Point cloud surface reconstruction method and device based on parameterized expression, terminal and medium

Abstract

The invention provides a parameterized expression-based point cloud surface reconstruction method and device, a terminal and a medium, and the method comprises the steps: obtaining a to-be-processed point cloud corresponding to a target object, determining a parameterized curved surface of an anchor point based on parameterized expression, and representing an object surface of the to-be-processed point cloud through the parameterized curved surface; converting the parameterized curved surface into a triangular mesh to reconstruct a three-dimensional surface of the target object; wherein the parameterized expression is composed of any number of anchor points, the anchor points are located inside or outside the target object and face the surface of the target object to observe the target object, observation information expressed based on the positions and orientations of the anchor points and coefficients of a pre-constructed primary function is obtained, and the parameterized curved surface of the anchor points is expressed through the observation information. According to the method, the object surface of the point cloud is represented based on the parameterized expression, the parameterized expression is converted into the triangular mesh, surface reconstruction of the point cloud is realized, and more accurate object surface information can be recovered on the premise of keeping relatively high calculation efficiency.

Description

Technical Field

[0001] The present invention relates to the technical field of point cloud surface reconstruction, and in particular to a point cloud surface reconstruction method, device, terminal and medium based on parameterized expression. Background Art

[0002] In fields such as computer graphics and computational geometry, the representation of three-dimensional shapes is crucial for applications such as virtual reality, games, advanced manufacturing, and scientific visualization. Traditional representation methods for three-dimensional shapes include voxel grids, point clouds, and triangular meshes. Each representation method has its own unique advantages and limitations. Among them, triangular meshes are widely used in computer graphics, virtual reality, game development, and scientific visualization due to their simple structure, convenient processing, and ability to provide accurate surface geometry information and support efficient visualization. However, although point cloud data is one of the easiest data to collect from the real world and can provide sparse and high-resolution surface information, it lacks the ordered structure and topological relationship of triangular meshes, making point clouds more complex to process and difficult to use directly in applications that require precise geometric operations. Therefore, many studies are devoted to converting point clouds into various different expressions and efficiently and accurately converting them into triangular meshes.

[0003] At present, the schemes for reconstructing triangular meshes based on point clouds can be roughly divided into four categories. For example, voxel grids can naturally extend the previous contour extraction methods in two-dimensional space to three-dimensional space to achieve volume shape estimation; point clouds can provide sparse and high-resolution data and allow surface shape estimation based on local point cloud distribution; in addition, with the maturity of deep learning technology, many works have begun to describe the geometric information of objects with implicit expressions such as signed distance fields and extract triangular meshes from them, but the existing point cloud surface reconstruction algorithms also face the problem of difficult balance between representation accuracy and computational efficiency. In addition, since expressions such as voxel grids and signed distance fields require dense division of three-dimensional space, the computational cost of methods based on such expressions is too high when reconstructing the high-resolution surface of objects, and it will also lead to the problem that only low-resolution object surfaces can be reconstructed within an acceptable time. On the other hand, since point cloud data lacks an ordered structure and may be noisy, it is difficult to process and there are challenges in representing complex topology. Therefore, when reconstructing surfaces directly from point clouds, it is easy to misestimate the surface information corresponding to the object, resulting in unreasonable reconstruction results.

[0004] In summary, how to accurately recover the corresponding surface information from any given object point cloud while maintaining high computational efficiency and represent it as an explicit triangular mesh is a problem that technicians in this field currently need to solve. Summary of the invention

[0005] The technical problem to be solved by the present invention is to provide a point cloud surface reconstruction method, device, terminal and medium based on parametric expression in response to the above-mentioned defects of the prior art, which can efficiently describe the complex geometric information of the object and can restore more accurate object surface information while maintaining high computing efficiency.

[0006] The technical solution adopted by the present invention to solve the technical problem is as follows:

[0007] A point cloud surface reconstruction method based on parameterized expression, wherein the method comprises:

[0008] Acquire a point cloud to be processed corresponding to the target object, and determine a parameterized surface of an anchor point based on a parameterized expression, so as to use the parameterized surface to represent the object surface of the point cloud to be processed;

[0009] Converting the parameterized surface into a corresponding triangular mesh to reconstruct the three-dimensional surface of the target object;

[0010] The parametric expression is composed of any number of anchor points, and the anchor points are located inside or outside the target object and face the surface of the target object, and the target object is observed to obtain observation information based on the position, orientation and coefficients of the pre-constructed basis function of the anchor points, so as to use the observation information to represent the parametric surface of the anchor points.

[0011] In one implementation, the basis function includes a spherical harmonic basis function and a triangular basis function; wherein the spherical harmonic basis function is used to represent the distance from the center of the anchor point to the surface of the target object along different directions, and the triangular basis function is used to represent a mask along the direction of the anchor point.

