Point cloud denoising is a fundamental yet challenging task in computer graphics. Existing solutions typically rely on supervised training on synthesized noise. However, real-world noise often exhibits greater complexity, causing learning-based methods trained on synthetic noise to struggle when encountering unseen noise-a phenomenon we refer to as noise misalignment. To address this challenge, we propose LaPDA (Latent-space Point cloud Denoising with Adaptivity), a neural network explicitly designed to mitigate noise misalignment and enhance denoising robustness. LaPDA consists of two key stages. First, we adaptively model noise in the latent space, aligning unseen noise distributions with the known training distributions or adjusting them toward distributions with lower noise scales. Training objectives at this stage are formulated based on controlled synthetic noise with varying intensity levels. Second, we introduce a gradual noise removal module that optimizes the spatial distribution of the adaptively adjusted noisy points. Extensive experiments conducted on both synthetic and scanned datasets demonstrate that LaPDA achieves enhanced accuracy and robustness compared to state-of-the-art methods.

For large-scale point cloud processing, resampling takes the important role of controlling the point number and density while keeping the geometric consistency. However, current methods cannot balance such different requirements. Particularly with large-scale point clouds, classical methods often struggle with decreased efficiency and accuracy. To address such issues, we propose a weighted Poisson-disk (WPD) resampling method to improve the usability and efficiency for the processing. We first design an initial Poisson resampling with a voxel-based estimation strategy. It is able to estimate a more accurate radius of the Poisson-disk while maintaining high efficiency. Then, we design a weighted tangent smoothing step to further optimize the Voronoi diagram for each point. At the same time, sharp features are detected and kept in the optimized results with isotropic property. Finally, we achieve a resampling copy from the original point cloud with the specified point number, uniform density, and high-quality geometric consistency. Experiments show that our method significantly improves the performance of large-scale point cloud resampling for different applications, and provides a highly practical solution.

In magnetic resonance imaging (MRI), anisotropic volumes with low through-plane resolution are typically acquired. Recently, diffusion models have shown strong performance in anisotropic MRI super-resolution (SR). However, iterative sam-pling limits the clinical applicability of diffusion models. To address this problem, we propose a One-Step Denoising Diffusion Probabilistic Model (OS-DDPM) for anisotropic MRI SR, which can generate isotropic High-Resolution (HR) data in a single sampling step. Firstly, we construct a Dual-Domain One-Step Generator (DDOS-Generator) comprising a student network for initial reconstruction in the spatial domain and a wavelet denoising module for noise suppression and detail refinement in the wavelet domain. Secondly, variational score distillation is applied to distill the generative prior from the pre-trained multi-step DDPM (teacher) to OS-DDPM, which can produce high-quality one-step SR data comparable to multi-step SR data. Finally, diffusion-based noise-aware contrastive learning is designed to bridge the distribution mismatch between one-step SR data and HR data. Extensive experiments on two public datasets demonstrate that the proposed method offers a fast inference speed and outperforms existing anisotropic SR methods and its teacher diffusion model in most metrics.

Probabilistic Partial Least Squares (PPLS) extends Partial Least Squares (PLS) by incorporating a probabilistic framework and identifiability constraints. PPLS models the relationship between two datasets as the sum of a joint component comprising correlated latent vectors and a noise component of isotropic normal random vectors. However, estimating PPLS model parameters involves a challenging nonconvex constrained optimization problem. We propose the Scalar Likelihood Method (SLM) to estimate the parameters of the PPLS model using a scalar likelihood function of the observed variables, derived via a novel rank n update technique. This technique avoids introducing additional constraints that would compromise the model’s dimension reduction properties. In addition, we derive a closed-form solution for the noise distribution in the observed data, significantly reducing parameter coupling in the objective function, thereby greatly improving parameter estimation quality. Through simulation studies, as well as association analysis and prediction tasks, we demonstrate the effectiveness and efficiency of SLM, highlighting its potential in practical applications.

