Quadriplanar surface retopology method based on frame field prediction and electronic device

Abstract

This invention provides a quadrilateral retopology method and electronic device based on frame field prediction. The quadrilateral retopology method based on frame field prediction includes: inputting a triangular mesh model into a frame field neural network model for direction regression and amplitude diffusion conditioned on direction to obtain the corresponding frame field; deforming the frame field to obtain a deformed mesh model; isotropically re-meshing the deformed mesh model to obtain an initial quadrilateral mesh model; and inversely deforming 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 re-meshing, and inverse deformation, the quality of the final generated quadrilateral mesh is guaranteed, thereby achieving the goal of improving the quality of the quadrilateral mesh.

Description

Technical Field

[0001] This invention belongs to the field of three-dimensional model technology, and in particular relates to a quadrilateral retopology method and electronic device based on frame field prediction. Background Technology

[0002] Quadrilateral meshes play a crucial role in computer graphics applications; however, automatically generating high-quality quadrilateral meshes remains challenging. With the rapid development of generative modeling techniques and 3D content representation, 3D model generation has received significant attention from the community in recent years. In particular, 3D models defined using quadrilateral meshes play a vital role in computer-aided design, physical simulation, and character animation. However, designing high-quality quadrilateral meshes is labor-intensive and requires domain-specific knowledge. Therefore, developing a method to automatically generate high-quality quadrilateral meshes from intuitive user input is of great value. Contemporary 3D content generation and reconstruction methods have achieved remarkable success by employing 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 quadrilateral-dominated meshes created by professional artists. This quality discrepancy, particularly in mesh topology and element alignment, has prompted the development of robust quadrilateralization techniques to bridge the gap between neural field reconstructions and production-ready assets.

[0003] Existing techniques have the following problems when generating quadrilateral meshes:

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

[0005] 2. Inability to effectively handle non-manifold meshes: Existing mesh-based neural architectures struggle to handle non-manifold meshes, which constitute a large proportion of real-world 3D content.

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

[0007] In view of 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 quality of quadrilateral mesh in the prior art.

[0008] In a first aspect, embodiments of this disclosure provide a quadrilateral retopology method based on frame field prediction, including:

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

[0010] The deformed mesh model is obtained by deformation based on the frame field;

[0011] The deformed mesh model is re-meshed using isotropic quadrilaterals to obtain the 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 triangular mesh model into the frame field neural network model includes:

[0014] The triangular mesh model is re-meshed isotropically to obtain the re-meshed triangular mesh model.

[0015] Uniform sampling is performed on the divided triangular mesh model to obtain sampling points;

[0016] Input the center point and sampling point of each triangular grid into the frame field neural network model.

[0017] Optionally, the deformation of the mesh model based on the frame field includes:

[0018] Each frame of the frame field is decomposed into the product of a linear SPD mapping and a cross product;

[0019] The vertex positions after deformation are determined by minimizing the ARAP energy function;

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

[0021] Optionally, the step of isotropically re-meshing the deformed mesh model to obtain an initial quadrilateral mesh model includes:

[0022] The deformed mesh model is re-meshed using an isotropic quadrilateral re-meshing algorithm with cross-product field constraints.

[0023] Optionally, the isotropic quadrilateral re-meshing algorithm with cross-product field constraints is used to re-mesh the deformed mesh model isotropically, including:

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

[0025] When using QuadriFlow, after local alignment, the cross product at the vertex is calculated as the sum of the cross products on the face by weighting the areas of adjacent faces.

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

[0027] The deformation transfer algorithm is used to perform inverse deformation on 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 by multiple vectors.

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

[0030]

[0031] Optionally, the frame field neural network model uses diffusion for amplitude prediction, which 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 Let α represent the amplitude, ∈ is the random noise extracted from the standard normal distribution. t ,β t These are pre-calculated constants related to the noise scheduler.

[0034] Secondly, embodiments of this disclosure also provide 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 executable by the at least one processor, which enable the at least one processor to perform the quad-face retopology method based on frame field prediction as described in any of the first aspects.

