Four-side surface re-topology method based on frame field prediction and electronic equipment

Abstract

The invention provides a quadrilateral surface re-topology method based on frame field prediction and electronic equipment. The quadrilateral surface re-topology method based on frame field prediction comprises the following steps: inputting a triangular mesh model into a frame field neural network model, and carrying out direction regression and amplitude diffusion taking the direction as the condition to obtain a corresponding frame field; performing deformation based on the frame field to obtain a deformed grid model; performing isotropic quadrilateral re-mesh division on the deformed mesh model to obtain an initial quadrilateral mesh model; and performing inverse deformation on the initial quadrilateral mesh model to obtain a quadrilateral mesh model corresponding to the triangular mesh model. Through the steps of frame field inference, deformation, isotropic quadrilateral grid re-division and inverse deformation, the quality of the finally generated quadrilateral grid is ensured, so that the purpose of improving the quality of the quadrilateral grid is achieved.

Description

Technical Field

[0001] The present invention belongs to the technical field of three-dimensional models, and in particular relates to a quadrilateral retopology method based on frame field prediction and an electronic device. Background Art

[0002] Quad meshes play a crucial role in computer graphics applications, yet automatically generating high-quality quad meshes remains challenging. With the booming development of generative modeling techniques and 3D content representation, 3D model generation has received significant attention in the community over the past few years. In particular, 3D models defined with quad meshes play a vital role in computer-aided design, physics simulation, and character animation. However, designing high-quality quad meshes is labor-intensive and requires domain-specific knowledge. Therefore, developing methods that automatically generate high-quality quad meshes from intuitive user input is of great value. Contemporary 3D content generation and reconstruction methods have achieved remarkable success by adopting neural fields as their underlying geometric representation. This representation naturally adapts to generative methods and enables high-fidelity shape synthesis. While these methods typically use established field discretization techniques to extract triangular meshes from implicit surfaces, the resulting triangulated geometry often lacks the geometric quality and structural regularity inherent in quad-dominant meshes created by professional artists. This quality disparity, particularly in terms of mesh topology and element alignment, has motivated the development of robust quadrangularization techniques to bridge the gap between neural field reconstructions and production-ready assets.

[0003] The existing technology has the following problems when generating quadrilateral meshes:

[0004] 1. Reliance on local geometric features and manual constraints: Traditional quadrilateral mesh generation methods rely primarily on local geometric features or manually specified constraints to guide the alignment of mesh elements. This results in suboptimal generated quadrilateral layouts in areas where local difference properties do not provide sufficient guidance (e.g., nearly flat areas or areas with complex curvature patterns), failing to capture global shape semantics.

[0005] 2. Unable to effectively process non-manifold meshes: Existing grid-based neural architectures have difficulty processing non-manifold meshes, which account for a large proportion of real-world 3D content.

[0006] 3. Lack of large-scale high-quality datasets: Early learning-based methods have limited training data due to the lack of large-scale high-quality datasets, which may hinder their generalization ability. Summary of the Invention

[0007] In response to the problems existing in the prior art, the present invention provides a quadrilateral retopology method and electronic device based on frame field prediction, which at least partially solves the problem of low quadrilateral mesh quality existing in the prior art.

[0008] In a first aspect, an embodiment of the present disclosure provides a quad-face retopology method based on frame field prediction, comprising:

[0009] The triangular mesh model is input into the frame field neural network model to perform direction regression and amplitude diffusion conditioned on direction to obtain the corresponding frame field.

[0010] Deform the mesh model based on the frame field;

[0011] Perform isotropic quadrilateral re-meshing on the deformed mesh model to obtain an initial quadrilateral mesh model;

[0012] The initial quadrilateral mesh model is inversely deformed to obtain a quadrilateral mesh model corresponding to the triangular mesh model.

[0013] Optionally, inputting the triangle mesh model into the frame field neural network model includes:

[0014] Perform isotropic remeshing on the triangular mesh model to obtain a divided triangular mesh model;

[0015] Perform uniform sampling on the divided triangular mesh model to obtain sampling points;

[0016] The center point and sampling point of each triangle mesh are input into the frame field neural network model.

[0017] Optionally, the deforming based on the frame field to obtain a deformed mesh model includes:

[0018] Decompose each frame of the frame field into the product of a linear SPD map and a cross product;

[0019] The ARAP energy function is minimized to solve the vertex position after deformation;

[0020] The deformed mesh model is obtained based on the deformed vertex positions.

[0021] Optionally, performing isotropic quadrilateral re-meshing on the deformed mesh model to obtain an initial quadrilateral mesh model includes:

[0022] The deformed mesh model is subjected to isotropic quadrilateral remeshing using an isotropic quadrilateral remeshing algorithm with a cross product field constraint.