Intracranial aneurysms (IAs) pose a significant risk due to their potential to rupture, leading to severe clinical outcomes. Accurate quantification of aneurysm morphology and assessment of rupture risk are crucial for timely intervention and treatment. In this study, we present an approach for the geometric quantification of IAs and clinical rupture risk evaluation based on the relationship between these measurements. Our approach includes a comprehensive set of geometric characteristics, such as height, width, neck width, arterial diameter, area, and volume. We applied these measurements to the public IntrA dataset, and to our knowledge, this is the first geometric analysis conducted on this dataset. By integrating these morphological characteristics with expert assessments, we developed a predictive model for IA rupture risk. Our findings reveal a strong correlation between aneurysm depth and rupture risk, with even stronger associations observed for higher-order dimension metrics like surface area and volume. This highlights the critical role of 3D automatic quantification in evaluating rupture risk. This research provides a foundation for further geometric analysis of IAs and offers potential advancements in automated diagnostics and precision medicine.

Saliency is an important characteristic in 3D analysis, and saliency detection for 3D meshes has been extensively studied in visual computing. However, insufficient feature description poses a significant challenge for 3D mesh saliency maps, which consist with human visual perception that is independent of the surroundings. We propose a multi-level fusion saliency detection method that leverages multiple eigenfunctions of the Laplacian-Beltrami operator(LBO) through a non-linear suppression operator, effectively integrating information across various levels. This method is based on reconstruction error and sparse matrix within the feature space constructed through dictionary learning (DL) at each level. The effectiveness of this method has been validated on the SchellingData, as demonstrated through both visualization and quantization. The method can be widely applied to down-stream tasks such as mesh simplification, object detection and so on.

Accurate segmentation of cerebral aneurysms from 3D vessel meshes is an essential yet challenging task, complicated by diverse imaging modalities that produce multi-resolution representations. Existing methods often struggle to handle meshes of varying granularity and orientations while maintaining segmentation accuracy. In this paper, we propose an end-to-end multi-scale graph-based segmentation framework that incorporates SE(3)-equivariance and an uncertainty-aware loss function. Our approach constructs a multi-scale graph representation on the 3D mesh and leverages a self-attention mechanism over graph edges to achieve adaptive neighborhood awareness, enabling the network to effectively handle multiple mesh resolutions simultaneously. By introducing an SE(3)-equivariant backbone, rotational variations in aneurysm orientation are naturally accommodated, ensuring relevant and effective feature learning. Furthermore, we develop an uncertainty-aware loss that adaptively emphasizes ambiguous regions, improving segmentation quality and confidence. Experimental results on the public datasets IntrA demonstrate that our method outperforms existing techniques, offering improved accuracy, consistency and stability across different mesh resolutions for 3D aneurysm segmentation. Code is available on https://github.com/Dolphin4mi/se3meshseg.

Tubular-like system shape analysis is quite difficult in geometry and topology, while it is widely used in plants and organs analysis in practice. However, traditional discrete representations such as voxels and point clouds often require substantial storage and may lead to the loss of fine-grained geometric and topological details. To address these challenges, we propose SE(3)-BBSCformerGCN, a novel framework for learning shape-aware representations from continuous tubular topological manifolds with equivariance to rotations and translations. Our approach leverages Ball B-Spline Curve (BBSC) to define tubular manifolds and its functional space. We provide a formal mathematical definition and analysis of the resulting manifolds and the BBSC functional space, and incorporate an equivariant mapping that preserves geometric and topological stability. Compared to the point cloud and voxel based representations, our manifold-based formulation significantly reduces data complexity while preserving geometric attributes together with topological features. We validate our method on the branch classification task for Circle of Willis (CoW) on the TopCoW 2024 dataset and the clinical dataset. Our method consistently outperforms voxel and point cloud based baselines in terms of classification performance, generalization ability, convergence speed, and robustness to overfitting.

ABSTRACT Accurate 3D craniofacial landmark detection is critical for applications in medicine and computer animation, yet remains challenging due to the complex geometry of craniofacial structures. In this work, we propose a coarse‐to‐fine framework for anatomical landmark localization on 3D craniofacial models. First, we introduce a Diffused Two‐Stream Network (DTS‐Net) for heatmap regression, which effectively captures both local and global geometric features by integrating pointwise scalar flow, tangent space vector flow, and spectral features in the Laplace‐Beltrami space. This design enables robust representation of complex anatomical structures. Second, we propose a heat kernel‐based energy optimization method to extract landmark coordinates from the predicted heatmaps. This approach exhibits strong performance across various geometric regions, including boundaries, flat surfaces, and high‐curvature areas, ensuring accurate and consistent localization. Our method achieves state‐of‐the‐art results on both a 3D cranial dataset and the BU‐3DFE facial dataset.