[0038] This invention provides a quadrilateral retopology method and electronic device based on frame field prediction. The method predicts both direction and amplitude separately, and uses a conditional diffusion model to improve the accuracy of amplitude prediction, thereby generating a higher-quality quadrilateral mesh. Through frame field inference, deformation, isotropic quadrilateral remeshing, and inverse deformation steps, the quality of the final generated quadrilateral mesh is guaranteed, thus achieving the goal of improving the quality of the quadrilateral mesh. Attached Figure Description

[0039] The above and other objects, features and advantages of this disclosure will become more apparent from the accompanying drawings, in which like reference numerals generally denote like parts.

[0040] Figure 1 A flowchart of a quadrilateral retopology method based on frame field prediction provided in an embodiment of this disclosure;

[0041] Figure 2 A schematic diagram illustrating the effect of the quadrilateral retopology method based on frame field prediction provided in this embodiment of the disclosure;

[0042] Figure 3 This is a schematic block diagram of an electronic device provided in an embodiment of the present disclosure. Detailed Implementation

[0043] The embodiments of this disclosure will now be described in detail with reference to the accompanying drawings.

[0044] It should be understood that the following specific examples illustrate the implementation of this disclosure, and those skilled in the art can easily understand other advantages and effects of this disclosure from the content disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of this disclosure, and not all of them. This disclosure can also be implemented or applied through other different specific implementation methods, and the details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this disclosure. It should be noted that, in the absence of conflict, the following embodiments and features in the embodiments can be combined with each other. Based on the embodiments in this disclosure, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this disclosure.

[0045] It should be noted that various aspects of embodiments within the scope of the appended claims are described below. It will be apparent that the aspects described herein can be embodied in a wide variety of forms, and any particular structure and / or function described herein is merely illustrative. Based on this disclosure, those skilled in the art will understand that one 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 set forth herein can be used to implement the device and / or practice the method. Additionally, this device and / or method can be implemented using structures and / or functionalities other than one or more of the aspects set forth herein.

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

[0047] Furthermore, specific details are provided in the following description to facilitate a thorough understanding of the examples. However, those skilled in the art will understand that the described aspects can be practiced without these specific details.

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

[0049] Step S101: Input the triangular mesh model into the frame field neural network model to perform direction regression and amplitude diffusion conditioned on direction to obtain the corresponding frame field;

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

[0051] Step S103: Re-mesh the deformed mesh model using isotropic quadrilaterals to obtain the initial quadrilateral mesh model;

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

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

[0054] The triangular mesh model is re-meshed isotropically to obtain the re-meshed triangular mesh model.

[0055] Uniform sampling is performed on the divided triangular mesh model to obtain sampling points;

[0056] Input the center point and sampling point of each triangular grid into the frame field neural network model.

[0057] Optionally, the deformation of the mesh model based on the frame field includes:

[0058] Each frame of the frame field is decomposed into the product of a linear SPD mapping and a cross product;

[0059] The vertex positions after deformation are determined by minimizing the ARAP energy function;

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

[0061] Optionally, the step of isotropically re-meshing the deformed mesh model to obtain an initial quadrilateral mesh model includes:

[0062] The deformed mesh model is re-meshed using an isotropic quadrilateral re-meshing algorithm with cross-product field constraints.

[0063] Optionally, the isotropic quadrilateral re-meshing algorithm with cross-product field constraints is used to re-mesh the deformed mesh model isotropically, including:

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

[0065] When using QuadriFlow, after local alignment, the cross product at the vertex is calculated as the sum of the cross products on the face by weighting the areas of adjacent faces.

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

[0067] The deformation transfer algorithm is used to perform inverse deformation on 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 by multiple vectors.

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

[0070]

[0071] Optionally, the frame field neural network model uses diffusion for amplitude prediction, which 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 Let α represent the amplitude, ∈ is the random noise extracted from the standard normal distribution. t ,β t These are pre-calculated 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 quadrilateralizing anisotropic meshes. The framework comprises two stages: frame field prediction and quadrilateral mesh extraction. Mesh extraction involves three steps: deformation, parameterization, and quadrilateral mesh extraction. In these steps, parameterization is typically handled by MIQ implemented in libigl. While it can sometimes provide seamless global parameterization, it has two significant drawbacks that hinder practical use. The MIQ algorithm implemented in libigl has a high error rate, especially on deformed surfaces with complex structures and self-intersecting surfaces. Furthermore, the time complexity varies depending on the mesh and increases significantly with the number of faces. In some cases, MIQ may take several hours to complete parameterization. Therefore, this embodiment develops an alternative that consists of a similar three-step process and integrates other open-source algorithms, including deformation, isotropic quadrilateral remeshing, and inverse deformation.

