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

Abstract

This invention provides a point cloud surface reconstruction method, apparatus, terminal, and medium based on parametric representation. The method includes: acquiring a point cloud to be processed corresponding to a target object; determining a parametric surface of anchor points based on the parametric representation, so as to represent the object surface of the point cloud to be processed using the parametric surface; converting the parametric surface into a triangular mesh to reconstruct the three-dimensional surface of the target object; wherein the parametric representation consists of an arbitrary number of anchor points, and the anchor points are located inside or outside the target object and facing the surface of the target object, observing the target object, and obtaining observation information based on the position, orientation, and coefficients of pre-constructed basis functions of the anchor points, so as to represent the parametric surface of the anchor points using the observation information. This invention represents the object surface of the point cloud based on the parametric representation and converts the parametric representation into a triangular mesh to realize the surface reconstruction of the point cloud, and can recover more accurate object surface information while maintaining high computational efficiency.

Description

Technical Field

[0001] This invention relates to the field of point cloud surface reconstruction technology, and in particular to a point cloud surface reconstruction method, apparatus, terminal and medium based on parametric expression. Background Technology

[0002] In fields such as computer graphics and computational geometry, the representation of 3D shapes is crucial for applications such as virtual reality, games, advanced manufacturing, and scientific visualization. Traditional methods for representing 3D shapes include voxel meshes, point clouds, and triangular meshes, each with its unique advantages and limitations. Among these, triangular meshes are widely used in computer graphics, virtual reality, game development, and scientific visualization due to their simple structure, ease of processing, ability to provide accurate surface geometry information, and support for efficient visualization. However, while point cloud data is one of the easiest types of data to collect from the real world and can provide sparse and high-resolution surface information, it lacks the ordered structure and topological relationships of triangular meshes, making point clouds more complex to process and difficult to use directly in applications requiring precise geometric operations. Therefore, much research has focused on feasible solutions for converting point clouds into various representations and then efficiently and accurately converting them into triangular meshes.

[0003] Currently, point cloud-based triangular mesh reconstruction schemes can be broadly categorized into four types. For example, voxel meshes naturally extend contour extraction methods from two-dimensional space to three dimensions, enabling volume shape estimation. Point clouds provide sparse, high-resolution data and allow for surface shape estimation based on local point cloud distributions. Furthermore, with the maturity of deep learning technologies, many works have begun to describe the geometric information of objects using implicit representations such as signed distance fields and extract triangular meshes from them. However, existing point cloud surface reconstruction algorithms also face the challenge of balancing representation accuracy and computational efficiency. Since voxel meshes and signed distance fields require dense partitioning of three-dimensional space, the computational cost of reconstructing high-resolution object surfaces is too high, leading to the limitation of reconstructing only low-resolution object surfaces within an acceptable timeframe. On the other hand, point cloud data lacks ordered structure, may contain noise, and is difficult to process, posing challenges when representing complex topologies. Therefore, directly reconstructing surfaces from point clouds can easily lead to incorrect estimation of the object's surface information, 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 needs to be solved by those skilled in the art. 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, which can efficiently describe the complex geometric information of objects and restore more accurate object surface information while maintaining high computational efficiency.

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

[0007] A point cloud surface reconstruction method based on parametric representation, wherein the method includes:

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

[0009] The parametric surface is converted into a corresponding triangular mesh to reconstruct the three-dimensional surface of the target object;

[0010] The parameterized representation consists of any number of anchor points, which are located inside or outside the target object and face the surface of the target object. The target object is observed to obtain observation information based on the position and orientation of the anchor points and the coefficients of pre-constructed basis functions, so as to represent the parameterized surface of the anchor points using the observation information.

[0011] In one implementation, the basis functions include spherical harmonic basis functions and trigonometric 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 in different directions, and the trigonometric basis functions are used to represent the masking along the orientation of the anchor point.

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

[0013] Select the corresponding initial point cloud from the point cloud to be processed, and determine the initial point cloud as the center of the object surface area of ​​interest of the anchor point;

[0014] With the initial point as the center, the parameters of the anchor point are initialized so that the parameterized surface of the anchor point is represented as a planar circular piece with a preset radius.