This article presents Diffusing Winding Gradients (DWG) for reconstructing watertight surfaces from unoriented point clouds. Our method exploits the alignment between the gradients of the screened generalized winding number (GWN) field—a robust variant of the standard GWN field—and globally consistent normals to orient points. Starting with an unoriented point cloud, DWG initially assigns a random normal to each point. It computes the corresponding screened GWN field and extracts a level set whose iso-value is the average of GWN values across all input points. The gradients of this level set are then utilized to update the point normals. This cycle of recomputing the screened GWN field and updating point normals is repeated until the screened GWN level sets stabilize and their gradients cease to change. Unlike conventional methods, DWG does not rely on solving linear systems or optimizing objective functions, which simplifies its implementation and enhances its suitability for efficient parallel execution. Experimental results demonstrate that DWG significantly outperforms existing methods in terms of runtime performance. For large-scale models with 10 to 20 million points, our CUDA implementation on an NVIDIA GTX 4090 GPU achieves speeds 30 to 120 times faster than iPSR, the leading sequential method, tested on a high-end PC with an Intel i9 CPU. Furthermore, by employing a screened variant of GWN, DWG demonstrates enhanced robustness against noise and outliers and proves effective for models with thin structures and real-world inputs with overlapping and misaligned scans. For source code and additional results, visit our project webpage: https://dwgtech.github.io/ .

A fast and fully automatic design of 3D cranial implants is highly desired in cranioplasty, and is key to the treatment of skull trauma. We have defined the repair of skull defects as a 3D shape completion task by proposing a two-stage diffusion model based on the representation of 3D shapes using signed distance function (SDF). Specifically, we design a diffusion model conditioned on partial shapes, we compress the 3D shape into a compact latent representation using the encoder in the vector quantized variational autoencoder (VQ-VAE) and learn the diffusion model based on this compressed discrete representation. Encoding the latent space with the autoencoder can achieve high-quality 3D cranial shape completion. In order to accurately capture local and fine-grained shape details, the training data is geometrically encoded from a compactly learned code-book. The two-stage diffusion generator with a coarse-to-fine approach possesses precise and expressive structural modeling capabilities to ensure the supplementation of detailed geometric information. Experimental results verified sufficient expressiveness of our model with generating high-fidelity results with fine-grained local details, outperforming the state-of-the-art methods.

Automated, accurate and robust segmentation of CT scans on abdominal organs remains a formidable challenge due to the blurred boundaries and subtle features of adjacent structures of abdominal organs. MedSAM, the fully fine-tuned model based on the Segment Anything Model (SAM) for medical image, fails to perform well relying solely on box prompt. Besides, utilizing the contextual information in the 3D volume data is tricky. To address above issues, we develop a MedSAM-based model for abdominal multi-organ CT segmentation. A feature selection network is introduced to extract entropy and curvature information. Together with the image embedding from the image encoder of MedSAM, the extracted information is processed during the inference. Low-Rank Adaptation (LoRA) is also applied to the image encoder and mask decoder of MedSAM for efficient fine-tuning on the FLARE2022 dataset. During the inference, mask prompts from segmentation results of last adjacent structure together with the expanded box prompt are used to improve the performance in continued context, thereby achieving an automated workflow. The experimental results suggest that the proposed method demonstrates a state-of-the-art performance and a potential clinical promise.

