Artificial intelligence generated content (AIGC) has received significant attention at present. As the numerous generative models proposed, the emerging diffusion model has attracted extensive attention due to its highly interpretable mathematical properties and the ability to generate high-quality and diverse results. Nowadays, diffusion models have achieved remarkable results in the field of condition-guided image generation. This achievement promotes the development of diffusion models in other conditional tasks and has various applications in areas such as movies, games, paintings, and virtual reality. For instance, the diffusion model can generate high-resolution images in text-guided image generation tasks while ensuring the quality of the generated images. In this paper, we first introduce the definition and background of diffusion models. Then, we present a review of the development history and latest progress of conditional image generation based on diffusion models. Finally, we conclude this survey with discussions on challenges and future research directions of diffusion models.

To address the problem that the performance of existing methods is unsatisfactory for detecting intrinsic symmetry in two-dimensional shapes, based on the flexible function mapping framework, we propose a spectral optimization method, named FM-2DSISD, to compute dense point maps for two-dimensional intrinsic symmetric shapes. Firstly, we design an algorithm robust to noise to extract sparse feature symmetry point maps. Secondly, using the feature symmetric point maps and the functional map framework, a mathematical model is developed whose optimization objective is to maintain the diagonality and orthogonality of each principal submatrix of the functional map matrix. We prove that the defined optimization objective can preserve the isometry of intrinsic symmetry maps. To solve the formula, we give an alternating iterative algorithm between the spatial and spectral domains via the spectral up-sampling technique. Numerical experiments show that the proposed algorithm performs better than the state-of-the-art methods on two-dimensional smooth shapes and noisy shapes.

In visualization field, Focus+Context techniques have been developed to visualize large, complex models on the display device with limited resolution. In this work, we propose a novel method for Focus+Context visualization based on optimal mass transportation. An optimal mass transportation map deforms a volume to itself, transforms the source measure (volumetric element) to the target measure with the minimal transportation cost. Solving the optimal mass transportation problem is equivalent to a convex optimization, and can be converted to computing power Voronoi diagrams in classical computational geometry. Comparing to existing approaches, the proposed method has solid theoretic foundation, which guarantees the existence, uniqueness and the smoothness of the solution. It allows the user to accurately control the target measure, and select multiple focus regions with irregular shapes. The resulting deformation is globally smooth and flipping free. Experiments with several volume data sets from medical applications and scientific simulations demonstrate the effectiveness and efficiency of our method.

Marching cubes (MC) is a classic algorithm for isosurface extraction. However, it can only be used to reconstruct closed surfaces, as it requires dividing the space into inside and outside. To solve this problem, a neural marching cubes algorithm for open surfaces is proposed. The key to our method is to introduce a new sort of point position called irrelative point. Since no isosurface exists between irrelevant points and inside or outside points, thus connecting the inside and outside of the target shapes. The determination of irrelevant points does not require complex networks or calculations, and can be directly determined by the distance from points to the surface. Meanwhile, a residual module introducing attention mechanism is adopted to replace the original network. In addition, new tessellations are designed, and open surfaces can be reconstructed with the help of irrelative points. Finally, a smoothing process is incorporated to improve the reconstruction quality of the border. By testing on both closed and open surfaces under various metrics, our experiments show that the proposed method achieves high-quality reconstruction of open surfaces while maintaining the capability of reconstructing closed surfaces.

Accurate and high-quality shape generation of individual teeth from cone-beam computerized tomography (CBCT) is essential for computer-aided dentistry. Existing methods need post-process to extract isosurfaces and the output meshes cannot be directly used as the input for most subsequent applications (such as finite element analysis (FEA). In this paper, we propose the network that directly learns the multi-resolution mesh guided by diffeomorphic deformation. Overall, our solution is a classic two-stage schema widely used in tooth reconstruction. Firstly, we adopt a revised anchor-free detector to locate each individual tooth with high precision. Then, we design the top-to-bottom flows from the multi-level features of each individual, referred to as pyramid flows, to predict diffeomorphic deformation from a sphere to a detailed tooth. Finally, we validate the effectiveness and efficiency of the proposed approach by comparing with the previous segmentation methods and other explicit surface learning-based methods in the experiment.

Atherosclerosis is a critical cause of cardiovascular disease and stroke. Simulating and visualizing this process is crucial to relevant medical research. To tackle the problems of existing methods regarding the difficulties on realistic simulation and low efficiency, we propose a novel and highly efficient atherosclerotic plaque simulation solution based on a fluid-solid coupled incompressible smoothed particle hydrodynamics (SPH) method. Firstly, we discretize the blood into incompressible fluid particles using fluid-solid coupled in compressible SPH to control the stability of blood. Then, we adopt the plaque generation model to model blood, monocytes and other particles to control plaque generation based on pathological analysis of blood composition. Finally, we compute the physical properties of blood and plaque by coupling fluid-solid particles to simulate the plaque clogging effect. To make the simulation as in real-time as possible, parallel accelerated computation is implemented in CUDA architecture. Several realistic renderings of plaque simulations are provided.The results show that our method can achieves fast simulation of plaque generation in blood while avoiding the high computational cost associated with the partial differential equation model for plaque generation.