[0023] Optionally, performing isotropic quadrilateral remeshing on the deformed mesh model using an isotropic quadrilateral remeshing algorithm with a cross product field constraint includes:

[0024] Use QuadriFlow to re-mesh the deformed mesh model into the initial quadrilateral mesh model;

[0025] When using QuadriFlow, after local alignment of directions, the cross product on the vertex is calculated as the sum of the cross products on the faces weighted by the areas of the neighboring faces.

[0026] Optionally, performing inverse deformation on the initial quadrilateral mesh model includes:

[0027] The deformation transfer algorithm is used to inversely deform the initial quadrilateral mesh model. In the deformation transfer algorithm, the deformed mesh model is regarded as the source mesh, the initial quadrilateral mesh model is regarded as the target mesh, and the triangular mesh model is regarded as the pose source mesh.

[0028] Optionally, in the training of the frame field neural network model, the frame field is regarded as a point attribute, geometric information is encoded using points with normals, and the frame is represented using multiple vectors.

[0029] Optionally, the direction prediction of the frame field neural network model includes, for a point cloud sampled from a triangular mesh, using a loss function to represent the predicted direction vector d and the true value d of d gt , the loss function formula is:

[0030]

[0031] Optionally, the frame field neural network model uses diffusion for amplitude prediction. Using diffusion for amplitude prediction includes:

[0032] Use logarithmic magnitude as the diffusion target;

[0033] In each training step, the time step t is uniformly sampled in {1,...,T}, and the forward diffusion process is z i，t =α t z i，0 +β t ∈, where z i represents the amplitude, ∈ is the random noise drawn from the standard normal distribution, α t , β t are precomputed constants related to the noise scheduler.

[0034] In a second aspect, an embodiment of the present disclosure further provides an electronic device, the electronic device comprising:

[0035] at least one processor; and,

[0036] a memory communicatively connected to the at least one processor; wherein,

[0037] The memory stores instructions that can be executed by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute any of the four-sided face retopology methods based on framework field prediction described in the first aspect.

[0038] The present invention provides a quadrilateral retopology method and electronic device based on frame field prediction. The method generates a higher-quality quadrilateral mesh by separately predicting direction and amplitude and using a conditional diffusion model to improve the accuracy of amplitude prediction. The quality of the resulting quadrilateral mesh is guaranteed through frame field inference, deformation, isotropic quadrilateral remeshing, and inverse deformation steps, thereby achieving the goal of improving the quality of the quadrilateral mesh. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] The above and other objects, features and advantages of the present disclosure will become more apparent through a more detailed description of exemplary embodiments of the present disclosure with reference to the accompanying drawings, wherein like reference numerals generally represent like components throughout the exemplary embodiments of the present disclosure.

[0040] Figure 1 A flowchart of a four-sided face retopology method based on frame field prediction provided in an embodiment of the present disclosure;

[0041] Figure 2 A schematic diagram of the effect of a four-sided face retopology method based on frame field prediction provided by an embodiment of the present disclosure;

[0042] Figure 3 A block diagram of an electronic device according to an embodiment of the present disclosure. DETAILED DESCRIPTION

[0043] The embodiments of the present disclosure are described in detail below with reference to the accompanying drawings.

[0044] It should be clear that the following embodiments of the present disclosure are described through specific concrete examples, and those skilled in the art can easily understand other advantages and effects of the present disclosure from the contents disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of the present disclosure, rather than all the embodiments. The present disclosure can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present disclosure. It should be noted that the following embodiments and features in the embodiments can be combined with each other in the absence of conflict. Based on the embodiments in the present disclosure, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present disclosure.

[0045] It should be noted that various aspects of the embodiments within the scope of the appended claims are described below. It should be apparent that the aspects described herein can be embodied in a wide variety of forms, and any specific structure and / or function described herein is merely illustrative. Based on this disclosure, it should be understood by those skilled in the art that an aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects described herein can be used to implement an apparatus and / or practice a method. In addition, other structures and / or functionalities other than one or more of the aspects described herein can be used to implement this apparatus and / or practice this method.

[0046] It should also be noted that the illustrations provided in the following embodiments are only schematic illustrations of the basic concept of the present disclosure. The illustrations only show components related to the present disclosure and are not drawn according to the number, shape and size of components in actual implementation. In actual implementation, the type, quantity and proportion of each component can be changed at will, and the component layout type may also be more complicated.

[0047] Additionally, in the following description, specific details are provided to provide a thorough understanding of the examples. However, one skilled in the art will appreciate that the aspects described can be practiced without these specific details.