[0012] In one implementation, the using the parameterized surface to represent the object surface of the point cloud to be processed includes:

[0013] Selecting a corresponding initial point cloud from the point cloud to be processed, and determining the initial point cloud as the center of the surface area of ​​the object concerned by the anchor point;

[0014] Taking the initial point as the center, initializing the parameters of the anchor point to represent the parameterized surface of the anchor point as a plane circular piece with a radius of a preset value;

[0015] Determine a corresponding sampling direction, and perform sampling along the sampling direction on the parameterized surface to obtain a corresponding initial sampling point set;

[0016] Performing farthest point sampling on the initial sampling point set using a farthest point sampling algorithm to obtain a corresponding sampling point set;

[0017] Performing uniform sampling on the boundary of the parameterized surface of the anchor point to obtain a corresponding boundary sampling point set;

[0018] Calculating a first distance between the sampling point sets corresponding to all the parameterized surfaces and the point cloud to be processed, and sequentially calculating a second distance between the boundary sampling point set corresponding to one parameterized surface among all the parameterized surfaces and the boundary sampling point sets corresponding to other parameterized surfaces;

[0019] The first distance and the second distance are minimized so that the parameterized surface fits and represents the object surface of the point cloud to be processed.

[0020] In one implementation, the point cloud surface reconstruction method based on parameterized expression further includes:

[0021] The sampling point on the parameterized surface is determined based on the position of the anchor point, the sampling direction, and the distance between the anchor point and the sampling point in the sampling point set.

[0022] In one implementation, converting the parameterized surface into a corresponding triangular mesh to reconstruct the three-dimensional surface of the target object includes:

[0023] Using a preset gradient calculation formula, the normal of the sampling point in the sampling point set is calculated to obtain a corresponding first normal field;

[0024] A triangular mesh corresponding to the isosurface is extracted from the first normal field to reconstruct the three-dimensional surface of the target object.

[0025] In one implementation, after calculating the normal of the sampling point in the sampling point set by using a preset gradient calculation formula to obtain the corresponding first normal field, the method further includes:

[0026] Using a preset normal estimation algorithm, estimating the normal direction of the sampling points in the sampling point set that is consistent with the global direction to obtain a second normal field;

[0027] Performing weighted processing on the first normal direction in the first normal field and the second normal direction in the second normal field according to a preset weighted calculation formula to obtain a corresponding target normal field;

[0028] Wherein, the preset weighted calculation formula is:

[0029]

[0030] in, represents the target normal in the target normal field, represents the first normal in the first normal field, represents the second normal in the second normal field;

[0031] The extracting a triangular mesh corresponding to an isosurface from the first normal field to reconstruct a three-dimensional surface of the target object includes:

[0032] A triangular mesh corresponding to the isosurface is extracted from the target normal field to reconstruct the three-dimensional surface of the target object.

[0033] In one implementation, the point cloud surface reconstruction method based on parameterized expression further includes:

[0034] When the first normal in the first normal field and the second normal in the second normal field have opposite normal directions, the parameterized surface corresponding to the first normal field is marked, and the first normal in the first normal field is flipped.

[0035] The present invention also discloses a point cloud surface reconstruction device based on parameterized expression, wherein the device comprises:

[0036] A point cloud acquisition module is used to obtain the to-be-processed point cloud corresponding to the target object;

[0037] A parameterized surface representation module, used for determining a parameterized surface of an anchor point based on a parameterized expression, so as to use the parameterized surface to represent the object surface of the point cloud to be processed;

[0038] A parameterized surface conversion module, used for converting the parameterized surface into a corresponding triangular mesh to reconstruct the three-dimensional surface of the target object;

[0039] The parametric expression is composed of any number of anchor points, and the anchor points are located inside or outside the target object and face the surface of the target object, and the target object is observed to obtain observation information based on the position, orientation and coefficients of the pre-constructed basis function of the anchor points, so as to use the observation information to represent the parametric surface of the anchor points.

[0040] The present invention also discloses a terminal, which includes: a memory, a processor, and a point cloud surface reconstruction program based on parametric expression stored in the memory and executable on the processor, wherein the point cloud surface reconstruction program based on parametric expression, when executed by the processor, implements the steps of the point cloud surface reconstruction method based on parametric expression as described above.

[0041] The present invention also discloses a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, and the computer program can be executed to implement the steps of the point cloud surface reconstruction method based on parametric expression as described above.

[0042] The present invention provides a point cloud surface reconstruction method, device, terminal and medium based on parametric expression, the point cloud surface reconstruction method based on parametric expression includes: obtaining a point cloud to be processed corresponding to a target object, and determining a parametric surface of an anchor point based on the parametric expression, so as to use the parametric surface to represent the object surface of the point cloud to be processed; converting the parametric surface into a corresponding triangular mesh to reconstruct the three-dimensional surface of the target object; wherein the parametric expression is composed of any number of anchor points, and the anchor points are located inside or outside the target object and face the surface of the target object, and the target object is observed to obtain observation information represented by the position, orientation and coefficients of a pre-constructed basis function of the anchor point, so as to use the observation information to represent the parametric surface of the anchor point. It can be seen that the present invention converts the object point cloud into a parametric expression for representing the surface of the object, and converts the parametric expression into a triangular mesh, thereby realizing surface reconstruction of the point cloud, and can efficiently describe the complex geometric information of the object, and can restore more accurate object surface information while maintaining high computational efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 It is a flow chart of a preferred embodiment of a point cloud surface reconstruction method based on parameterized expression in the present invention;

[0044] Figure 2 It is a schematic diagram of the surface area of ​​an object that can be observed by a single anchor point disclosed in the present invention;

[0045] Figure 3 It is a specific parameterized expression schematic diagram disclosed in the present invention;

[0046] Figure 4 It is a specific schematic diagram of differentiable surface point sampling based on parameterized expression disclosed in the present invention;

[0047] Figure 5 It is a schematic diagram of an anchor point-based inversion transformation disclosed in the present invention;