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

[0016] The initial set of sampling points is sampled from the farthest point using the farthest point sampling algorithm to obtain the corresponding set of sampling points.

[0017] Uniform sampling is performed on the boundary of the parameterized surface at the anchor point to obtain the corresponding set of boundary sampling points;

[0018] Calculate the first distance between the sampling point set corresponding to all the parameterized surfaces and the point cloud to be processed, and sequentially calculate the second distance between the boundary sampling point set corresponding to one of the parameterized surfaces and the boundary sampling point set corresponding to other parameterized surfaces.

[0019] By minimizing the first distance and the second distance, 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 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.

[0022] In one implementation, converting the parametric 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 points in the sampling point set is calculated to obtain the corresponding first normal field;

[0024] The 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 vector of the sampling points in the sampling point set using a preset gradient calculation formula to obtain the corresponding first normal field, the method further includes:

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

[0027] The first normal in the first normal field and the second normal in the second normal field are weighted according to the preset weighted calculation formula to obtain the corresponding target normal field;

[0028] The preset weighted calculation formula is as follows:

[0029]

[0030] in, Indicates the target normal in the target normal field. This represents the first normal direction in the first normal field. This represents the second normal direction in the second normal field;

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

[0032] The 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 normal directions of the first normal in the first normal field and the second normal in the second normal field are opposite, 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 parametric expression, wherein the device comprises:

[0036] The point cloud acquisition module is used to acquire the point cloud to be processed corresponding to the target object;

[0037] A parametric surface representation module is used to determine a parametric surface with anchor points based on a parametric expression, so as to represent the object surface of the point cloud to be processed using the parametric surface;

[0038] The parametric surface conversion module is used to convert the parametric surface into a corresponding triangular mesh to reconstruct the three-dimensional surface of the target object;

[0039] The parameterized representation consists of any number of anchor points, which are located inside or outside the target object and face the surface of the target object. The target object is observed to obtain observation information based on the position and orientation of the anchor points and the coefficients of pre-constructed basis functions, so as to represent the parameterized surface of the anchor points using the observation information.

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

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

[0042] This invention provides a point cloud surface reconstruction method, apparatus, terminal, and medium based on parametric representation. The point cloud surface reconstruction method based on parametric representation includes: acquiring a point cloud to be processed corresponding to a target object, and determining a parametric surface of anchor points based on the parametric representation, so as to represent the object surface of the point cloud to be processed using the parametric surface; converting the parametric surface into a corresponding triangular mesh to reconstruct the three-dimensional surface of the target object; wherein the parametric representation consists of an arbitrary number of anchor points, and the anchor points are located inside or outside the target object and facing the surface of the target object, and the target object is observed to obtain observation information based on the position, orientation, and coefficients of pre-constructed basis functions of the anchor points, so as to represent the parametric surface of the anchor points using the observation information. Therefore, this invention converts the object point cloud into a parametric representation for representing the object surface, and converts the parametric representation into a triangular mesh, thereby realizing the surface reconstruction of the point cloud, efficiently describing the complex geometric information of the object, and restoring more accurate object surface information while maintaining high computational efficiency. Attached Figure Description

[0043] Figure 1 This is a flowchart of a preferred embodiment of the point cloud surface reconstruction method based on parameterized expression in this invention;

[0044] Figure 2 This is a schematic diagram of the surface area of ​​an object that can be observed from a single anchor point as disclosed in this invention;

[0045] Figure 3 This is a specific parameterized representation diagram disclosed in this invention;

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

[0047] Figure 5 This is a schematic diagram of an anchor-based inverse transformation disclosed in this invention;

[0048] Figure 6 This is a schematic diagram of a point sampling strategy and boundary continuity loss term for a parametric surface disclosed in this invention.