[0048] For ease of understanding, Figure 1 As shown, this embodiment discloses a quadrilateral retopology method based on frame field prediction, including:

[0049] Step S101: inputting the triangular mesh model into the frame field neural network model to perform direction regression and amplitude diffusion with direction as a condition to obtain the corresponding frame field;

[0050] Step S102: deforming the mesh model based on the frame field to obtain a deformed mesh model;

[0051] Step S103: performing isotropic quadrilateral re-meshing on the deformed mesh model to obtain an initial quadrilateral mesh model;

[0052] Step S104: performing inverse deformation on the initial quadrilateral mesh model to obtain a quadrilateral mesh model corresponding to the triangular mesh model.

[0053] Optionally, inputting the triangle mesh model into the frame field neural network model includes:

[0054] Perform isotropic remeshing on the triangular mesh model to obtain a divided triangular mesh model;

[0055] Perform uniform sampling on the divided triangular mesh model to obtain sampling points;

[0056] The center point and sampling point of each triangle mesh are input into the frame field neural network model.

[0057] Optionally, the deforming based on the frame field to obtain a deformed mesh model includes:

[0058] Decompose each frame of the frame field into the product of a linear SPD map and a cross product;

[0059] The ARAP energy function is minimized to solve the vertex position after deformation;

[0060] The deformed mesh model is obtained based on the deformed vertex positions.

[0061] Optionally, performing isotropic quadrilateral re-meshing on the deformed mesh model to obtain an initial quadrilateral mesh model includes:

[0062] The deformed mesh model is subjected to isotropic quadrilateral remeshing using an isotropic quadrilateral remeshing algorithm with a cross product field constraint.

[0063] Optionally, performing isotropic quadrilateral remeshing on the deformed mesh model using an isotropic quadrilateral remeshing algorithm with a cross product field constraint includes:

[0064] Use QuadriFlow to re-mesh the deformed mesh model into the initial quadrilateral mesh model;

[0065] When using QuadriFlow, after local alignment of directions, the cross product on the vertex is calculated as the sum of the cross products on the faces weighted by the areas of the neighboring faces.

[0066] Optionally, performing inverse deformation on the initial quadrilateral mesh model includes:

[0067] The deformation transfer algorithm is used to inversely deform the initial quadrilateral mesh model. In the deformation transfer algorithm, the deformed mesh model is regarded as the source mesh, the initial quadrilateral mesh model is regarded as the target mesh, and the triangular mesh model is regarded as the pose source mesh.

[0068] Optionally, in the training of the frame field neural network model, the frame field is regarded as a point attribute, geometric information is encoded using points with normals, and the frame is represented using multiple vectors.

[0069] Optionally, the direction prediction of the frame field neural network model includes, for a point cloud sampled from a triangular mesh, using a loss function to represent the predicted direction vector d and the true value d of d gt , the loss function formula is:

[0070]

[0071] Optionally, the frame field neural network model uses diffusion for amplitude prediction. Using diffusion for amplitude prediction includes:

[0072] Use logarithmic magnitude as the diffusion target;

[0073] In each training step, the time step t is uniformly sampled in {1,...,T}, and the forward diffusion process is z i，t =α t z i，0 +β t ∈, where z i represents the amplitude, ∈ is the random noise drawn from the standard normal distribution, α t , β t are precomputed constants related to the noise scheduler.

[0074] In a specific application scenario, such as Figure 2 As shown, this embodiment proposes a quadrilateral retopology method based on frame field prediction for quadrilateralization of anisotropic meshes. The framework consists of two stages: the first stage is frame field prediction, and the second stage is quadrilateral mesh extraction. Mesh extraction consists of three steps: deformation, parameterization, and quadrilateral mesh extraction. Among these steps, parameterization is usually solved by MIQ implemented in libigl. Although it can sometimes provide seamless global parameterization, it has two significant shortcomings that hinder practical use. The MIQ algorithm implemented in libigl has a high error rate, especially on surfaces with complex structures and self-intersections after deformation. In addition, the time complexity varies for different meshes and increases significantly with the number of faces. In some cases, MIQ can take up to several hours to complete parameterization. Therefore, this embodiment develops an alternative solution that consists of a similar three-step process and integrates other open source algorithms. It includes deformation, isotropic quadrilateral remeshing, and inverse deformation.

[0075] Frame field inference: The triangular mesh model is input into the frame field neural network model for direction regression and amplitude diffusion conditioned on the direction to obtain the corresponding frame field: Given an input triangular mesh S, first, depending on the source of the mesh, a preliminary isotropic re-meshing step is optionally performed on S. The purpose of this step is to make the triangular faces more uniform, which is conducive to a relatively uniform point cloud. Deformation requires a frame field for each face. Therefore, the centers of all triangular faces and additional uniform sampling points are used as input to the trained neural network. After direction regression and amplitude diffusion conditioned on the direction, the frame field at the face center is used as the subsequent pre-face frame field.