[0048] Figure 6 It is a schematic diagram of a point sampling strategy and boundary continuity loss term of a parameterized surface disclosed in the present invention;

[0049] Figure 7 It is a schematic diagram of normal estimation of a parameterized surface sampling point disclosed in the present invention;

[0050] Figure 8 It is a schematic diagram of the normal direction of a parameterized surface after visualization and optimization of the normal direction difference disclosed in the present invention;

[0051] Fig. 9It is a schematic diagram comparing the surface reconstruction results of different methods disclosed in the present invention on the ShapeNetV2 dataset;

[0052] Fig.10 It is a functional principle block diagram of a preferred embodiment of a point cloud surface reconstruction device based on parameterized expression in the present invention;

[0053] Fig.11 It is a functional principle block diagram of a preferred embodiment of the terminal in the present invention. DETAILED DESCRIPTION

[0054] In order to make the purpose, technical solution and advantages of the present invention clearer and more specific, the present invention is further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0055] See also Figure 1 , Figure 1 is a flow chart of the point cloud surface reconstruction method based on parameterized expression in the present invention. Figure 1 As shown, the point cloud surface reconstruction method based on parameterized expression described in the embodiment of the present invention includes:

[0056] Step S11, obtaining the point cloud to be processed corresponding to the target object, and determining the parametric surface of the anchor point based on the parametric expression, so as to use the parametric surface to represent the object surface of the point cloud to be processed; wherein the parametric expression is composed of any number of the anchor points, and the anchor points are located inside or outside the target object and face the surface of the target object, and the target object is observed to obtain observation information represented by the position, orientation and coefficients of the pre-constructed basis function of the anchor point, so as to use the observation information to represent the parametric surface of the anchor point.

[0057] In this embodiment, after obtaining the to-be-processed point cloud corresponding to the target object, the object point cloud corresponding to the target object is converted into a parametric expression for representing the object surface, that is, a parametric surface for determining anchor points based on the parametric expression, so as to use the parametric surface to represent the object surface of the to-be-processed point cloud. Among them, converting the obtained object point cloud into a parametric expression for representing the object surface achieves a stronger object surface expression capability, and can also greatly reduce the amount of data required to represent the surface information of the same object, thereby saving a certain amount of storage overhead.

[0058] It can be understood that converting the point cloud expression into a parametric expression to represent the object surface through the parametric expression, that is, converting the object surface represented by the point cloud expression into the parametric surface of each anchor point in the parametric expression to represent the object surface, can achieve the ability to directly represent the surface geometry (shape) information of the object similar to the triangular mesh, and the parametric expression also has stronger expression ability, can efficiently represent complex object geometry information, and further support fast triangular mesh conversion, providing high-quality object geometry information for many triangular mesh-based applications.

[0059] It should be pointed out that the parametric expression is composed of an arbitrary number of anchor points, and the anchor points are located inside or outside the target object and face the surface of the target object, and the target object is observed to obtain observation information represented by the position, orientation and coefficients of the pre-constructed basis functions of the anchor points, so as to use the observation information to represent the parametric surface of the anchor points, and the basis functions include spherical harmonic basis functions and triangular basis functions; among which, the spherical harmonic basis functions are used to represent the distance from the center of the anchor point to the surface of the target object along different directions, and the triangular basis functions are used to represent the mask along the orientation of the anchor point.

[0060] For example, see Figure 2 As shown in , first, the parametric expression consists of an arbitrary number of anchor points, each of which is located inside or outside the object and faces the surface of the object to observe the object, and then the observation information is represented by the position, orientation and coefficients of the basis function of the anchor point, thereby realizing a complete parametric expression of the observation information. Figure 3 The spherical harmonic basis function shown in the upper part is the basis function of the distance function from a single anchor point to the surface of the object. The spherical harmonic basis function is used to represent the distance from the center of the anchor point to the surface of the object in different directions. However, the functions corresponding to these distances may appear as described above. Figure 2 The discontinuity caused by occlusion is shown, therefore, see the Figure 3 The triangular basis function shown in the lower part is the basis function of the mask function used to define the effective field of view on a single anchor point. The mask along the direction of the anchor point can be represented by the triangular basis function, thereby representing the surface area of ​​the object that can be effectively represented by the anchor point. The continuous surface area of ​​the object that can actually be accurately represented by a single anchor point can be seen in the Figure 3 Shown on the right.

[0061] In this embodiment, converting the object point cloud corresponding to the target object into a parametric expression for representing the object surface may specifically include: selecting a corresponding initial point cloud from the point cloud to be processed, and determining the initial point cloud as the center of the object surface area concerned by the anchor point; initializing the parameters of the anchor point with the initial point as the center to represent the parameterized surface of the anchor point as a plane disk with a preset radius; determining a corresponding sampling direction, and sampling along the sampling direction on the parameterized surface to obtain a corresponding initial sampling point set; performing farthest point sampling on the initial sampling point set using a farthest point sampling algorithm to obtain a corresponding sampling point set; performing uniform sampling on the boundary of the parameterized surface of the anchor point to obtain a corresponding boundary sampling point set; calculating a first distance between the sampling point set corresponding to all the parameterized surfaces and the point cloud to be processed, and sequentially calculating a second distance between the boundary sampling point set corresponding to a parameterized surface among all the parameterized surfaces and the boundary sampling point sets corresponding to other parameterized surfaces; minimizing the first distance and the second distance so that the parameterized surface fits and represents the object surface of the point cloud to be processed.

