step 5-1: Add 2 control points to all the straight lines fitted in Step 4, and combine with the endpoints to transform them into the form of a 3rd-order rational B-spline curve. Each curve is determined by 4 control points; Interpolate N points on each B-spline curve, and add Gaussian noise with a standard deviation of 0.005; i Step 5-2: Restore all the spherical Gaussian basis elements deleted in Step 4-3, calculate the weighted chamfer distance between all B-spline curves and the centers of all spherical Gaussian basis elements, and iteratively optimize the control points on all B-spline curves several times to minimize this weighted chamfer distance;

[0036] Step 5 includes the following steps:

[0037] Step 5-1: Add 2 control points to all the straight lines fitted in Step 4, and combine with the endpoints to transform them into the form of a 3rd-order rational B-spline curve. Each curve is determined by 4 control points; Interpolate N points on each B-spline curve, and add Gaussian noise with a standard deviation of 0.005; s Step 5-2: Restore all the spherical Gaussian basis elements deleted in Step 4-3, calculate the weighted chamfer distance between all B-spline curves and the centers of all spherical Gaussian basis elements, and iteratively optimize the control points on all B-spline curves several times to minimize this weighted chamfer distance;

[0038] Step 5-2: Restore all the spherical Gaussian basis elements deleted in Step 4-3, calculate the weighted chamfer distance between all B-spline curves and the centers of all spherical Gaussian basis elements, and iteratively optimize the control points on all B-spline curves several times to minimize this weighted chamfer distance;

[0039] Step 5-3: The curve generated by the control points of all optimized third-order rational Bézier curves is the final three-dimensional edge reconstruction result of the multi-view image.

[0040] In Step 5-2, calculate the weighted chamfer distance between all Bézier curves and the centers of all spherical Gaussian basis elements. The specific formula is as follows:

[0041]

[0042] where l all represents the interpolation points on all Bézier curves, P(G) represents the centers of all spherical Gaussian basis elements, and o y represents the opacity attribute of the y-th spherical Gaussian basis element. γ is a distance balance parameter, generally taken around 2. Increasing it will increase the recall rate and decrease the precision; decreasing it will decrease the recall rate and increase the precision. By optimizing the control point positions and weights of all rational Bézier curves, the weighted chamfer distance is minimized. At this time, the curve represented by all control points fits all spherical Gaussians.

[0043] Beneficial effects:

[0044] 1) This method introduces spherical 3D Gaussian basis elements as the three-dimensional edge representation medium, and uses the edge detection information of two-dimensional images to optimize the attributes of spherical 3D Gaussian basis elements, thus achieving the extraction of three-dimensional edge information from two-dimensional images. This method uses 3D Gaussian splashing technology as the supervision of the attributes of spherical 3D Gaussians, ensuring the consistency of spherical 3D Gaussian basis elements in two-dimensional rendering and three-dimensional representation.

[0045] 2) This method uses the generated spherical 3D Gaussian basis elements to successively fit straight lines and rational Bézier curves in three-dimensional space, enabling the final edge result to be parametrically reconstructed.

[0046] 3) The method for reconstructing three-dimensional edges from multi-view images based on 3D Gaussian splashing technology directly processes the input multi-view images without the need for any additional three-dimensional information assistance, enabling this invention to be completed under the condition of only having two-dimensional image capture devices such as mobile phones or cameras, which is very convenient to use. Moreover, the memory and time overheads in the entire algorithm process are very small. Description of the drawings

[0047] Figure 1 is the flow chart of the method of the present invention.

[0048] Figure 2 is a schematic diagram of extracting edge information and generating curves by spherical 3D Gaussian basis elements in two dimensions and three dimensions.

[0049] Figure 3 is the input multi-view image.

[0050] Figure 4 It is the 3D edge reconstruction result of multi-view images. Detailed implementation manners

[0051] In view of the technical pain points, the present invention proposes a method for reconstructing 3D edges of multi-view images based on 3D Gaussian splashing technology. The aim is to efficiently and accurately reconstruct parametric edge information in space by using the associative representation of spherical 3D Gaussian basis elements between two dimensions and three dimensions. The core lies in using the results of 2D edge detection of images to train and generate corresponding spherical Gaussian basis elements, and then successively fitting straight lines and rational Bezier curves in space according to the generated spherical Gaussian basis elements, and finally completing the parametric reconstruction of 3D edges.