[0075] Frame field inference: The frame field is obtained by inputting a triangular mesh model into a frame field neural network model and performing orientation regression and orientation-conditional amplitude diffusion. Given an input triangular mesh S, an initial isotropic re-mesh step is optionally performed on S based on the mesh's origin. The purpose of this step is to make the triangular faces more uniform, thus contributing to a relatively uniform point cloud. Deformation requires the frame field for each face. Therefore, the centers of all triangular faces, along with additional uniformly sampled points, are used as input to the trained neural network. After orientation regression and orientation-conditional amplitude diffusion, the frame field at the face centers is used as the subsequent pre-face frame field.

[0076] Deformation: This involves deforming the mesh model based on the frame field. Each frame is first decomposed into the product of a linear SPD mapping and a 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 the ARAP, which takes into account the optimal deformation, thus forming the deformable surface S. deform .

[0077] Isotropic Quadrilateral Remeshing: This involves isotropically remeshing the deformed mesh model to obtain an initial quadrilateral mesh model. After deformation, the frame field approximates a cross-product field with unit and orthogonal components. The closest cross-product field calculated using SVD serves as the directional 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 efficiency, this embodiment uses QuadriFlow to process the S... deform Re-grid However, the above deformation only provides the cross product field on the surface, while QuadriFlow requires directional field constraints on the vertices. Therefore, after locally aligning the directions, the cross product on the vertices is calculated as the sum of the cross products on the surfaces by weighting the areas of adjacent faces. Some constraints can also be selectively set to preserve the crease edges of the CAD model.

[0078] Inverse deformation: This involves performing inverse deformation on the initial quadrilateral mesh model to obtain a quadrilateral mesh model corresponding to the triangular mesh model. The required quadrilateral version of the mesh is input. They share the same connectivity and the same overall shape as S. Ideally, S can be driven to S by an application. deform The inverse transform will Transform back to S quad However, the deformation is defined only at the vertices of the input mesh. Therefore, the classic deformation propagation algorithm is adopted, where S deform , S and S are considered as the source mesh, target mesh, and pose source mesh, respectively. This results in the final quadrilateral mesh.

[0079] To learn frame fields from real-world mesh datasets, a key challenge is choosing the 3D representation to train neural networks to represent and learn these fields. While treating frame fields as surface properties, as Dielen et al. did, is natural, this proves impractical on large-scale datasets. The difficulties manifest in several ways. First, a robust backbone network for mesh computation and processing remains undeveloped. Graph neural networks are not as extensively explored as Transformer-based networks. The spiral network used by Dielen et al. relies on the manifold 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 surface S should be invariant to changes in connectivity of the triangular version of S. A neural network operating on a mesh cannot be expected to give similar predictions on two meshes representing the same surface with different connectivity unless several remeshing versions are created from the quadrilateral mesh and trained using all these paired augmented data. Instead, this work treats frame fields as point properties and trains neural networks specifically designed for point clouds to predict them. By using points with normals to efficiently encode geometric information, all the aforementioned difficulties are circumvented. Point clouds provide a connectivity-independent proxy for the underlying surface of the triangular 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 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 manner similar to that of Dielen et al. For each sample point p, find the quadrilateral face containing p, and interpolate the vectors of the sides by the distances from p to the two sides to compute one of the representative vectors.

[0081] However, using a direct frame vector regression network to predict it is not ideal, with difficulties mainly in three aspects. First, the representative vectors of the frames are fuzzy. Frames are symmetric under rotation and arrangement. This fuzziness makes training regression or diffusion models difficult because a large amount of augmentation is required. Second, for the same surface, there are essentially an infinite number of plausible frame fields, ranging from homogeneous and isotropic to non-homogeneous and anisotropic. Therefore, some generative model should be used to model the distribution of possible frame fields conditioned on the sampled point cloud. Finally, the overall scale of the frame field is fuzzy. Suppose there is a quadrilateral grid and a grid of the same grid 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, these problems are addressed in three aspects. First, and most importantly, a unique representation of the frame is computed in a given tangent space. A 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 derived 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 framework can be transformed into the coefficients of this complex polynomial, i.e.