[0049] Figure 7 This is a schematic diagram of normal estimation for parameterized surface sampling points disclosed in this invention;

[0050] Figure 8 This is a schematic diagram of the parametric surface normal after visualization and optimization of normal difference disclosed in this invention;

[0051] Figure 9This is a schematic diagram comparing the surface reconstruction results of different methods disclosed in this invention on the ShapeNetV2 dataset;

[0052] Figure 10 This is a functional principle block diagram of a preferred embodiment of the point cloud surface reconstruction device based on parameterized expression in this invention;

[0053] Figure 11 This is a functional principle block diagram of a preferred embodiment of the terminal in this invention. Detailed Implementation

[0054] To make the objectives, technical solutions, and advantages of this invention clearer and more explicit, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0055] Please see Figure 1 , Figure 1 This is a flowchart of the point cloud surface reconstruction method based on parameterized expression in this invention. For example... Figure 1 As shown in the embodiments of the present invention, the point cloud surface reconstruction method based on parameterized expression includes:

[0056] Step S11: Obtain the point cloud to be processed corresponding to the target object, and determine the parameterized surface of the anchor point based on the parameterized expression, so as to use the parameterized surface to represent the object surface of the point cloud to be processed; wherein, the parameterized expression consists 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 based on 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 parameterized surface of the anchor point.

[0057] In this embodiment, after obtaining the point cloud corresponding to the target object, the point cloud is converted into a parametric representation of the object's surface. This is achieved by determining the anchor points based on the parametric representation, and then using the parametric surface to represent the object's surface in the point cloud. Converting the obtained point cloud into a parametric representation of the object's surface enhances the ability to represent the object's surface and significantly reduces the amount of data required to represent the surface information of the same object, thus saving storage overhead.

[0058] It is understandable that converting point cloud representations into parametric representations to represent object surfaces is equivalent to converting the representation of object surfaces from point cloud representations to parametric surfaces representing object surfaces through anchor points in the parametric representation. This enables the ability to directly represent the geometric (shape) information of object surfaces, similar to triangular meshes. Furthermore, parametric representations have stronger expressive power, can efficiently represent complex object geometry, and further support rapid triangular mesh conversion, providing high-quality object geometry information for numerous triangular mesh-based applications.

[0059] It should be noted that the parametric representation consists of an arbitrary number of anchor points, which are located inside or outside the target object and face the surface of the target object. The target object is observed to obtain observation information based on the position and orientation of the anchor points and the coefficients of pre-constructed basis functions. The observation information is used to represent the parametric surface of the anchor points, and the basis functions include spherical harmonic basis functions and trigonometric basis functions. 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 in different directions, and the trigonometric basis functions are used to represent the masking along the orientation of the anchor point.

[0060] For example, see Figure 2 As shown, firstly, this parameterized representation consists of an arbitrary number of anchor points, each located inside or outside the object and facing the object's surface to observe the object. Then, the observation information is represented by the position and orientation of the anchor points and the coefficients of the basis functions, thus achieving a complete parameterized representation of the observation information. See also... Figure 3 The spherical harmonic basis functions shown in the upper part are the basis functions of the distance function from a single anchor point to the surface of an object. These spherical harmonic basis functions are used to represent the distance from the center of the anchor point to the surface of the object in different directions. However, because the functions corresponding to these distances may exhibit the following characteristics... Figure 2 The discontinuity shown is due to occlusion; therefore, see the description. Figure 3 The trigonometric basis functions shown in the lower part, which are the basis functions of the masking function used to define the effective field of view at a single anchor point, can be used to represent the masking along the direction of the anchor point, thereby representing the object surface area that the anchor point can effectively represent. For the continuous object surface area that a single anchor point can accurately represent, please refer to the description below. Figure 3 As shown on the right.

[0061] In this embodiment, converting the point cloud corresponding to the target object into a parameterized representation of the object surface can 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 region of interest to 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 planar circular piece with a preset radius; determining the corresponding sampling direction, and sampling along the sampling direction on the parameterized surface to obtain a corresponding initial sampling point set; using the farthest point sampling algorithm to perform farthest point sampling on the initial sampling point set to obtain a corresponding sampling point set; uniformly 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 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 and the boundary sampling point set 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 noted that in the process of calculating sampling points on a parametric surface, the sampling points on the parametric surface are determined based on the position of the anchor points, the sampling direction, and the distance between the sampling points in the sampling point set and the anchor points, thereby realizing the calculation of sampling points on the parametric surface. For example, see... Figure 4 As shown, for each anchor point, firstly, its position p and orientation v can be determined. Any sampling direction located inside the mask and including the edge can be represented 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] Where r(ω,β) represents the sampling direction, ω represents the difference weight between the orientation and the edge masking direction, and β represents the angle between the edge masking direction and the initial coordinate axis to the right of the orientation along the projection of the orientation. β This indicates the direction of the edge masking, and v indicates the orientation of the anchor point.