[0076] Deformation: Deformation is performed based on the frame field to obtain the deformed mesh model: Each frame is first decomposed into the product of linear SPD mapping and cross product. The linear SPD mapping further derives the ideal deformation. The vertex positions of the input mesh are optimized to minimize the energy term of ARAP, which takes into account the optimal deformation, thereby forming the deformed surface S deform .

[0077] Isotropic quadrilateral remeshing: that is, isotropic quadrilateral remeshing is performed on the deformed mesh model to obtain the initial quadrilateral mesh model. After deformation, the frame field is close to the cross product field with unit and orthogonal components. The closest cross product field calculated using SVD serves as the direction constraint for the deformed mesh remeshing. In this step, any isotropic quadrilateral remeshing algorithm with cross product field constraints can be used. Considering stability and effectiveness, this embodiment uses QuadriFlow to convert S deform Re-mesh However, the above deformation only provides a cross product field on the face, while QuadriFlow requires direction field constraints on the vertices. Therefore, after locally aligning the directions, the cross product on the vertex is calculated as the sum of the cross products on the face, weighted by the area of ​​the adjacent faces. Some constraints can also be optionally set to preserve the crease edges of the CAD model.

[0078] Inverse deformation: that is, the initial quadrilateral mesh model is inversely deformed to obtain a quadrilateral mesh model corresponding to the triangular mesh model. The quadrilateral version required by the input mesh is the same as share the same connectivity and the same overall shape as S. Ideally, one could drive S to S by applying deform The inverse transformation of Transform back to S quad However, the deformation is defined only on the vertices of the input mesh. Therefore, the classic deformation transfer algorithm is adopted, where S deform , and S are considered as the source mesh, target mesh, and pose source mesh respectively. This results in the final quad mesh.

[0079] To learn frame fields from real-world mesh datasets, a key issue is how to choose a 3D representation to train a neural network to represent and learn frame fields. While it is natural to consider frame fields as surface attributes, as Dielen et al. do, this has been found to be impractical on large-scale datasets. This difficulty arises from several aspects. First, there is still a lack of robust backbone networks for mesh computation and processing. Graph neural networks are not as well explored as Transformer-based networks. The spiral network used by Dielen et al. relies on the manifold nature of the input mesh, which is difficult to maintain on real-world meshes (unlike SMPL templates). Second, pairs of quadrilateral meshes and their triangular counterparts are required to train the model. The remeshing process is time-consuming and can lead to surface misalignment. Finally, the quadrilateralization of the surface S should be invariant to changes in the connectivity of the triangular version of S. A neural network operating on meshes cannot be expected to give similar predictions on two meshes representing the same surface with different connectivity unless several remeshed versions are made from the quadrilateral mesh and trained using all of these pairs of augmented data. Instead, in this work, frame fields are considered point attributes, and a neural network designed specifically for point clouds is trained to predict them. Using points with normals to efficiently encode geometric information circumvents all of the above difficulties. Point clouds provide a connectivity-independent proxy for the underlying surface of the triangle mesh and are robust to non-manifold properties.

[0080] Given a mesh M, sample points {pi} and normals {ni} on its surface. The goal is to predict point-wise frames {fi}, which are interpreted as two representative vectors {(ui,vi)} for each frame. The representative vectors should lie on the tangent plane at pi. Given a quadrilateral mesh, the ground truth frame field can be computed in a similar manner to Dielen et al. For each sample point p, find the quadrilateral face containing p and interpolate the vector of the opposite edge by the distance from p to the two edges to compute one of the representative vectors.

[0081] However, using a direct frame vector regression network to predict it is not ideal, and the difficulties mainly manifest themselves in three aspects. First, the representative vector of the frame is ambiguous. The frame is symmetric under rotation and permutation. This ambiguity makes it difficult to train regression or diffusion models because a lot of augmentation is required. Second, for the same surface, there are essentially infinite plausible frame fields, ranging from uniform and isotropic to non-uniform and anisotropic. Therefore, some generative model should be used to model the distribution of possible frame fields conditioned on the sampled point cloud. Finally, there is ambiguity in the overall scale of the frame field. Consider a quadrilateral mesh and the same mesh after a Catmull-Clark subdivision. Their respective frame fields differ in magnitude by a factor of 2, and the point clouds sampled from them are indistinguishable.