[0062] It should be pointed out that in the process of calculating the sampling points on the parameterized surface, the sampling points on the parameterized surface are determined based on the position of the anchor point, the sampling direction, and the distance between the sampling points in the sampling point set and the anchor point, thereby realizing the calculation of the sampling points on the parameterized surface. Figure 4 As shown, for each anchor point, first, its position p and orientation v can be determined. Any sampling direction inside the mask and including the edge can be expressed as the difference between the orientation of the corresponding anchor point and the edge mask direction, that is:

[0063] r(ω,β)=ω·r β +(1-ω)·v;

[0064] Among them, r(ω,β) represents the sampling direction, ω represents the difference weight between the direction and the edge mask direction, β represents the angle of the edge mask direction along the direction projection relative to the initial coordinate axis on the right side of the direction, and r β represents the edge mask direction, and v represents the direction of the anchor point.

[0065] Then, after obtaining the sampling direction, the distance from the sampling point to the anchor point position obtained along each sampling direction is calculated, that is, for the Figure 4 For any sampling direction r(ω,β), the corresponding standard spherical coordinates are (θ,φ)=(ωα(β),β), where α(β) represents the angle between the edge mask direction and the orientation, that is:

[0066]

[0067] Among them, a0 represents the initial parameter corresponding to the mask part, a k Indicates the second parameter corresponding to the mask part, b k It represents the third parameter corresponding to the mask part, and K represents the order of the basis function used for the edge mask.

[0068] Then, the distance from the sampling point to the anchor point along each sampling direction can be calculated by the standard spherical harmonic basis function calculation formula to obtain the distance in the corresponding sampling direction, that is:

[0069]

[0070] in, Represents the parameters corresponding to the anchor point distance function, Y l m represents the parameters corresponding to the spherical harmonic basis function, and L represents the order of the spherical harmonic basis function used by the anchor point distance function.

[0071] Finally, based on the position of the anchor point, the sampling direction, and the distance from the sampling point to the anchor point along each sampling direction, the following equation can be obtained: Figure 4 Sample points on the parameterized surface of the anchor point shown.

[0072] Furthermore, since the spherical harmonics are better at representing spheres or curved surfaces but cannot accurately represent planes, the sampling points can be inverted to allow them to represent planes and further enhance the representation capability of the parameterized expression.

[0073] For example, see Figure 5 The two points p before and after the inversion transformation shown in the upper part inv and p fit Assuming that the dotted circle is the inversion circle, its center is O and its radius is R, the inversion transformation requires any two points p inv and p fit Need to satisfy vector multiplication (p inv -O)(p fit -O)=R 2 First, determine the position p of the anchor point and the distance r along its direction v, and use them to construct the Figure 5 The solid circle in the upper part, and then take the intersection of the ray corresponding to the direction opposite to the anchor point and the small circle as the center O of the inversion circle, and the radius of the inversion circle is twice that of the small circle. Then, through the inversion transformation, a one-to-one correspondence can be established between the small circle and a straight line tangent to both the inversion circle and the small circle, and any pair of inversion points can be calculated using the following formula:

[0074]

[0075] See the description Figure 5 The lower part shows the positional relationship of the object surface before and after inversion, as well as the difference in the ability to represent the object surface brought about by the inversion transformation. Through the inversion transformation, the surface of an object changes from the shape on the left to the shape on the right. At this time, relative to the anchor point, the observed surface area of ​​the object is converted into a shape that approximates a spherical surface, allowing the same number of parameters to be used to represent a wider range of object surface information.

[0076] For example, the parameterized surface of a single anchor point is represented by the position and orientation of the anchor point and the coefficients of the pre-constructed basis function, that is:

[0077]

[0078] Among them, p is the spatial position of the anchor point, v is the orientation of the anchor point, and a i ,b j is the parameter of the anchor point mask part, is the parameter of the anchor point distance function.

[0079] Then, by placing a preset number of anchor points {V1,…,V M} is placed near the surface of the target object, it can accurately represent the complete surface information of the object. Therefore, for a given object point cloud, it only needs to be converted into a parametric expression to obtain the object surface information corresponding to the point cloud.

[0080] It should be pointed out that when calculating the sampling points on the parameterized surface of each anchor point, the three-dimensional coordinates {x, y, z} of the sampling point are calculated according to the calculation formula of the aforementioned sampling point. The gradient of each parameter in the parameterized expression V is calculated, realizing the differentiable calculation from the parameterized expression to the sampling point, so as to further implement the corresponding stochastic gradient descent algorithm in the future.

[0081] Assuming that M parameterized surfaces are needed to jointly compose and represent the surface of a given object point cloud, first, M points are selected from the point cloud to be processed as the center of the object surface area concerned by the M anchor points, which are used as the initial points. Then, the parameters of the corresponding anchor points are randomly initialized near each initial point, so that the parameterized surface of the anchor point represents a radius of r. init A plane disk with a radius r init It can be pre-set according to actual situation or experience, and then Figure 6As shown in the upper part, the corresponding sampling direction is determined, and sampling is performed along the sampling direction on the parameterized surface corresponding to each anchor point to obtain the initial sampling point set P of a single anchor point. However, since the shape of the parameterized surface of the anchor point is arbitrary, even if the sampling direction is set evenly, it is difficult to obtain a uniformly distributed sampling point set P. Therefore, it may cause excessive sampling of relatively flat areas and too few sampling of relatively complex surface areas, resulting in a lot of unnecessary calculations when estimating the parameterized expression and causing problems such as decreased surface expression accuracy. Therefore, the farthest point sampling algorithm is used to resample the initial sampling point set P of the parameterized surface corresponding to each anchor point, that is, the farthest point sampling is performed on the basis of the initial sampling point set P to obtain a more uniform sampling point set P. FPS , and use it as the final internal sampling point set of the anchor point.