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

[0066]

[0067] Where a0 represents the initial parameters corresponding to the masked portion, a k The second parameter, b, represents the part to be masked. k The third parameter represents the part to be masked, and K represents the order of the basis functions used for edge masking.

[0068] Furthermore, using the standard formula for calculating spherical harmonic basis functions, the distance from the sampling point to the anchor point along each sampling direction can be calculated to obtain the distance for the corresponding sampling direction, i.e.:

[0069]

[0070] in, Y represents the parameter corresponding to the anchor point distance function. 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 distance function.

[0071] Finally, based on the anchor point's location, the sampling direction, and the distance from the sampling point to the anchor point along each sampling direction, the result can be obtained as described above. Figure 4 The sampling points on the parametric surface of the anchor points shown.

[0072] Furthermore, since the aforementioned spherical harmonic functions are better suited to representing spheres or curved surfaces but cannot accurately represent planes, the sampling points can be inversely transformed to allow them to represent planes and further enhance the representational capability of this parameterized expression.

[0073] For example, see Figure 5 The upper part shows the two points p before and after the inverse transformation. inv and p fit The correspondence is given by assuming the large dashed circle is the inversion circle, with center O and radius R. The inversion transformation requires any two points p inv and p fit Vector multiplication (p) must be satisfied 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 In the upper half, take the solid circle and the intersection of the ray corresponding to the opposite direction of the anchor point with the small circle as the center O of the inversion circle. The radius of the inversion circle is twice that of the small circle. Then, through inversion transformation, a one-to-one correspondence can be established between the small circle and a straight line that is tangent to both the inversion circle and the small circle. Furthermore, the relationship between any pair of inversion points can be calculated using the following formula:

[0074]

[0075] See the above Figure 5 The lower half shows the positional relationship of the object's surface before and after the inversion, as well as the difference in the object's surface representation capability brought about by whether or not the inversion transformation is considered. Through the above inversion transformation, the surface of an object will change from the shape on the left to the shape on the right. At this time, relative to the anchor point, the observed object surface area is transformed into an approximately spherical shape, thus allowing the same number of parameters to represent a larger range of object surface information.

[0076] For example, the parameterized surface of a single anchor point can be represented by the anchor point's position, orientation, and the coefficients of pre-constructed basis functions, i.e.:

[0077]

[0078] Where p is the spatial position of the anchor point, v is the orientation of the anchor point, and a i ,b j These are the parameters for the anchor point masking portion. These are the parameters of the anchor point distance function.

[0079] Then, by using a preset number of anchor points {V1,…,V M By placing the point cloud near the surface of the target object, the complete surface information of the object can be accurately represented. Therefore, for a given object point cloud, the object's surface information can be obtained simply by converting it into a parametric representation.

[0080] It should be noted that when calculating the sampling points on the parameterized surface of each anchor point, the gradient of the three-dimensional coordinates {x,y,z} of the sampling point with respect to each parameter in the parameterized expression V is calculated simultaneously according to the aforementioned calculation formula for the sampling points. This realizes the differentiability calculation from the parameterized expression to the sampling points, so as to further implement the corresponding stochastic gradient descent algorithm.

[0081] Suppose we need to use M parametric surfaces to jointly form and represent the surface of a given object point cloud. First, we select M points from the point cloud to be processed as the centers of the object surface regions of interest for the M anchor points, using them as initial points. Then, we randomly initialize the parameters of the corresponding anchor points near each initial point, so that the parametric surface of the anchor point represents a surface with radius r. init A planar circular disc, where the radius r init It can be preset according to the actual situation or experience, and then it can be achieved through, for example... 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, it is difficult to obtain a uniformly distributed sampling point set P even if the sampling direction is set uniformly. This may lead to oversampling of relatively flat areas and undersampling of relatively complex surface areas, resulting in many unnecessary calculations when estimating the parameterized representation and causing a decrease in the accuracy of the surface representation. 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, 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 set of internal sampling points for that anchor point.