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

[0085] This is called multi-vector representation. Secondly, the direction itself, i.e., the unit frame field, is typically much smaller than the amplitude. Therefore, the task is divided into two phases: direction prediction and amplitude prediction conditioned on direction. Finally, instead of directly predicting absolute amplitudes, relative amplitudes excluding the global scale are predicted, which is achieved by scaling them with the inverse of the mean.

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

[0087] We randomly select tangent bases and train a directional regression network (DR) to output multi-vector representations of 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 and yi are the x-axis and y-axis of the tangent plane at pi, and [] denotes connection. The parameters of DR are the coordinates of the point and the features of the input point, respectively. The transformation from complex polynomial to direction CP2DIR can be easily achieved by solving the complex equation P(z) = 0 and finding the square roots of the two roots. The transformation and normalization process from 2D coordinates to 3D direction is 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 orientation field is invariant with respect to the permutation of its two orientation vectors, a matching loss function is applied to eliminate ambiguity:

[0093]

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

[0095]

[0096] Given a point cloud {(pi,ni)} and the predicted orientation field {di} from the previous section, the goal is to construct a diffusion model to generate amplitude. So that the frame field obtained is Logarithmic amplitude was used As a diffusion target, this brings two main advantages. On the one hand, The distribution follows a similar log-normal distribution. On the other hand, with this activation, no additional post-processing is needed to ensure a positive amplitude.

[0097] The diffusion model is trained and inferred within the DDIM framework. For simplicity, z is used. i =log(l i The value t represents the amplitude, and an index 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 extracted from the standard normal distribution, α t ,β t These are pre-computed constants related to the noise scheduler. To ensure that the predictions are invariant across the four orientations, a pair of attention-based encoders and decoders are added before and after the point cloud backbone network, respectively. 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 where a reasonable frame cannot be assigned, masked MSE loss is applied for diffusion training:

[0102]

[0103] The point cloud representation in this implementation can be replaced by other 3D representation methods such as voxels and polygon meshes. However, voxel representation typically requires a large amount of storage space, while polygon mesh representation struggles to handle non-manifold meshes. In contrast, point cloud representation offers 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 alternatives: besides the method combining direction and magnitude prediction, other methods such as direct regression and generative adversarial networks can also be used to predict frame fields. However, direct regression methods struggle to handle the ambiguity in frame fields, while generative adversarial networks are unstable during training. The method proposed in this embodiment can effectively handle the ambiguity in frame fields and achieve stable training.

[0105] The quadrilateral mesh generation method in this embodiment can be replaced by the following alternatives: besides the frame field-guided mesh quadrilateralization process, other methods can be used to generate quadrilateral meshes, such as parameter-based methods and optimization-based methods. However, parameter-based methods typically have high computational complexity, while optimization-based methods are prone to getting trapped in local optima. 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 employs point cloud-based geometric encoding combined with multi-vector representation to achieve robust handling of arbitrary mesh connectivity, while resolving inherent ambiguities in frame fields and improving learning dynamics. Traditional mesh processing methods typically rely on mesh structure and struggle with non-manifold meshes. This invention, through point cloud representation, eliminates the dependence on mesh connectivity and can handle various complex mesh structures. The use of multi-vector representation uniquely represents frame fields, resolving the ambiguity problem in frame field representation and making model learning more efficient and accurate.

[0108] Decomposition of the frame field prediction task: This embodiment decomposes the frame field prediction task into two sub-tasks: direction prediction and amplitude prediction. Direction prediction is achieved through regression, while amplitude prediction is achieved through a conditional diffusion model. This decomposition method can effectively handle the ill-posed 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 improves the accuracy of amplitude prediction by predicting direction and amplitude separately and using a conditional diffusion model, thereby generating higher-quality quadrilateral meshes.