[0052] Embodiment:

[0053] A method for reconstructing 3D edges of multi-view images includes the following steps:

[0054] Step 1, perform 2D image edge detection on multi-view images (as shown in Figure 3 ) to obtain an edge map and obtain a structured point cloud through the COLMAP (Structure-from-Motion pose estimation and Multi-View Stereo multi-view stereo matching) method;

[0055] Step 2, initialize spherical 3D Gaussian basis elements based on the structured point cloud;

[0056] Step 3, use the edge map to supervise and optimize the number and attributes of spherical 3D Gaussian basis elements;

[0057] Step 4, roughly perform straight line fitting on spherical 3D Gaussian basis elements based on interpolation;

[0058] Step 5, further optimize the straight line fitting result to a 3rd-order rational Bezier curve to obtain the final 3D edge reconstruction result of multi-view images (as shown in Figure 4 ).

[0059] Specifically, Step 1 is as follows:

[0060] Step 1-1, normalize a set of multi-view input images to a unified resolution size; (The Gaussian optimization process requires the input images to have the same resolution)

[0061] Step 1-2, use the COLMAP method to estimate the camera pose of each image and obtain a structured point cloud;

[0062] Step 1-3, use the PiDiNet (Pixel Difference Network) network as a detector to perform 2D edge detection on each input image to obtain the edge map of each image.

[0063] Step 2 is specifically as follows: The center positions and quantities of the initialized 3D Gaussian basis elements are consistent with the structural point cloud obtained in Step 1-2 (the position of each point in the point cloud corresponds to the center of a Gaussian, so the quantity is consistent with the point cloud). The shape is uniformly set to a sphere with a radius of 0.005, the color attribute only retains the grayscale value, and the rotation, scaling, and spherical harmonic function attributes are removed.

[0064] In Step 3, it specifically includes the following steps:

[0065] Step 3-1: Using the edge map in the edge detection result for supervision, rendering the Gaussian image using the 3D Gaussian splashing technique, and calculating the edge pixel loss L edge , and the calculation formula is as follows:

[0066]

[0067] where N I represents the total number of pixels in the image, E I represents the number of edge pixels (grayscale value greater than 0.3) in the edge map, I i and respectively represent the corresponding pixels in the edge map and the Gaussian rendering result map, represents the L2 loss function, that is, the square of the absolute difference; this loss makes the rendering results of the spherical Gaussian basis elements as close as possible to the real edge map from multiple perspectives;

[0068] Step 3-2: Calculating the color opacity consistency loss L oc of the spherical Gaussian basis elements, and the calculation formula is as follows;

[0069]

[0070] where N SG represents the current number of spherical Gaussian basis elements, o i and the opacity attribute of each spherical Gaussian basis element, c i represents the color grayscale value attribute of each spherical Gaussian basis element; this loss enables the spherical Gaussian to render an edge result map without perspective occlusion;

[0071] Step 3-3: Calculating the regularization loss L reg of the spherical Gaussian basis elements, and the calculation formula is as follows;

[0072]

[0073] where N SG represents the current number of spherical Gaussian basis elements, o i represents the opacity attribute of each spherical Gaussian basis element; this loss enables the overall opacity of the 3D spherical Gaussian basis elements to be minimized as much as possible, so as to remove redundant basis elements in the subsequent process and streamline the final result;

[0074] Step 3-4, combine the edge pixel loss (boundary pixel loss) L edge , color opacity consistency loss L oc and regularization loss L reg to perform iterative optimization on all spherical Gaussian basis elements; during the Gaussian optimization iteration process, eliminate the Gaussian basis elements with opacity and color gray value less than a certain threshold.

[0075] In step 3-4, specifically: use the total loss function L = 0.8L edge +2L oc +0.01L reg to perform 6000 rounds of iterative optimization on all spherical Gaussian basis elements. Split and clone the Gaussian basis elements every 200 rounds, reset the opacity attribute of all Gaussians to 0.1 every 1000 rounds, and eliminate all Gaussian basis elements with opacity less than 0.5 and color gray value less than 0.1 every 3000 rounds; the remaining spherical Gaussian basis elements after the final iteration will be used for 3D edge reconstruction.

[0076] Step 4 is specifically as follows:

[0077] Step 4-1, in the spherical Gaussian basis elements optimized in step 3, randomly select the centers of two Gaussian basis elements as the endpoints to initialize a straight line. Interpolate N s points evenly on this straight line, and add Gaussian noise with a standard deviation of 0.005 to these interpolated points;

[0078] Step 4-2, calculate the average chamfer distance between the centers of all spherical Gaussian basis elements within a distance of δ1 from these N s interpolated points, and iteratively optimize the endpoint positions of this straight line several times to make this average chamfer distance reach the minimum value;

[0079] Step 4-3, record the optimized straight line endpoints, and temporarily delete all spherical Gaussian basis elements within a distance of δ1 from the straight line;

[0080] Step 4-4, repeat the above steps several times until the number of remaining spherical Gaussian basis elements is less than the threshold N0.