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

[0083] Since the parametric representation uses a set of parametric surfaces to represent the object surface, it is crucial to ensure good continuity between the boundaries of adjacent parametric surfaces. Only by ensuring good continuity between the boundaries of adjacent parametric surfaces 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 set of sampling points P can be obtained. FPS Furthermore, a set of boundary sampling points can be uniformly sampled on the boundary of each parametric surface to obtain the corresponding boundary sampling point set P. bound .

[0085] Then, the boundaries of the parametric surfaces at each anchor point are considered traversally to obtain the boundary sampling point sets corresponding to the parametric surfaces at all anchor points. The second distance between the boundary sampling point set corresponding to each parametric surface and the remaining point sets is calculated, that is, the boundary sampling point set P corresponding to each parametric surface is calculated sequentially. bound The boundary sampling points in the model represent the boundary sampling point set P corresponding to all other parameterized surfaces. bound The distance between the boundary sampling points in the overall point set is used to minimize the distance error, thereby ensuring a high-quality connection between adjacent parametric surfaces. See [link to relevant documentation]. Figure 6The lower half shows the loss function used to encourage high-quality continuity of the parametric surface boundaries between different anchor points.

[0086] For example, given an object point cloud represented by a parametric surface with 5 anchor points, we iteratively consider the boundaries of the parametric surface at each anchor point to obtain the boundary sampling point sets corresponding to these 5 anchor points, namely A, B, C, D, and E. Then, we calculate the distances between each boundary sampling point set in the 5 boundary sampling point sets and the overall point set formed by the remaining point sets. For example, the distances between boundary sampling point set A and the overall point set formed by the union of boundary sampling point sets B, C, D, and E, respectively; the distances between boundary sampling point set B and the overall point set formed by the union of boundary sampling point sets A, C, D, and E, respectively; and the distances between boundary sampling point set B and the overall point set formed by the union of boundary sampling point sets A, C, D, and E, respectively. The distances between the four boundary sampling point sets E and the overall point set formed by the union of the four boundary sampling point sets B, C, D, and E, respectively, the distances between the boundary sampling point set D and the overall point set formed by the union of the four boundary sampling point sets A, B, C, and E, and the distances between the boundary sampling point set E and the overall point set formed by the union of the four boundary sampling point sets A, B, C, and D are minimized to ensure high-quality connectivity between the parametric surfaces.

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

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

[0089] In this embodiment, a parametric surface is used to determine the anchor points based on a parametric representation. After representing the object surface of the point cloud to be processed using this parametric surface, 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 is understood that triangular meshes have become a carrier and universal representation for various geometry-related tasks. Therefore, in order to apply this representation more quickly and widely to other fields or tasks, it is necessary to convert this parametric representation into an explicit triangular mesh data structure.

[0090] Specifically, using a preset gradient calculation formula, the normals of the sampling points in the sampling point set are calculated to obtain the corresponding first normal field; the triangular mesh corresponding to the 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 parametric surface and calculating the accurate normal of each sampling point, and the isosurface is extracted from it to obtain the corresponding triangular mesh.

[0091] See Figure 7 As shown, since the sampling point calculation process is differentiable, the gradient information from the calculation process can be reused to obtain the normal vector n of each sampling point, thereby obtaining the accurate normal vector information of each parameterized surface, i.e.:

[0092]

[0093] It should be noted that while the normal vector calculated using the gradient formula is completely accurate within the parametric surface, it only constrains the boundary continuity of adjacent parametric surfaces. This can lead to insufficient continuity of the normal vectors between adjacent parametric surfaces, resulting in a decrease in the smoothness of the transformed normal field and further affecting the quality of the final triangular mesh. Therefore, after calculating the normal vectors of the sampling points in the sampling point set using the preset gradient calculation formula to obtain the corresponding first normal field, the method can further include: estimating the globally consistent normal vectors of the sampling points in the sampling point set using a preset normal estimation algorithm to obtain a second normal field; and weighting the first normal vector in the first normal field and the second normal vector in the second normal field according to a preset weighted calculation formula to obtain the corresponding target normal field; wherein the preset weighted calculation formula is:

[0094]

[0095] in, Indicates the target normal in the target normal field. This represents the first normal direction in the first normal field. This represents the second normal direction in the second normal field;