In response to the low computational efficiency in the context of multi-scale structural topology design, an efficient asymptotic homogenization GPU parallel strategy is presented. The strategy leverages the graphics processing unit (GPU) and investigates parallel strategies for level set initialization, large sparse stiffness matrix equations solving and constitutive properties computing. Experimental results demonstrate that the computing efficiency of the asymptotic homogenization can be greatly improved by adopting the parallel strategies, in particular, when refining a three-dimensional unit cell grid to a resolution of 100 000, the GPU parallel strategy achieves a speedup of two orders of magnitude compared to the CPU serial.

This paper proposes a novel dense correspondence method based on generalized unsupervised learning. First, multilayer perceptron (MLP) and residual network are constructed to learn deep point features. Secondly, the approximate geodesic distance of the point cloud is calculated and a feature embedding space is established through feature decomposition. By employing the attention mechanism, it effectively learns the generalized basis function representation. Furthermore, the proposed method combines point features with generalized basis function to generate deep feature representations of 3D shapes. Finally, an unsupervised function mapping network is constructed to obtain dense corresponding representations between shapes. We also propose a tri-regularization mechanism that combines reconstruction loss, descriptor loss, and distance loss for shape matching, effectively improving learning performance and shape corresponding accuracy from the feature and spatial domains. Extensive experimental results have shown that the generalized basis function representation and unsupervised functional map learning mechanism are suitable for arbitrary 3D shapes, breaking through the limitations of previous methods on continuous 2D manifolds, it achieves better performance in arbitrary 3D shape matching.

The UNet network can be used to predict the dense displacement field in the full-resolution spatial domain, and has achieved great success in the field of medical image registration. However, for three-dimensional images with large deformation, there are still shortcomings such as long running time, inability to effectively maintain the topological structure, and easily leading to the loss of spatial features. A large kernel multi-scale deformable medical image registration network based on cross-attention (LK-CAUNet) is proposed. Based on the classical UNet network, the cross-attention module is introduced to achieve efficient and multi-level semantic feature fusion. The large kernel asymmetric parallel convolution is equipped. It has the ability to learn multi-scale features and complex structures. Besides, an additional square and scaling module is added to let it have the advantages of topological conservation and transform reversibility. Using the brain MRI dataset, it is demonstrated that the proposed method has significantly improved the registration performance compared with the eighteen classical registration methods. Especially compared with the most advanced TransMorph registration method, the Dice score can be improved by 8%, and the parameter quantity is only one fifth of it.

In recent years, the utilization of neural networks to represent 3D scenes for novel view synthesis has emerged as a new research focus in computer graphics, known as neural rendering. Neural networks can also be applied to efficiently represent the geometry and materials of scenes, enabling the reconstruction of high-quality meshes and texture maps under the supervision of 2D photometric images in inverse rendering, thus serving existing graphics pipelines. In this paper, we extend the latest inverse rendering by optimizing neural SDFs and materials from photometric images (IRON) neural rendering model by introducing a multiresolution hash encoding technique and employing strategies such as freezing parameters to enhance the training speed of the original model. Through comparative evaluations on multiple datasets, we achieve approximately 40% improvement in training speed compared to the original model, while producing reconstructions with more details.

V-system is a kind of complete orthogonal piecewise polynomial function system on L^{\mathrm{2}}[\mathrm{0,1}], because of the discontinuous nature of its basis functions, it has significant advantages in the expression and analysis of discontinuous signals. However, in the current V-system transformation algorithm, for a signal with a length of N, it not only needs to generate and store an N-order orthogonal matrix in advance, but also its time complexity is as high as \mathrm{{\rm O}}(N^{\mathrm{3}}). Therefore, in order to adapt to the efficient processing needs, this paper designs and implements a fast decomposition and reconstruction algorithm for V-systems from the perspective of multi-resolution analysis of V-systems. This fast algorithm does not need to store additional information, and its time complexity is only \mathrm{{\rm O}}(N^{\mathrm{2}}). The test results show that the fast algorithm proposed in this paper can meet the requirements of high-efficiency processing of large-scale data, which lays the foundation for the application of V-system in more fields.

To address the limitations of current mainstream networks, which rely solely on local neighborhoods for feature aggregation and suffering from insufficient feature extraction capabilities and information loss due to max-pooling, we propose an attention-based point cloud processing network that combines both local and global information. First, we introduce channel attention for local feature aggregation to minimize information loss. Next, we design a dynamic key point learning method to capture the remote dependency information of points and obtain global information. Finally, we develop a spatial attention fusion module to allow each point to learn the global con-textual information. Our proposed method has been benchmarked on several point cloud analysis tasks. It achieved an overall classification accuracy of 94.0% and an average classification accuracy of 91.7% on the ModelNet40 classification task. On the ScanObjectNN classification task, our method reached an overall class fication accuracy of 81.5% and an average classification accuracy of 78.1%. In the ShapeNet segmentation task, we obtained a mean intersection over union of 86.5%. The experimental results show that the proposed network has significantly improved accuracy compared to classical networks such as PointNet, PointNet++, and DGCNN in classification and segmentation tasks, and has also achieved improvement in deferent degree compared to other point cloud processing networks.