[0082] Then, calculate the sampling point set corresponding to the parameterized surface of all anchor points The L1-Chamfer Distane between the given target point cloud is minimized to fit and represent the complete surface of the object through a set of parameterized surfaces.

[0083] Among them, since the parametric expression uses a set of parametric surfaces to jointly represent the surface of the object, for the parametric expression, how to ensure that the boundaries of adjacent parametric surfaces have good continuity is crucial. Only by ensuring that the boundaries of adjacent parametric surfaces have good continuity can such a set of parametric surfaces be successfully converted into a complete object surface. Therefore, the boundary continuity between adjacent parametric surfaces can be evaluated and optimized by calculating the boundary continuity loss.

[0084] For example, in addition to using the farthest point sampling algorithm to sample on the parameterized surface corresponding to each anchor point, a more uniform sampling point set P is obtained. FPS , we can also uniformly sample a set of boundary sampling points on the boundary of each parameterized surface to obtain the corresponding boundary sampling point set P bound .

[0085] Then, the boundary of the parameterized surface of each anchor point is considered traversally to obtain the boundary sampling point set corresponding to the parameterized surface of all anchor points, and the second distance between the boundary sampling point set corresponding to each parameterized surface and the remaining point set is calculated, that is, the boundary sampling point set P corresponding to each parameterized surface is calculated in turn. bound The boundary sampling points in the to the boundary sampling point set P corresponding to all other parameterized surfaces bound The distance between the boundary sampling points in the constructed overall point set is minimized to ensure that the adjacent parameterized surfaces have a higher quality connection relationship, see Figure 6The loss function shown in the lower part is used to encourage high-quality continuity of parameterized surface boundaries between different anchor points.

[0086] For example, a given object point cloud is represented by a parameterized surface of 5 anchor points. The boundary of the parameterized surface of each anchor point is traversed to obtain the boundary sampling point sets corresponding to the parameterized surfaces of the 5 anchor points, which are A, B, C, D, and E. Then, the distance between each boundary sampling point set in the 5 boundary sampling point sets and the overall point set composed of the remaining point sets is calculated in turn, such as the distance between the boundary sampling point set A and the overall point set composed of the four boundary sampling point sets B, C, D, and E, and the distance between the boundary sampling point set B and the overall point set composed of the four boundary sampling point sets A, C, D, and E. The distance between the four boundary sampling point sets of A, B, C, D, and E constitutes the overall point set, the distance between the boundary sampling point set of C and the overall point set constituted by the four boundary sampling point sets of B, C, D, and E respectively, the distance between the boundary sampling point set of D and the overall point set constituted by the four boundary sampling point sets of A, B, C, and E respectively, and the distance between the boundary sampling point set of E and the overall point set constituted by the four boundary sampling point sets of A, B, C, and D respectively. By minimizing this distance, the parameterized surfaces have a higher quality connection relationship.

[0087] Among them, see Figure 6 As shown in the lower part, for two parameterized surfaces that are far apart, the distance d between their boundary sampling points f (floating distance) represents the floating error of adjacent parameterized surfaces. For two parameterized surfaces with a certain overlapping area, the distance d between their boundary sampling points o (overlapping distance) represents the overlapping error of adjacent parameterized surfaces.

[0088] Step S12: converting the parameterized surface into a corresponding triangular mesh to reconstruct the three-dimensional surface of the target object.

[0089] In this embodiment, after determining the parametric surface of the anchor point based on the parametric expression and using the parametric surface to represent the surface of the object of the point cloud to be processed, the parametric surface is converted into a corresponding triangular mesh to reconstruct the three-dimensional surface of the target object, thereby achieving more accurate surface reconstruction of the point cloud. It can be understood that the triangular mesh has become a carrier and universal expression for various geometry-related tasks. Therefore, in order to be able to apply the expression more quickly and widely in other fields or tasks, it is necessary to convert the parametric expression into an explicit triangular mesh data structure.

[0090] Specifically, a preset gradient calculation formula is used to calculate the normal of the sampling point in the sampling point set to obtain a corresponding first normal field; a triangular mesh corresponding to an isosurface is extracted from the first normal field to reconstruct the three-dimensional surface of the target object. It can be understood that an implicit normal field is obtained by sampling the parameterized surface and calculating the accurate normal of each sampling point, and an isosurface is extracted from it to obtain a corresponding triangular mesh.