[0096] Then, the 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 using the gradient formula and the normal estimated by a preset normal estimation algorithm using an adaptive weighting method. Specifically, the normal information calculated using the gradient formula is preserved as much as possible within the parametric surface. While the smooth normal vector at the parameterized surface boundary is as close as possible to the normal vector estimated by the preset normal vector estimation algorithm, For each sampling point, a weight ω is calculated, equal to the proportion of that sampling point located on the line connecting the center point of the parametric surface to the boundary. The closer ω is to 0, the closer the sampling point is to the center point of the parametric surface; conversely, the closer it is to the boundary. Then, the optimized normal vector is calculated. (Target normal) thus optimizes 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. Then, the triangular mesh corresponding to the isosurface is extracted from the obtained normal field to be used as the estimated object surface.

[0098] In this embodiment, when the normal directions of the first normal in the first normal field and the second normal in the second normal field are opposite, the parameterized surface corresponding to the first normal field is marked, and the first normal in the first normal field is flipped. It is understood that due to the different orientations of different anchor points, this may result in the normal orientations of two adjacent parameterized surfaces being opposite. To detect and correct this situation, a preset normal estimation algorithm is used to obtain the globally consistent normal orientation corresponding to the sampling point set, such as... Figure 8 As shown on the left, when most of the normals calculated by the preset gradient calculation formula are opposite to the normal directions estimated by the preset normal estimation algorithm, the current parameterized surface will be marked and all its normals will be flipped.

[0099] As can be seen, in this embodiment of the invention, the object point cloud is converted into a parameterized representation of the object surface, and the parameterized representation is converted into a triangular mesh, thereby realizing the surface reconstruction of the point cloud, which can efficiently describe the complex geometric information of the object, and can restore more accurate object surface information while maintaining high computational efficiency.

[0100] It should be noted that in the embodiments of this application, in the process of using parametric surfaces to represent the object surface of the point cloud, additional geometric constraints can be set, such as the continuity of normals between parametric surfaces. Furthermore, in the process of transforming the parametrically expressed triangular mesh, different reconstruction effects can be obtained by combining it with other different normal estimation methods. Moreover, compared to other existing point cloud surface reconstruction methods, the point cloud surface reconstruction based on parametric expression implemented through the technical solution of this application, due to the use of parametric surfaces, can fit any number of given object point clouds, thereby supporting more accurate object surface estimation and recovery.

[0101] See Figure 9As shown, the point cloud surface reconstruction based on parameterized representation implemented in this application is comprehensively compared with other existing point cloud surface reconstruction methods. First, the open-source complete dataset ShapeNetV2 is selected as the comparison data. This dataset contains 55 different semantic categories and triangular mesh representations of more than 50,000 different objects. The surface of each shape is sampled using the farthest point sampling algorithm to obtain the point cloud representation of that shape. Then, different point cloud surface reconstruction methods are applied to this point cloud, and the errors between the reconstructed surface and the real surface of the object are compared. Among them, the classic Poisson reconstruction (SPR+PCA) relies heavily on the accuracy of the estimated point cloud normal, thus reconstructing completely incorrect results on many complex objects. The two deep learning-based methods, ARONet and ConvONet, also have large reconstruction errors due to the limitations of network prediction errors and the acceptable resolution of the input point cloud. Although the surface reconstruction based on the number of twists and the Gaussian equation (PGR) has a relatively small average error, its reconstruction results on many narrow or thin structures show obvious errors or degradation. In comparison, the point cloud surface reconstruction based on parametric representation achieved by the technical solution of this application achieves a lower average error and is also able to better recover the surface of the aforementioned elongated or thin structure of the object. Therefore, the technical solution of this application can achieve more accurate object surface reconstruction than other methods.

[0102] In one embodiment, such as Figure 10 As shown, based on the above-described point cloud surface reconstruction method based on parametric expression, the present invention also provides a point cloud surface reconstruction device based on parametric expression, comprising:

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

[0104] The parameterized surface representation module 12 is used to determine the parameterized surface of the anchor point based on the parameterized expression, so as to represent the object surface of the point cloud to be processed using the parameterized surface;

[0105] Parametric surface conversion module 13 is used to convert the parametric surface into a corresponding triangular mesh to reconstruct the three-dimensional surface of the target object;

[0106] The parameterized representation consists of any number of anchor points, which are located inside or outside the target object and face the surface of the target object. The target object is observed to obtain observation information based on the position and orientation of the anchor points and the coefficients of pre-constructed basis functions, so as to represent the parameterized surface of the anchor points using the observation information.