[0109] Establishment and utilization of large-scale datasets: This embodiment establishes and utilizes a large-scale quadrilateral grid dataset, thereby achieving powerful generalization capabilities. The size and diversity of the dataset are crucial to the performance of machine learning models. This embodiment improves the model's generalization ability by constructing a large-scale dataset, enabling it to adapt to various different input grids and generate high-quality quadrilateral grids.

[0110] Frame Field-Guided Mesh Quadrilateralization: This embodiment proposes a complete frame field-guided mesh quadrilateralization process that can convert the predicted frame field into a semantically aligned quadrilateral mesh. The process includes steps such as frame field inference, deformation, isotropic quadrilateral re-meshing, and inverse deformation. Each step is crucial and collectively ensures the quality of the final generated quadrilateral mesh.

[0111] Capable of handling arbitrary mesh connectivity: Some existing methods rely on mesh structure and struggle to handle non-manifold meshes. This embodiment, however, employs point cloud-based geometric encoding, eliminating the dependence on mesh connectivity and enabling the handling of various complex mesh structures, including non-manifold meshes.

[0112] This invention addresses the ambiguity issue in frame field representation: Existing frame field representations suffer from ambiguity, impacting the model's learning efficiency and accuracy. This embodiment utilizes multi-vector representation to uniquely represent the frame field, resolving the ambiguity issue and enabling more efficient and accurate model learning.

[0113] Improved accuracy of frame field prediction: Existing technologies suffer from ill-posedness in frame field prediction, affecting its accuracy. This embodiment decomposes the frame field prediction task into two sub-tasks: direction prediction and amplitude prediction. A conditional diffusion model is used to improve the accuracy of amplitude prediction, thereby enhancing the overall accuracy of frame field prediction.

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

[0115] Generating Higher-Quality Quadrilateral Meshes: The method proposed in this embodiment can generate higher-quality quadrilateral meshes that not only possess high geometric quality but also achieve superior semantic alignment. Compared to existing technologies, the quadrilateral meshes generated in this embodiment are closer to manually designed meshes in both geometry 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. The non-volatile memory may, for example, include read-only memory (ROM), hard disk, 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 this disclosure, the processor is used to execute computer-readable instructions stored in the memory, causing the electronic device to perform all or part of the steps of the frame field prediction-based quad-plane retopology method of the foregoing embodiments of this disclosure.

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

[0119] like Figure 3 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present disclosure. It illustrates a structural schematic diagram suitable for implementing the electronic device in the embodiment of the present disclosure. Figure 3 The electronic device shown is merely an example and should not be construed as limiting the functionality and scope of the embodiments disclosed herein.

[0120] like Figure 3 As shown, an electronic device may include a processing unit (such as a central processing unit, graphics processing unit, etc.) that can perform various appropriate actions and processes based on a program stored in read-only memory (ROM) or a program loaded from a storage device into random access memory (RAM). The RAM also stores various programs and data required for the operation of the electronic device. The processing unit, ROM, and RAM are interconnected via a bus. Input / output (I / O) interfaces are 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 displays; storage devices, such as magnetic tapes or hard drives; and communication devices. Communication devices allow electronic devices to communicate wirelessly or wiredly with other devices (such as edge computing devices) to exchange data. Although Figure 3 Electronic devices with various devices are shown, but it should be understood that it is not required to implement or have all of the devices shown. More or fewer devices may be implemented or have alternatively.

[0122] In particular, according to embodiments of this disclosure, the processes described above with reference to the flowcharts can be implemented as computer software programs. For example, embodiments of this disclosure include a computer program product comprising a computer program carried on a non-transitory computer-readable medium, the computer program containing program code for performing the methods shown in the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network via 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 quadrilateral retopology method based on frame field prediction according to embodiments of this disclosure are performed.

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

[0124] The computer-readable storage medium disclosed in this embodiment stores non-transitory computer-readable instructions. When these non-transitory computer-readable instructions are executed by a processor, all or part of the steps of the quad-plane retopology method based on frame field prediction described in the foregoing embodiments of this disclosure are performed.

[0125] The aforementioned computer-readable storage media include, but are not limited to: optical storage media (e.g., CD-ROM and DVD), magneto-optical storage media (e.g., MO), magnetic storage media (e.g., magnetic tape or portable hard drive), media with built-in rewritable non-volatile memory (e.g., memory card), and media with built-in ROM (e.g., ROM cartridge).