[0081] In step 4-2, when calculating the average chamfer distance between the straight line interpolated points and the centers of all spherical Gaussian basis elements within a distance of δ1 from them, the following formula is specifically used:

[0082]

[0083] where p and q represent the two endpoints of the current straight line, l p,q represents all the interpolated points on the straight line, x represents an interpolated point on l p,q on, P(Gi ) represents all the centers of the spherical Gaussian basis elements within a distance of δ1 from the current straight line, and y represents one of the centers of the spherical Gaussian basis elements in P(G i ). By optimizing the positions of p and q, the calculated average chamfer distance is minimized. At this time, the straight line represented by p and q fits the spherical Gaussian within the surrounding distance of δ1.

[0084] Step 5 includes the following steps:

[0085] Step 5-1: Add 2 control points to all the straight lines fitted in Step 4, and combine with the endpoints to transform them into the form of a 3rd-order rational Bezier curve. Each curve is determined by 4 control points; Interpolate N s points on each Bezier curve, and add Gaussian noise with a standard deviation of 0.005;

[0086] Step 5-2: Restore all the spherical Gaussian basis elements deleted in Step 4-3, calculate the weighted chamfer distance between all the Bezier curves and all the centers of the spherical Gaussian basis elements, and iterate the control points on all the Bezier curves several times to make this weighted chamfer distance reach the minimum value;

[0087] Step 5-3: The curve generated by the control points of all the optimized 3rd-order rational Bezier curves is the final 3D edge reconstruction result of the multi-view picture.

[0088] In Step 5-2, when calculating the weighted chamfer distance between all the Bezier curves and all the centers of the spherical Gaussian basis elements, the following formula is specifically used:

[0089]

[0090] where, l all represents the interpolation points on all the Bezier curves, P(G) represents all the centers of the spherical Gaussian basis elements, o y represents the opacity attribute of the y-th spherical Gaussian basis element, and γ is a distance balance parameter, generally taken as about 2. Increasing it will increase the recall rate and decrease the precision; decreasing it will decrease the recall rate and increase the precision. By optimizing the positions and weights of the control points of all the rational Bezier curves, this weighted chamfer distance is minimized. At this time, the curve represented by all the control points fits all the spherical Gaussians.

[0091] Finally, the process and results as shown in Figure 2 can be obtained. Figure 2 shows the entire process from a 2D picture to generating 3D parametric edges. The 2D module shows the process of extracting 2D edge features from the spherical 3D Gaussian basis elements, and the 3D module shows the process of generating parametric edge curves from the spherical 3D Gaussian basis elements. It shows that the present invention constructs a good bridge between 2D and 3D, and enables good spatial consistency between the input and output.

[0092] The present invention provides a method for reconstructing three-dimensional edges of multi-view images. There are many methods and ways to specifically implement this technical solution. The above description is only a preferred embodiment of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention. Each component not clearly defined in this embodiment can be implemented by using the prior art.

Claims

1. A three-dimensional edge reconstruction method for multi-view images, characterized in that, Including the steps: Step 1: Conduct two-dimensional image edge detection on multi-view images to obtain an edge map and calculate a structural point cloud; Step 2: Initialize spherical 3D Gaussian basis elements based on the structural point cloud; Step 3: Use the edge map to supervise and optimize the number and properties of the spherical 3D Gaussian basis elements; Step 4: Perform linear fitting on the optimized spherical 3D Gaussian basis elements based on interpolation; Step 5: Further optimize the linear fitting result to a third-order rational Bezier curve to obtain the final three-dimensional edge reconstruction result of the multi-view image.

2. The multi-view image reconstruction three-dimensional edge method according to claim 1, characterized in that Specifically, Step 1 is as follows: Step 1-1: Normalize a set of multi-view input images to a unified resolution size; Step 1-2: Estimate the camera pose of each image and obtain a structural point cloud; Step 1-3: Conduct two-dimensional edge detection on each input image to obtain the edge map of each image.

3. A method for reconstructing three-dimensional edges of multi-view images according to claim 2, characterized in that, Specifically, Step 2 is: The center position and number of the initialized 3D Gaussian basis elements are the same as the structural point cloud obtained in Step 1-2. The shape is uniformly set to spherical, and only the gray value is retained for the color attribute. Rotation, scaling, and spherical harmonic function attributes are removed.