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

[0108] The memory 501, the processor 502, and the computer program stored on the memory 501 and capable of running on the processor 502.

[0109] When the processor 502 executes the program, it implements the point cloud surface reconstruction method based on parameterized expression provided in the above embodiments.

[0110] Furthermore, the terminal also includes:

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

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

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

[0114] If the memory 501, processor 502, and communication interface 503 are implemented independently, they can be interconnected via a bus to communicate with each other. The bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus, etc. Buses can be categorized as address buses, data buses, control buses, etc. For ease of representation, only one line is used in the diagram, but this does not imply that there is only one bus or one type of bus.

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

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

[0117] This embodiment also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the point cloud surface reconstruction method based on parameterized expression as described above.

[0118] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

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

[0120] Any process or method description in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or N executable instructions for implementing custom logic functions or processes, and the scope of the preferred embodiments of this application includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as should be understood by those skilled in the art to which embodiments of this application pertain.

[0121] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a ordered list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can read and execute instructions from or in conjunction with such an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by or in conjunction with an instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of computer-readable media include: an electrical connection having one or more wires (electronic device), a portable computer disk drive (magnetic device), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). In addition, computer-readable media can even be paper or other suitable media on which programs can be printed, because programs can be obtained electronically by optically scanning paper or other media, then editing, interpreting or otherwise processing them as necessary, and then storing them in computer memory.

[0122] It should be understood that the various parts of this application can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiments, the N steps or methods can be implemented using software or firmware stored in memory and executed by a suitable instruction execution system. If implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0123] Those skilled in the art will understand that all or part of the steps of the methods described in the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, it includes one or a combination of the steps of the method embodiments.

[0124] Furthermore, the functional units in the various embodiments of this application can be integrated into a processing module, or each unit can exist physically separately, or two or more units can be integrated into a module. The integrated module can be implemented in hardware or as a software functional module. If the integrated module is implemented as a software functional module and sold or used as an independent product, it can 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 is understood that the above embodiments are exemplary and should not be construed as limiting the present application. Persons skilled in the art may make changes, modifications, substitutions, and variations to 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 examples above. Those skilled in the art can make improvements or modifications based on the above description, and all such improvements and modifications should fall within the protection scope of the appended claims.

Claims

1. A point cloud surface reconstruction method based on parametric representation, characterized in that, The method includes: Obtain the point cloud to be processed corresponding to the target object, and determine the parameterized surface of the anchor point based on the parameterized expression, so as to use the parameterized surface to represent the object surface 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; The parameterized representation consists 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. The target object is observed to obtain observation information based on the position and orientation of the anchor points and the coefficients of pre-constructed basis functions, so as to use the observation information to represent the parameterized surface of the anchor points. Furthermore, the basis functions include spherical harmonic basis functions and trigonometric 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 in different directions, and the trigonometric basis functions are used to represent the masking along the orientation of the anchor point; The step of using the parametric surface to represent the object surface of the point cloud to be processed includes: Select the corresponding initial point cloud from the point cloud to be processed, and determine the initial point cloud as the center of the object surface area of ​​interest of the anchor point; With the initial point as the center, the parameters of the anchor point are initialized so that the parameterized surface of the anchor point is represented as a planar circular piece with a preset radius. Determine the corresponding sampling direction, and sample along the sampling direction on the parameterized surface to obtain the corresponding initial sampling point set; The initial set of sampling points is sampled from the farthest point using the farthest point sampling algorithm to obtain the corresponding set of sampling points. Uniform sampling is performed on the boundary of the parameterized surface at the anchor point to obtain the corresponding set of boundary sampling points; Calculate the first distance between the sampling point set corresponding to all the parameterized surfaces and the point cloud to be processed, and sequentially calculate the second distance between the boundary sampling point set corresponding to one of the parameterized surfaces and the boundary sampling point set corresponding to other parameterized surfaces. By minimizing the first distance and the second distance, the parameterized surface fits and represents the object surface of the point cloud to be processed; The step of converting the parametric surface into a corresponding triangular mesh to reconstruct the three-dimensional surface of the target object includes: Using a preset gradient calculation formula, the normal of the sampling points in the sampling point set is calculated to obtain the corresponding first normal field; The triangular mesh corresponding to the isosurface is extracted from the first normal field to reconstruct the three-dimensional surface of the target object.