[0082] To reduce the difficulty of learning frame fields, we address these issues from three perspectives. First and foremost, we attempt to compute a unique representation of the frame in a given tangent space. The frame at point p defined in the tangent space TpM can be uniquely represented as a vector set {u, -u, v, -v}, which can be further transformed from a complex polynomial and used as the root set: P(z) = z 4 +c0z 2 +c1=(zu)(z+u)(zv)(z+v)

[0083] Therefore, the frame can be converted into the coefficients of this complex polynomial, namely

[0084] c0=-(u 2 +v 2 ), c1=u 2 v 2 ,

[0085] This is called a multi-vector representation. Second, the direction itself, i.e., the unit frame field, is typically much less informative than the magnitude. Therefore, the task is split into two stages: direction prediction and magnitude prediction conditioned on the direction. Finally, instead of predicting the absolute magnitude directly, relative magnitudes are predicted that exclude the global scale, which is achieved by scaling them by the inverse of the mean.

[0086] Given a point cloud {(p i ,n i )}, where pi is the point coordinate and ni is the surface normal at pi. The task is to infer the direction {di} of the frame field {fi}. Call the {di} direction field. di can be represented by two vectors (diu,div) in the tangent plane at pi. They have the same direction as (ui,vi), except that they are unit vectors:

[0087] The tangent basis is randomly selected and a directional regression network DR is trained to output a multi-vector representation about them. The forward process is:

[0088] {[c i，0 , c i，1 ]}=DR({p i},{p i , n i , x i ,y i ]})

[0089]

[0090] Where xi, yi are the x-axis and y-axis of the tangent plane at pi, and [] represents a connection. The parameters of DR are the coordinates of the point and the input point features, respectively. The conversion from complex polynomial to direction CP2DIR can be easily implemented by solving the complex equation P(z) = 0 and finding the square root of the two roots. The conversion and normalization process from 2D coordinates to 3D directions are omitted here. Since the direction field is rotationally symmetric, the following loss function is used to represent the predicted direction vector d and its true value d gt :

[0091]

[0092] Since the direction field is invariant to the permutation of its two direction vectors, a matching loss function is applied to disambiguate it:

[0093]

[0094] Furthermore, since most meshes in the dataset are not pure quadrilateral meshes, it is difficult to compute reasonable directions on those pi sampled from triangular faces. Therefore, a point-wise mask m is used. i The above loss function is extended. For those p sampled from triangular faces i ,m i =0, otherwise, m i =1.

[0095]

[0096] Given the point cloud {(pi,ni)} and the direction field {di} predicted in the previous section, the goal is to build a diffusion model to generate the amplitude So that the obtained frame field is Logarithmic magnitude is used as a diffusion target. This brings two main advantages. On the one hand, The distribution of follows a log-normal-like distribution. On the other hand, with this activation, there is no need to perform additional post-processing to ensure positive amplitudes.

[0097] The diffusion model is trained and inferred in the DDIM framework. For simplicity, z i =log(l i ) represents the amplitude, and a subscript is added to indicate the time step. In each training step, the time step t is uniformly sampled in {1,...,T}, and the forward diffusion process is z i，t =α t z i，0 +β t ∈, where ∈ is random noise drawn from a standard normal distribution, α t , β t is a precomputed constant related to the noise scheduler. To ensure that the prediction is invariant to the permutations of the four directions, a pair of attention-based encoders and decoders are added before and after the point cloud backbone network. A denoising network is trained to estimate the original samples:

[0098]

[0099] g i =Denoise({p i},{[h i , m i ]};t)

[0100]

[0101] Since there are points that cannot be assigned a reasonable frame, mask MSE loss is applied for diffusion training:

[0102]

[0103] The point cloud used in this implementation can be replaced with other 3D representations, such as voxels and polygon meshes. However, voxel representations typically require a large amount of storage space, while polygon mesh representations have difficulty handling non-manifold meshes. In contrast, point cloud representations offer advantages such as high storage efficiency and the ability to handle arbitrary topologies.

[0104] The frame field prediction in this embodiment can be replaced by the following scheme: In addition to the method combining direction prediction and amplitude prediction, other methods such as direct regression and generative adversarial networks can also be used to predict the frame field. However, direct regression methods have difficulty handling the ambiguity of the frame field, and generative adversarial networks are unstable in training. The method proposed in this embodiment can effectively handle the ambiguity of the frame field and achieve stable training.

[0105] The quadrilateral mesh generation in this embodiment can be replaced by the following scheme: In addition to the frame field-guided mesh quadrilateralization process, other methods can also be used to generate quadrilateral meshes, such as parameterized methods and optimization-based methods. However, parameterized methods generally have high computational complexity, while optimization-based methods are prone to falling into local optimal solutions. The method proposed in this embodiment can efficiently generate high-quality quadrilateral meshes.