4. A method for reconstructing a three-dimensional edge of a multi-view image according to claim 2, characterized in that, In Step 3, specifically, the following steps are: Step 3-1, using the edge map in the edge detection results as supervision, rendering the Gaussian image using the 3D Gaussian splashing technique, and calculating the edge pixel loss L edge , and the calculation formula is as follows: Among them, N I represents the total number of pixels in the image, E I represents the number of edge pixels in the edge map, I i and respectively represent the corresponding pixels in the edge map and the Gaussian rendering result map, represents the L2 loss function; Step 3-2: Calculate the color opacity consistency loss L of the spherical Gaussian basis elements, and the calculation formula is as follows; oc , where N SG represents the number of current spherical Gaussian basis elements, and o i and the opacity attribute of each spherical Gaussian basis element, c i represents the color grayscale value attribute of each spherical Gaussian basis element; Step 3-3, calculate the regularization loss L of the spherical Gaussian basis element reg , and the calculation formula is as follows; Among them, N SG represents the number of current spherical Gaussian basis elements, and o i represents the opacity attribute of each spherical Gaussian basis element; Step 3-4, combining the edge pixel loss L edge , the color opacity consistency loss L oc and the regularization loss L reg perform iterative optimization on all spherical Gaussian basis elements, and the iterative process is the same as the 3D Gaussian splashing method in Step 3-1.

5. A method for reconstructing three-dimensional edges of multi-view images according to claim 4, characterized in that, In step 3-4, specifically: using the total loss function L = 0.8L edge + 2L oc + 0.01L reg Iteratively optimize all spherical Gaussian basis elements. During the iteration process, split and clone the Gaussian basis elements at a certain period, reset the opacity attributes of all Gaussians at a certain period, and remove all Gaussian basis elements whose opacity and color grayscale values do not meet the threshold at a certain period; the remaining spherical Gaussian basis elements after the final iteration will be used for 3D edge reconstruction.

6. A method for reconstructing a three-dimensional edge of a multi-view image according to claim 5, characterized in that Specifically, Step 4 is: Step 4-1, in the optimized spherical Gaussian basis element in Step 3, randomly select the centers of two Gaussian basis elements as endpoints to initialize a straight line, interpolate N s points evenly on this straight line, and add Gaussian noise to these interpolated points; Step 4-2, calculate the average chamfer distance between the centers of all spherical Gaussian basis elements within a distance of δ1 from these N s interpolation points and their surroundings, and iteratively optimize the endpoint positions of this line several times to minimize this average chamfer distance; Step 4-3: Record the endpoints of the optimized line and temporarily delete all spherical Gaussian basis elements within a distance of δ1 around the line; Step 4-4: Repeat the above steps several times until the number of the remaining spherical Gaussian basis elements is less than the threshold N0.

7. A method for reconstructing a three-dimensional edge of a multi-view image according to claim 6, characterized in that In Step 4-2, calculate the average chamfer distance between the linear interpolation points and the centers of all spherical Gaussian basis elements within a distance of δ1 around them. Specifically, the following formula is used: Among them, p and q represent the two endpoints of the current straight line, and l p,q represents all the interpolation points on the straight line, x represents an interpolation point on l p,q , and P(G i ) represents all the spherical Gaussian basis element centers within a distance of δ1 from the current straight line, y represents a spherical Gaussian basis element center in P(G i ), and by optimizing the positions of p and q to minimize the calculated average chamfer distance, the straight line represented by p and q at this time fits the spherical Gaussians within the surrounding distance of δ1.

8. A method for reconstructing three-dimensional edges of multi-view pictures according to claim 7, characterized in that Step 5 includes the following steps: Step 5-1, add 2 control points to all the lines fitted in Step 4, and combine with the endpoints to transform them into the form of 3rd-order rational Bezier curves, where each curve is determined by 4 control points; interpolate N s points on each Bezier curve, and add Gaussian noise; Step 5-2: Restore all the spherical Gaussian basis elements deleted in Step 4-3, calculate the weighted chamfer distance between all Bezier curves and the centers of all spherical Gaussian basis elements, and iterate the control points on all Bezier curves several times to make this weighted chamfer distance reach the minimum value; Step 5-3: The curve generated by the control points of all the optimized third-order rational Bezier curves is the final three-dimensional edge reconstruction result of the multi-view image.

9. A method for reconstructing three-dimensional edges of multi-view images according to claim 8, characterized in that, In Step 5-2, calculate the weighted chamfer distance between all Bezier curves and the centers of all spherical Gaussian basis elements. Specifically, the following formula is used: where, l all represents the interpolation points on all Bézier curves, P(G) represents the centers of all spherical Gaussian basis elements, o y represents the opacity attribute of the y-th spherical Gaussian basis element, γ is a distance balance parameter, and by optimizing the positions and weights of the control points of all rational Bézier curves, the weighted chamfer distance is minimized. At this time, the curves represented by all control points fit all spherical Gaussians.

10. A method for reconstructing a three-dimensional edge of a multi-view image according to claim 5, characterized in that, The iteration process is the same as the 3D Gaussian splashing method in Step 3-1.

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