2. The point cloud surface reconstruction method based on parametric representation according to claim 1, characterized in that, Also includes: 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.

3. The point cloud surface reconstruction method based on parametric representation according to claim 1, characterized in that, After calculating the normal vector of the sampling points in the sampling point set using a preset gradient calculation formula to obtain the corresponding first normal field, the method further includes: Using a preset normal estimation algorithm, the global direction of the sampling points in the sampling point set is estimated to obtain the second normal field; The first normal in the first normal field and the second normal in the second normal field are weighted according to the preset weighted calculation formula to obtain the corresponding target normal field; The preset weighted calculation formula is as follows: ； in, Indicates the target normal in the target normal field. This represents the first normal direction in the first normal field. ω represents the second normal in the second normal field, and ω represents the weight. The step of extracting the triangular mesh corresponding to the isosurface from the first normal field to reconstruct the three-dimensional surface of the target object includes: The triangular mesh corresponding to the isosurface is extracted from the target normal field to reconstruct the three-dimensional surface of the target object.

4. The point cloud surface reconstruction method based on parametric representation according to claim 3, characterized in that, Also includes: When the normal directions of the first normal in the first normal field and the second normal in the second normal field are opposite, the parameterized surface corresponding to the first normal field is marked, and the first normal in the first normal field is flipped.

5. A point cloud surface reconstruction device based on parametric expression, characterized in that, The device includes: The point cloud acquisition module is used to acquire the point cloud to be processed corresponding to the target object; A parametric surface representation module is used to determine a parametric surface with anchor points based on a parametric expression, so as to represent the object surface of the point cloud to be processed using the parametric surface; The parametric surface conversion module is used to convert the parametric surface into a corresponding triangular mesh to reconstruct the three-dimensional surface of the target object; The parameterized representation consists 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. The target object is observed to obtain observation information based on the position and orientation of the anchor points and the coefficients of pre-constructed basis functions, so as to use the observation information to represent the parameterized surface of the anchor points. Furthermore, the basis functions include spherical harmonic basis functions and trigonometric 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 in different directions, and the trigonometric basis functions are used to represent the masking along the orientation of the anchor point; Specifically, the parametric surface representation module is used for: Select the corresponding initial point cloud from the point cloud to be processed, and determine the initial point cloud as the center of the object surface area of ​​interest of the anchor point; With the initial point as the center, the parameters of the anchor point are initialized so that the parameterized surface of the anchor point is represented as a planar circular piece with a preset radius. Determine the corresponding sampling direction, and sample along the sampling direction on the parameterized surface to obtain the corresponding initial sampling point set; The initial set of sampling points is sampled from the farthest point using the farthest point sampling algorithm to obtain the corresponding set of sampling points. Uniform sampling is performed on the boundary of the parameterized surface at the anchor point to obtain the corresponding set of boundary sampling points; Calculate the first distance between the sampling point set corresponding to all the parameterized surfaces and the point cloud to be processed, and sequentially calculate the second distance between the boundary sampling point set corresponding to one of the parameterized surfaces and the boundary sampling point set corresponding to other parameterized surfaces. By minimizing the first distance and the second distance, the parameterized surface fits and represents the object surface of the point cloud to be processed; The parametric surface conversion module is specifically used for: Using a preset gradient calculation formula, the normal of the sampling points in the sampling point set is calculated to obtain the corresponding first normal field; The triangular mesh corresponding to the isosurface is extracted from the first normal field to reconstruct the three-dimensional surface of the target object.

6. A terminal, characterized in that, include: The device includes a memory, a processor, and a point cloud surface reconstruction program based on a parameterized expression stored in the memory and executable on the processor. When executed by the processor, the point cloud surface reconstruction program based on a parameterized expression implements the steps of the point cloud surface reconstruction method based on a parameterized expression as described in any one of claims 1 to 4.

7. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that 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 4.

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