Overhangs are usually inevitable when fabricating a part of complex shape in 3D printing. Meanwhile, the geometric error on the side surface of an overhang (i.e. the side loss) after fabricating is often significant, which seriously affects the accuracy of the overhang as well as its container (i.e. a part). To solve the above problem, a double-level intelligent improvement approach for overhangs on side loss (i.e. process parameter optimization and geometry pre-compensation) is proposed in this paper. Firstly, a series of experiments with different values concerning the critical design parameter and process parameters are designed based on the Taguchi method. Then, a deliberate measurement method is designed to get the side loss data from the fabricated inverted 'L'-shaped parts. Secondly, two types of side loss prediction networks are respectively constructed for the two sides (that is the overhang side and the non-overhang side) of each inverted 'L'-shaped part. They are mainly designed according to the requirements of support structures on an overhang. Aided with these networks, the geometric error of both sides of an overhang on an inverted 'L'-shaped part (with various values of the critical design parameter) can be predicted accurately. Thirdly, aiming at minimizing the side losses on both sides of an overhang, a single-objective and multiple-variables nonlinear programming problem is formulated. Hereby, the corresponding optimized side losses as well as their counterpart values of key process parameters can be determined. Finally, we compensate the geometries on the two sides of an overhang based on the above-optimized side losses by conducting an inverse modification first and then fabricate the overhang adopting the above-optimized values of key process parameters. Based on fused deposition modeling, experiments were implemented on various inverted 'L'-shaped parts except the ones used in constructing prediction networks, which verified the effectiveness of the proposed approach. Meanwhile, comparative analyses with state-of-the-art works were also carried out. The results show that our method is suitable for overhangs and has great potential to significantly improve their side losses.

A multi-morphology design method based on conformal mapping is proposed to design triply periodic minimal surface (TPMS) microchannels with freeform boundary constraints. This method first maps the boundary of a freeform surface to a plane, allowing for channel topology design in the 2D parametric domain; Then, a Beta growth function algorithm based on loop is proposed to achieve smooth transitions of various TPMS morphological features; Finally, by mapping the designed microchannels to the 3D space constrained by the free surface, the microchannels meet the design requirements. Our results show that the microchannels constructed by this method have good adaptability to complex surface boundaries and can achieve the design goals of internal morphological features.

In order to improve the efficiency and quality of parametric tread pattern retrieval, a novel method is proposed. Firstly, the tread pattern model in B-rep format is converted into an attribute adjacency graph, in which the edge compatibility is used for inexact matching of two attribute adjacency graphs and for the calculation of graph similarity. The geometric features reflected by the design parameters are used to define similarity of tread pattern models. Secondly, to improve query efficiency, various design parameters are used for rough space division and recursive clustering on the tread pattern database. An index structure based on the cluster tree is constructed to speed up model retrieval. Our experimental results show the superiority of the proposed method over the general model retrieval methods, both in search efficiency and quality. This demonstrates the advantage of utilizing design parameters and geometric information of the tread pattern in CAD model retrieval.

Improving the segmentation quality of 3D meshes is always an important problem to computer graphics. To handle this problem, this paper proposes a shape-aware graph attention network. The shape-aware graph attention coefficient is defined to better reflect the similarity between nodes, which not only expands the attention coefficient obtained by network learning with the help of edge features between nodes, but also introduces the attention coefficient related to the local shape information of nodes. On the other hand, the network architecture is adjusted by taking both shape features and labels of 3D mesh model as the input of graph attention network, which enables the participation of labels in network training and verification stages. Residual connection is further employed to make the network output more stable. A large number of experiments show that the proposed algorithm can obtain accurate segmentation boundaries. Compared with the existing classical segmentation algorithms on PSB dataset, the proposed algorithm improves 2% in accuracy, and achieves better Rand index. The reasonableness of the algorithm is proved by ablation experiment.

This paper proposes to employ matrix weighted NURBS surfaces to fit and fair quad meshes. For a quadrilateral mesh with given or estimated unit normals at vertices, a matrix weighted NURBS surface can be constructed by choosing the mesh vertices as control points and employing normals at each vertex for computing matrix weights. Compared with traditional NURBS surfaces, matrix weighted NURBS surfaces have quasi-cylindrical accuracy. When the input data is uniformly sampled from a smooth surface, the constructed matrix weighted NURBS surface has good smoothness and fits the mesh model well; if the input grid data contain noise, a fair fitting surface that approximates the original grid well can still be obtained by resampling control vertices on current fitting surfaces and re-calculating vertex normals based on the new quad meshes iteratively.