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

[0127] The basic principles of this disclosure have been described above with reference to specific embodiments. However, it should be noted that the advantages, benefits, and effects mentioned in this disclosure are merely examples and not limitations, and should not be considered as essential features of each embodiment of this disclosure. Furthermore, the specific details disclosed above are for illustrative and facilitative purposes only, and are not limitations. These details do not limit the scope of this disclosure to the necessity of employing the aforementioned specific details for implementation.

[0128] In this disclosure, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. The block diagrams of devices, apparatuses, devices, and systems involved in this 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 those skilled in the art will recognize, these devices, apparatuses, devices, and systems can be connected, arranged, and configured in any manner. Words such as "comprising," "including," "having," etc., are open-ended terms meaning "including but not limited to," and are used interchangeably with them. The terms "or" and "and" as used herein refer to the terms "and / or," and are used interchangeably with them unless the context clearly indicates otherwise. The term "such as" as used herein refers to the phrase "such as but not limited to," and is used interchangeably with it.

[0129] Additionally, as used herein, the “or” used in a list of items beginning with “at least one” indicates a separate list, such that a list of, for example, “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 imply that the described example is preferred or better than other examples.

[0130] It should also be noted that in the systems and methods of this disclosure, the components or steps can be decomposed and / or recombined. These decompositions and / or recombinations should be considered as equivalent solutions to this disclosure.

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

[0132] The above description of the disclosed aspects is provided to enable any person skilled in the art to make or use this 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 this disclosure. Therefore, this disclosure is not intended to be limited to the aspects shown herein, but rather to be carried out within the widest scope consistent with the principles and novel features disclosed herein.

[0133] The above description has been given for purposes of illustration and description. Furthermore, this description is not intended to limit the embodiments of this disclosure to the forms disclosed herein. Although numerous exemplary aspects and embodiments have been discussed above, those skilled in the art will recognize certain variations, modifications, alterations, additions, and sub-combinations therein.

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 for direction regression and amplitude diffusion conditioned on direction to obtain the corresponding frame field. The deformed mesh model is obtained by deformation based on the frame field; The deformed mesh model is re-meshed using isotropic quadrilaterals to obtain the initial quadrilateral mesh model. The initial quadrilateral mesh model is inversely deformed to obtain a quadrilateral mesh model corresponding to the triangular mesh model; In the training of the frame field neural network model, the frame field is regarded as a point attribute, geometric information is encoded by points with normals, and the frame is represented by multi-vectors. The orientation 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 ground truth of the predicted orientation vector d. The loss function formula is: ； 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... ,in, The amplitude is represented by ϵ, which is random noise extracted from the standard normal distribution. , These are pre-calculated constants related to the noise scheduler.

2. The quadrilateral retopology method based on frame field prediction according to claim 1, characterized in that, Inputting the triangular mesh model into the frame field neural network model includes: The triangular mesh model is re-meshed isotropically to obtain the re-meshed triangular mesh model. Uniform sampling is performed on the divided triangular mesh model to obtain sampling points; Input the center point and sampling point of each triangular grid 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 deformed mesh model obtained by deformation based on the frame field includes: Each frame of the frame field is decomposed into the product of a linear SPD mapping and a cross product; The vertex positions after deformation are determined by minimizing the ARAP energy function; The deformed mesh model is obtained based on the vertex positions after deformation.

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

5. The quadrilateral retopology method based on frame field prediction according to claim 4, characterized in that, The method of using an isotropic quadrilateral re-meshing algorithm with cross-product field constraints to re-mesh the deformed mesh model includes: Use QuadriFlow to remesh the deformed mesh model into the initial quadrilateral mesh model; When using QuadriFlow, after local alignment, the cross product at the vertex is calculated as the sum of the cross products on the face by weighting the areas of adjacent 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 perform inverse deformation on 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. An electronic device, characterized in that, The electronic device includes: At least one processor; and, A memory communicatively connected to the at least one processor; wherein, The memory stores instructions executable by the at least one processor, which, when executed by the at least one processor, enables the at least one processor to perform the quad-face retopology method based on frame field prediction as described in any one of claims 1-6.

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