[0091] See also Figure 7 As shown, since the sampling point calculation process is differentiable, the gradient information in the calculation process can be used again to obtain the normal n of each sampling point, thereby obtaining the accurate normal information of each parameterized surface, that is:

[0092]

[0093] It should be pointed out that the normal calculated by the gradient formula is completely accurate inside the parameterized surface, but since only the boundary continuity of adjacent parameterized surfaces is constrained, this may lead to insufficient normal continuity between adjacent parameterized surfaces, thereby reducing the smoothness of the converted normal field and further affecting the quality of the final triangular mesh. Therefore, after using the preset gradient calculation formula to calculate the normal of the sampling point in the sampling point set to obtain the corresponding first normal field, it can also specifically include: using a preset normal estimation algorithm to estimate the global direction of the sampling point in the sampling point set to obtain a second normal field; weighting the first normal in the first normal field and the second normal in the second normal field according to a preset weighted calculation formula to obtain a corresponding target normal field; wherein the preset weighted calculation formula is:

[0094]

[0095] in, represents the target normal in the target normal field, represents the first normal in the first normal field, represents the second normal in the second normal field;

[0096] Furthermore, a triangular mesh corresponding to the isosurface is extracted from the target normal field to reconstruct the three-dimensional surface of the target object.

[0097] For example, see Figure 8 As shown on the right, the optimized normal is obtained by weighting the normal calculated by the gradient formula and the normal estimated by the preset normal estimation algorithm through the adaptive weighting method. Specifically, the normal information calculated by the gradient formula is retained as much as possible inside the parameterized surface. The parameterized surface boundary is as close as possible to the smooth normal estimated by the preset normal estimation algorithm. The weight ω is calculated for each sampling point, making it equal to the proportion of the sampling point on the line connecting the center point of the parameterized surface to the boundary. When ω is closer to 0, it means that the sampling point is closer to the center point of the parameterized surface, and vice versa, it is closer to the boundary of the parameterized surface. Then the optimized normal is calculated. (target normal), thereby optimizing the normal orientation of all sampling points on each parameterized surface, making it have local accuracy, global consistency and good smoothness at the same time, thereby significantly improving the quality of the final extracted triangular mesh, and then extracting the triangular mesh corresponding to the isosurface from the obtained normal field as the estimated object surface.

[0098] In this embodiment, when the first normal in the first normal field is opposite to the second normal in the second normal field, the parameterized surface corresponding to the first normal field is marked, and the first normal in the first normal field is flipped. It can be understood that due to the different orientations of different anchor points, this may cause the normal orientations of two adjacent parameterized surfaces to be opposite. In order to discover and repair this situation, a preset normal estimation algorithm is used to obtain the normal orientation with the same global direction corresponding to the sampling point set, such as Figure 8 As shown in the left part, when most of the normals calculated by the preset gradient calculation formula are opposite to the normals estimated by the preset normal estimation algorithm, the current parameterized surface will be marked and all its normals will be flipped.

[0099] It can be seen that in the embodiment of the present invention, the object point cloud is converted into a parametric expression for representing the surface of the object, and the parametric expression is converted into a triangular mesh, so as to realize surface reconstruction of the point cloud, and can efficiently describe the complex geometric information of the object, and can realize the recovery of more accurate object surface information while maintaining high computational efficiency.

[0100] It should be pointed out that in the embodiment of the present application, in the process of using parameterized surfaces to represent the surface of the object of the point cloud, additional other geometric constraints can be set, such as normal continuity between parameterized surfaces, etc., and in the process of converting the triangular mesh of the parameterized expression, different reconstruction effects can be obtained by combining with other different normal estimation methods. Moreover, compared with other existing point cloud surface reconstruction methods, the point cloud surface reconstruction based on parametric expression implemented by the technical solution of the present application can fit any number of given object point clouds because of the use of parameterized surfaces, thereby supporting more accurate object surface estimation and recovery.

[0101] See also Fig. 9As shown, the point cloud surface reconstruction based on parameterized expression realized by the technical solution of the present application is comprehensively compared with the point cloud surface reconstruction of other existing methods. First, the open source complete data set ShapeNetV2 is selected as the comparison data. The data set contains 55 different semantic categories and more than 50,000 triangular mesh representations of different objects. The surface of each shape is sampled by the farthest point sampling algorithm to obtain the point cloud representation of the shape. Then different point cloud surface reconstruction methods are applied to the point cloud, and the error between the reconstructed surface and the real surface of the object is compared. Among them, the classic Poisson reconstruction (SPR+PCA) is highly dependent on the accuracy of the estimated point cloud normal, so it reconstructs completely wrong results on many more complex objects; and the two methods based on deep learning, namely ARONet and ConvONet, are also subject to large reconstruction errors due to the errors of network prediction and the resolution of the input point cloud acceptable to the network; although the average error of the work (PGR) for surface reconstruction based on the winding number and Gaussian equation is not too large, its reconstruction results in many narrow or thin structures will have obvious errors or degradation. In contrast, the average error of the point cloud surface reconstruction based on parameterized expression achieved by the technical solution of the present application can be lower, and the surface of the narrow or thin structure of the object can be better restored. Therefore, the technical solution of the present application can achieve more accurate object surface reconstruction than other methods.

[0102] In one embodiment, if Fig.10 As shown, based on the above-mentioned point cloud surface reconstruction method based on parameterized expression, the present invention also provides a point cloud surface reconstruction device based on parameterized expression, including:

[0103] The point cloud acquisition module 11 is used to acquire the to-be-processed point cloud corresponding to the target object;

[0104] A parameterized surface representation module 12, configured to determine a parameterized surface of an anchor point based on a parameterized expression, so as to use the parameterized surface to represent the object surface of the point cloud to be processed;

[0105] A parameterized surface conversion module 13, used for converting the parameterized surface into a corresponding triangular mesh to reconstruct the three-dimensional surface of the target object;

[0106] The parametric expression is composed of any number of anchor points, and the anchor points are located inside or outside the target object and face the surface of the target object, and the target object is observed to obtain observation information based on the position, orientation and coefficients of the pre-constructed basis function of the anchor points, so as to use the observation information to represent the parametric surface of the anchor points.