[0106] This implementation has the following effects:

[0107] Point cloud-based geometric encoding and multi-vector representation: This embodiment uses point cloud-based geometric encoding, combined with multi-vector representation, to achieve robust processing of arbitrary grid connectivity, while resolving inherent ambiguities in the frame field and improving learning dynamics. Traditional grid processing methods usually rely on grid structures and have difficulty processing non-manifold grids. The present invention, through point cloud representation, gets rid of the dependence on grid connectivity and can process various complex grid structures. The use of multi-vector representation can uniquely represent the frame field, resolve the ambiguity problem in the frame field representation, and make the model learning more efficient and accurate.

[0108] Decomposition of the frame field prediction task: This embodiment decomposes the frame field prediction task into two subtasks: direction prediction and amplitude prediction. Direction prediction is achieved through regression, while amplitude prediction is achieved through a conditional diffusion model. This decomposition method effectively addresses the ill-posedness problem in frame field estimation. The direction and amplitude of the frame field are key factors affecting the quality of quadrilateral mesh generation. This invention predicts the direction and amplitude separately and uses a conditional diffusion model to improve the accuracy of amplitude prediction, thereby generating a higher-quality quadrilateral mesh.

[0109] Establishing and utilizing a large-scale dataset: This example establishes and utilizes a large-scale quadrilateral mesh dataset, achieving strong generalization capabilities. The scale and diversity of a dataset are crucial to the performance of machine learning models. By constructing a large-scale dataset, this example improves the model's generalization capabilities, enabling it to adapt to a variety of input meshes and generate high-quality quadrilateral meshes.

[0110] Frame Field-Guided Mesh Quadrification: This example proposes a complete frame field-guided mesh quadrification process that converts a predicted frame field into a semantically aligned quadrilateral mesh. This process includes frame field inference, deformation, isotropic quadrilateral remeshing, and inverse deformation. Each step is crucial and collectively ensures the quality of the resulting quadrilateral mesh.

[0111] Ability to handle arbitrary mesh connectivity: Some existing methods rely on mesh structure and have difficulty handling non-manifold meshes. However, this embodiment uses point cloud-based geometric encoding, which eliminates the reliance on mesh connectivity and can handle various complex mesh structures, including non-manifold meshes.

[0112] Resolves ambiguity in frame field representation: Existing techniques for representing frame fields suffer from ambiguity, which impacts model learning efficiency and accuracy. This embodiment uses a multi-vector representation to uniquely represent the frame field, resolving this ambiguity and making model learning more efficient and accurate.

[0113] Improved accuracy of frame field prediction: Existing technologies suffer from ill-posedness in frame field prediction, which affects prediction accuracy. This embodiment decomposes the frame field prediction task into two subtasks: direction prediction and amplitude prediction. It also uses a conditional diffusion model to improve the accuracy of amplitude prediction, thereby improving the accuracy of frame field prediction.

[0114] Improved model generalization: Some existing methods lack large-scale, high-quality datasets, resulting in limited training data and insufficient generalization. This embodiment establishes and utilizes a large-scale quadrilateral mesh dataset, improving the model's generalization, enabling it to adapt to a variety of input meshes and generate high-quality quadrilateral meshes.

[0115] Generating Higher-Quality Quadrilateral Meshes: The method proposed in this embodiment generates higher-quality quadrilateral meshes that not only have high geometric quality but also achieve superior semantic alignment. Compared to existing techniques, the quadrilateral meshes generated in this embodiment are closer to manually designed meshes in terms of both geometric shape and semantic features.

[0116] The electronic device disclosed in this embodiment includes a memory and a processor. The memory is used to store non-transitory computer-readable instructions. Specifically, the memory may include one or more computer program products, which may include various forms of computer-readable storage media, such as volatile memory and / or non-volatile memory. The volatile memory may, for example, include random access memory (RAM) and / or cache memory (cache), etc. The non-volatile memory may, for example, include read-only memory (ROM), a hard disk, a flash memory, etc.

[0117] The processor may be a central processing unit (CPU) or other form of processing unit with data processing capabilities and / or instruction execution capabilities, and may control other components in the electronic device to perform desired functions. In one embodiment of the present disclosure, the processor is used to execute the computer-readable instructions stored in the memory, so that the electronic device performs all or part of the steps of the aforementioned four-sided face retopology method based on framework field prediction in each embodiment of the present disclosure.

[0118] Those skilled in the art should understand that in order to solve the technical problem of how to obtain a good user experience, this embodiment may also include well-known structures such as a communication bus and an interface, and these well-known structures should also be included in the scope of protection of this disclosure.