[0107] Fig.11A schematic diagram of the structure of a terminal provided in an embodiment of the present application. The terminal may include:

[0108] A memory 501 , a processor 502 , and a computer program stored in the memory 501 and executable on the processor 502 .

[0109] When the processor 502 executes the program, the point cloud surface reconstruction method based on parameterized expression provided in the above embodiment is implemented.

[0110] Furthermore, the terminal further includes:

[0111] The communication interface 503 is used for communication between the memory 501 and the processor 502 .

[0112] The memory 501 is used to store computer programs that can be executed on the processor 502 .

[0113] The memory 501 may include a high-speed RAM memory, and may also include a non-volatile memory (non-volatile memory), such as at least one disk memory.

[0114] If the memory 501, the processor 502 and the communication interface 503 are implemented independently, the communication interface 503, the memory 501 and the processor 502 can be connected to each other through a bus and communicate with each other. The bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component (PCI) bus or an Extended Industry Standard Architecture (EISA) bus. The bus can be divided into an address bus, a data bus, a control bus, etc. For ease of representation, only one line is used in the figure, but it does not mean that there is only one bus or one type of bus.

[0115] Optionally, in a specific implementation, if the memory 501, the processor 502 and the communication interface 503 are integrated on a chip, the memory 501, the processor 502 and the communication interface 503 can communicate with each other through an internal interface.

[0116] The processor 502 may be a central processing unit (CPU), or an application specific integrated circuit (ASIC), or one or more integrated circuits configured to implement the embodiments of the present application.

[0117] This embodiment also provides a computer-readable storage medium on which a computer program is stored. When the program is executed by a processor, the above-mentioned point cloud surface reconstruction method based on parameterized expression is implemented.

[0118] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present application. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or N embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples, without contradiction.

[0119] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include at least one of the features. In the description of this application, "N" means at least two, such as two, three, etc., unless otherwise clearly and specifically defined.

[0120] Any process or method description in a flowchart or otherwise described herein may be understood to represent a module, fragment or portion of code comprising one or N executable instructions for implementing the steps of a custom logical function or process, and the scope of the preferred embodiments of the present application includes additional implementations, in which the order shown or discussed may not be followed, including performing functions in a substantially simultaneous manner or in reverse order depending on the functions involved, which should be understood by technicians in the technical field to which the embodiments of the present application belong.

[0121] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as an ordered list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by an instruction execution system, device or apparatus (such as a computer-based system, a system including a processor, or other system that can read instructions from an instruction execution system, device or apparatus and execute instructions), or in combination with these instruction execution systems, devices or apparatuses. For the purpose of this specification, "computer-readable medium" can be any device that can contain, store, communicate, propagate or transmit a program for use by an instruction execution system, device or apparatus, or in combination with these instruction execution systems, devices or apparatuses. More specific examples of computer-readable media (a non-exhaustive list) include the following: an electrical connection with one or N wirings (electronic devices), a portable computer disk box (magnetic device), a random access memory (RAM), a read-only memory (ROM), an erasable and programmable read-only memory (EPROM or flash memory), a fiber optic device, and a portable compact disk read-only memory (CDROM). In addition, the computer-readable medium may even be paper or other suitable medium on which the program is printed, since the program may be obtained electronically by optically scanning the paper or other medium and then editing, interpreting or otherwise processing in a suitable manner if necessary and then storing it in a computer memory.

[0122] It should be understood that the various parts of the present application can be implemented by hardware, software, firmware or a combination thereof. In the above embodiment, the N steps or methods can be implemented by software or firmware stored in a memory and executed by a suitable instruction execution system. If implemented by hardware, as in another embodiment, it can be implemented by any one of the following technologies known in the art or their combination: a discrete logic circuit having a logic gate circuit for implementing a logic function for a data signal, a dedicated integrated circuit having a suitable combination of logic gate circuits, a programmable gate array (PGA), a field programmable gate array (FPGA), etc.

[0123] A person skilled in the art may understand that all or part of the steps in the method for implementing the above-mentioned embodiment may be completed by instructing related hardware through a program, and the program may be stored in a computer-readable storage medium. When the program is executed, it includes one or a combination of the steps of the method embodiment.

[0124] In addition, each functional unit in each embodiment of the present application may be integrated into a processing module, or each unit may exist physically separately, or two or more units may be integrated into one module. The above-mentioned integrated module may be implemented in the form of hardware or in the form of a software functional module. If the integrated module is implemented in the form of a software functional module and sold or used as an independent product, it may also be stored in a computer-readable storage medium.

[0125] The storage medium mentioned above may be a read-only memory, a magnetic disk or an optical disk, etc. Although the embodiments of the present application have been shown and described above, it can be understood that the above embodiments are exemplary and cannot be understood as limiting the present application. A person of ordinary skill in the art may change, modify, replace and modify the above embodiments within the scope of the present application.

[0126] It should be understood that the application of the present invention is not limited to the above examples. For ordinary technicians in this field, improvements or changes can be made based on the above description. All these improvements and changes should fall within the scope of protection of the claims attached to the present invention.