[0119] like Figure 3 The present invention provides a schematic structural diagram of an electronic device according to an embodiment of the present invention, which is suitable for implementing the electronic device according to an embodiment of the present invention. Figure 3 The electronic device shown is only an example and should not limit the functions and scope of use of the embodiments of the present disclosure.

[0120] like Figure 3 As shown, the electronic device may include a processing device (such as a central processing unit, a graphics processing unit, etc.), which can perform various appropriate actions and processes according to a program stored in a read-only memory (ROM) or a program loaded from a storage device into a random access memory (RAM). In the RAM, various programs and data required for the operation of the electronic device are also stored. The processing device, ROM, and RAM are connected to each other via a bus. An input / output (I / O) interface is also connected to the bus.

[0121] Typically, the following devices can be connected to the I / O interface: input devices such as sensors or visual information acquisition devices; output devices such as display screens; storage devices such as tapes and hard disks; and communication devices. The communication device allows the electronic device to communicate with other devices (such as edge computing devices) wirelessly or by wire to exchange data. Figure 3 The electronic device is shown with various devices, but it should be understood that it is not required to implement or possess all of the devices shown. More or fewer devices may be implemented or possessed instead.

[0122] In particular, according to an embodiment of the present disclosure, the process described above with reference to the flowchart can be implemented as a computer software program. For example, an embodiment of the present disclosure includes a computer program product, which includes a computer program carried on a non-transitory computer-readable medium, and the computer program contains program code for executing the method shown in the flowchart. In such an embodiment, the computer program can be downloaded and installed from a network through a communication device, or installed from a storage device, or installed from a ROM. When the computer program is executed by a processing device, all or part of the steps of the four-sided face retopology method based on framework field prediction of the embodiment of the present disclosure are executed.

[0123] For detailed description of this embodiment, please refer to the corresponding description in the aforementioned embodiments, which will not be repeated here.

[0124] The computer-readable storage medium disclosed in this embodiment stores non-transitory computer-readable instructions. When executed by a processor, the non-transitory computer-readable instructions execute all or part of the steps of the aforementioned four-sided face retopology method based on frame field prediction in each embodiment of the present disclosure.

[0125] The above-mentioned computer-readable storage media include, but are not limited to, optical storage media (e.g., CD-ROMs and DVDs), magneto-optical storage media (e.g., MOs), magnetic storage media (e.g., magnetic tapes or mobile hard disks), media with built-in rewritable non-volatile memory (e.g., memory cards), and media with built-in ROM (e.g., ROM cartridges).

[0126] For detailed description of this embodiment, please refer to the corresponding description in the aforementioned embodiments, which will not be repeated here.

[0127] The basic principles of the present disclosure have been described above in conjunction with specific embodiments. However, it should be noted that the advantages, strengths, and effects mentioned in this disclosure are merely illustrative and not restrictive, and should not be construed as necessarily possessed by each embodiment of the present disclosure. Furthermore, the specific details disclosed above are provided for illustrative purposes and to facilitate understanding, rather than as limitations. These details do not limit the present disclosure to necessarily being implemented using these specific details.

[0128] In the present disclosure, relational terms such as first and second, etc. are merely used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply that there is any such actual relationship or order between these entities or operations. The block diagrams of the devices, devices, equipment, and systems involved in the present disclosure are merely illustrative examples and are not intended to require or imply that they must be connected, arranged, or configured in the manner shown in the block diagrams. As will be appreciated by those skilled in the art, these devices, devices, equipment, and systems can be connected, arranged, or configured in any manner. Words such as "including," "comprising," "having," and the like are open-ended words, meaning "including but not limited to," and can be used interchangeably therewith. The words "or" and "and" used herein refer to the words "and / or" and can be used interchangeably therewith, unless the context clearly indicates otherwise. The word "such as" used herein refers to the phrase "such as but not limited to," and can be used interchangeably therewith.

[0129] Additionally, as used herein, "or" used in a list of items beginning with "at least one" indicates a separate list, so that, for example, a list of "at least one of A, B, or C" means A or B or C, or AB or AC or BC, or ABC (i.e., A and B and C). Furthermore, the word "exemplary" does not mean that the example described is preferred or better than other examples.

[0130] It should also be noted that in the system and method of the present disclosure, each component or each step can be decomposed and / or recombined. Such decomposition and / or recombination should be regarded as equivalent solutions of the present disclosure.

[0131] Various changes, substitutions, and modifications may be made to the technology described herein without departing from the teachings defined by the appended claims. Moreover, the scope of the claims of this disclosure is not limited to the specific aspects of the processes, machines, manufactures, compositions of things, means, methods, and actions described above. Currently existing or later developed processes, machines, manufactures, compositions of things, means, methods, or actions that perform substantially the same function or achieve substantially the same results as the corresponding aspects described herein may be utilized. Accordingly, the appended claims include within their scope such processes, machines, manufactures, compositions of things, means, methods, or actions.

[0132] The above description of the disclosed aspects is provided to enable any person skilled in the art to make or use the present disclosure. Various modifications to these aspects will be readily apparent to those skilled in the art, and the general principles defined herein may be applied to other aspects without departing from the scope of the present disclosure. Therefore, the present disclosure is not intended to be limited to the aspects shown herein, but rather to be accorded the widest scope consistent with the principles and novel features disclosed herein.

[0133] The above description has been provided for the purpose of illustration and description. In addition, this description is not intended to limit the embodiments of the present disclosure to the forms disclosed herein. Although a number of example aspects and embodiments have been discussed above, those skilled in the art will recognize certain variations, modifications, alterations, additions, and sub-combinations thereof.

Claims

1. A quadrilateral retopology method based on frame field prediction, characterized in that: include: The triangular mesh model is input into the frame field neural network model to perform direction regression and amplitude diffusion conditioned on direction to obtain the corresponding frame field. Deform the mesh model based on the frame field; Perform isotropic quadrilateral re-meshing on the deformed mesh model to obtain an initial quadrilateral mesh model; The initial quadrilateral mesh model is inversely deformed to obtain a quadrilateral mesh model corresponding to the triangular mesh model.

2. The quadrilateral retopology method based on frame field prediction according to claim 1, characterized in that: Inputting the triangle mesh model into the frame field neural network model involves: Perform isotropic remeshing on the triangular mesh model to obtain a divided triangular mesh model; Perform uniform sampling on the divided triangular mesh model to obtain sampling points; The center point and sampling point of each triangle mesh are input into the frame field neural network model.

3. The quadrilateral retopology method based on frame field prediction according to claim 1, characterized in that: The deforming based on the frame field to obtain a deformed mesh model includes: Decompose each frame of the frame field into the product of a linear SPD map and a cross product; The ARAP energy function is minimized to solve the vertex position after deformation; The deformed mesh model is obtained based on the deformed vertex positions.

4. The quadrilateral retopology method based on frame field prediction according to claim 1, characterized in that: The isotropic quadrilateral re-meshing of the deformed mesh model to obtain an initial quadrilateral mesh model includes: The deformed mesh model is subjected to isotropic quadrilateral remeshing using the isotropic quadrilateral remeshing algorithm with cross product field constraints.

5. The quadrilateral retopology method based on frame field prediction according to claim 4, characterized in that: The isotropic quadrilateral remeshing algorithm with a cross product field constraint is used to perform isotropic quadrilateral remeshing on the deformed mesh model, comprising: Use QuadriFlow to re-mesh the deformed mesh model into the initial quadrilateral mesh model; When using QuadriFlow, after local alignment of directions, the cross product on the vertex is calculated as the sum of the cross products on the faces weighted by the areas of the neighboring faces.

6. The quadrilateral retopology method based on frame field prediction according to claim 1, characterized in that: The inverse deformation of the initial quadrilateral mesh model includes: The deformation transfer algorithm is used to inversely deform the initial quadrilateral mesh model. In the deformation transfer algorithm, the deformed mesh model is regarded as the source mesh, the initial quadrilateral mesh model is regarded as the target mesh, and the triangular mesh model is regarded as the pose source mesh.

7. The quadrilateral retopology method based on frame field prediction according to claim 1, characterized in that: In the training of the frame field neural network model, the frame field is regarded as a point attribute, geometric information is encoded using points with normals, and the frame is represented using multiple vectors.

8. The quadrilateral retopology method based on frame field prediction according to claim 7, characterized in that: The direction prediction of the frame field neural network model includes, for the point cloud collected from the triangular mesh samples, using the loss function to represent the predicted direction vector d and the true value d of d gt , the loss function formula is:

9. The quadrilateral retopology method based on frame field prediction according to claim 7, characterized in that: The frame field neural network model uses diffusion for amplitude prediction. The use of diffusion for amplitude prediction includes: Use logarithmic magnitude as the diffusion target; In each training step, the time step t is uniformly sampled in {1,...,T}, and the forward diffusion process is z i，t =α t z i，0 +β t ∈, where z i represents the amplitude, ∈ is the random noise drawn from the standard normal distribution, α t , β t are precomputed constants related to the noise scheduler.

10. An electronic device, characterized in that: The electronic device comprises: at least one processor; and, a memory communicatively connected to the at least one processor; wherein, The memory stores instructions that can be executed by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute the four-sided face retopology method based on framework field prediction described in any one of claims 1-9.

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