Claims

1. A point cloud surface reconstruction method based on parametric expression, characterized in that: The method comprises: Acquire a point cloud to be processed corresponding to the target object, and determine a parameterized surface of an anchor point based on a parameterized expression, so as to use the parameterized surface to represent the object surface of the point cloud to be processed; Converting the parameterized surface into a corresponding triangular mesh to reconstruct the three-dimensional surface of the target object; The parametric expression is composed of any number of anchor points, and the anchor points are located inside or outside the target object and face the surface of the target object, and the target object is observed to obtain observation information based on the position, orientation and coefficients of the pre-constructed basis function of the anchor points, so as to use the observation information to represent the parametric surface of the anchor points.

2. The point cloud surface reconstruction method based on parameterized expression according to claim 1, characterized in that: The basis functions include spherical harmonic basis functions and triangular basis functions; wherein the spherical harmonic basis functions are used to represent the distance from the center of the anchor point to the surface of the target object along different directions, and the triangular basis functions are used to represent the mask along the direction of the anchor point.

3. The point cloud surface reconstruction method based on parameterized expression according to claim 1, characterized in that: The method of using the parameterized surface to represent the object surface of the point cloud to be processed includes: Filtering out a corresponding initial point cloud from the to-be-processed point cloud, and determining the initial point cloud as the center of the surface area of ​​the object concerned by the anchor point; Taking the initial point as the center, initializing the parameters of the anchor point to represent the parameterized surface of the anchor point as a plane circular piece with a radius of a preset value; Determine a corresponding sampling direction, and perform sampling along the sampling direction on the parameterized surface to obtain a corresponding initial sampling point set; Performing farthest point sampling on the initial sampling point set using a farthest point sampling algorithm to obtain a corresponding sampling point set; Performing uniform sampling on the boundary of the parameterized surface of the anchor point to obtain a corresponding boundary sampling point set; Calculating a first distance between the sampling point sets corresponding to all the parameterized surfaces and the point cloud to be processed, and sequentially calculating a second distance between the boundary sampling point set corresponding to one parameterized surface among all the parameterized surfaces and the boundary sampling point sets corresponding to other parameterized surfaces; The first distance and the second distance are minimized so that the parameterized surface fits and represents the object surface of the point cloud to be processed.

4. The point cloud surface reconstruction method based on parameterized expression according to claim 3 is characterized in that: Also includes: The sampling point on the parameterized surface is determined based on the position of the anchor point, the sampling direction, and the distance between the anchor point and the sampling point in the sampling point set.

5. The point cloud surface reconstruction method based on parameterized expression according to claim 4 is characterized in that: The step of converting the parameterized surface into a corresponding triangular mesh to reconstruct the three-dimensional surface of the target object comprises: Using a preset gradient calculation formula, the normal of the sampling point in the sampling point set is calculated to obtain a corresponding first normal field; A triangular mesh corresponding to the isosurface is extracted from the first normal field to reconstruct the three-dimensional surface of the target object.

6. The point cloud surface reconstruction method based on parameterized expression according to claim 5, characterized in that: After calculating the normal of the sampling point in the sampling point set by using the preset gradient calculation formula to obtain the corresponding first normal field, the method further includes: Using a preset normal estimation algorithm, estimating the normal direction of the sampling points in the sampling point set that is consistent with the global direction to obtain a second normal field; Performing weighted processing on the first normal direction in the first normal field and the second normal direction in the second normal field according to a preset weighted calculation formula to obtain a corresponding target normal field; Wherein, the preset weighted calculation formula is: in, represents the target normal in the target normal field, represents the first normal in the first normal field, represents the second normal in the second normal field; The extracting a triangular mesh corresponding to an isosurface from the first normal field to reconstruct a three-dimensional surface of the target object includes: A triangular mesh corresponding to the isosurface is extracted from the target normal field to reconstruct the three-dimensional surface of the target object.

7. The point cloud surface reconstruction method based on parameterized expression according to claim 6, characterized in that: Also includes: When the first normal in the first normal field and the second normal in the second normal field have opposite normal directions, the parameterized surface corresponding to the first normal field is marked, and the first normal in the first normal field is flipped.

8. A point cloud surface reconstruction device based on parametric expression, characterized in that: The device comprises: A point cloud acquisition module is used to obtain the to-be-processed point cloud corresponding to the target object; A parameterized surface representation module, used for determining a parameterized surface of an anchor point based on a parameterized expression, so as to use the parameterized surface to represent the object surface of the point cloud to be processed; A parameterized surface conversion module, used for converting the parameterized surface into a corresponding triangular mesh to reconstruct the three-dimensional surface of the target object; The parametric expression is composed of any number of anchor points, and the anchor points are located inside or outside the target object and face the surface of the target object, and the target object is observed to obtain observation information based on the position, orientation and coefficients of the pre-constructed basis function of the anchor points, so as to use the observation information to represent the parametric surface of the anchor points.

9. A terminal, characterized in that: include: A memory, a processor, and a point cloud surface reconstruction program based on parametric expression stored in the memory and executable on the processor, wherein the point cloud surface reconstruction program based on parametric expression, when executed by the processor, implements the steps of the point cloud surface reconstruction method based on parametric expression as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and the computer program can be executed to implement the steps of the point cloud surface reconstruction method based on parametric expression as described in any one of claims 1 to 7.

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