Unsupervised learning-based action recognition methods have shown immense potential by leveraging vast amounts of unlabeled data, yielding competitive performance in action recognition tasks. To capture semantic information in action, many efforts have focused on multi-stream fusion techniques, which makes the models heavier and less flexible to train. However, existing single-stream methods struggle to provide rich semantic information through data augmentation. To address these challenges, we propose a novel joint-level semantic augmentation method based on a constructed motion manifold, which achieves significant performance gains with virtually no additional training costs. Our approach introduces random perturbations on the motion manifold constructed based on evolutionary metrics. We propose several semantic augmentation strategies, including directional semantic perturbations, magnitude semantic perturbations, and initial pose perturbations. To pay greater attention to samples with significant semantic differences, we introduce the Semantic Adaptive Weighted Loss (SAWL) based on motion manifold distance. SAWL encourages the model to pay more attention to these samples, leading to the learning of an embedding space with semantic invariance. Extensive experiments were conducted on three large-scale datasets, i.e., NTU-60, NTU-120, and PKU-MMD II. The results demonstrate that our single-stream approach, empowered by joint-level semantic augmentation, achieves state-of-the-art (SOTA) performance among single-stream methods and competitive performance among multi-stream methods.

3D human motion prediction is a challenging task due to the highly non-linear nature of movements. Existing deep learning-based action prediction methods emphasize the design of sophisticated network architectures to achieve state-of-the-art performance on datasets. However, in real-life scenarios, changes in skeletal size lead to a shift in data distribution, which presents challenges for accurate motion prediction. Additionally, the presence of stretching artifacts in predicted bone sequences significantly impacts the quality of the predictions. To address these issues, we propose a framework that combines geometric encoding with neural networks to achieve size-invariant and high-quality motion prediction without stretching artifacts. We consider the constraint of bone length and construct a motion space using Riemannian manifold theory, which remains unaffected by changes in skeletal size and can fully represent human motion. Furthermore, we propose the trajectory transport square-root velocity function to encode motion sequences into a flattened space. This transformation simplifies the distance calculation and linearizes the optimization problem in non-flattened space. Experiments on the Human 3.6M and CMU MoCap datasets demonstrated that the proposed method has achieved competitive performance without any stretching artifacts and exhibits robustness to changes in skeletal size.

This paper presents a geometric model for achieving automatic 3D quantitative calculation of the femoroacetabular impingement (FAI) index on computed tomography (CT) images. The result is then used in subsequent work to reduce errors due to perspective differences in existing clinical measurements. This is the first automated quantitative method for a comprehensive FAI diagnostic index that does not rely on datasets. First, the geometric description and equation expression of the hip point cloud were obtained from CT images, fitting the key points and outlines required for the diagnostic index according to such geometric properties as Gaussian curvature. Then, an objective quantitative expression of the FAI index was calculated based on the 3D morphological definition. Next, we statistically analyzed 37 clinical data cases to verify our method’s effectiveness. Especially for the cases of hip dysplasia and acetabular boundary, there were unclear, strong correlations between manual and automatic measures (r = 0.88, ICC = 0.84).

Automatic detecting intracranial aneurysms (IAs) poses significant challenges due to their diversity, varying locations, and complex classifications by size, shape, and phenotype. Current shape-based IAs detection methods, while promising, often neglect the topological connectivity of IAs vertices and the variable traits of the aneurysm's neck, leading to fragmented detections. To address these issues, we present a mesh convolutional neural network based on gauge equivariant convolution to leverage the topological and geometric features of 3D mesh models. Our network comprises four key components: anisotropic message passing (AMP) on mesh surfaces, gauge equivariant convolution (GEC), vector-aware feature reconstruction (VFR), and a pooling-free convolutional architecture. AMP ensures accurate detection of IAs from surrounding vessels by utilizing topological connectivity and anisotropic relationships between mesh vertices. GEC offers rotational equivariance for consistently learning geometric features, improving feature learning stability and efficiency. VFR preserves the geometric and directional integrity of the vector features, enriching the representational capacity of the network. The pooling-free convolutional architecture captures local and global geometric nuances of 3D meshes, achieving precise IAs detection and producing sharper IAs boundaries. Tests on the IntrA dataset show our method outperforms the current best by 1.83% and 1.02% in mIoU and mDSC, respectively.

Traditional sign language teaching methods face challenges such as limited feedback and diverse learning scenarios. Although 2D resources lack reality sences, classroom teaching is constrained by a scarcity of teacher and methods based on VR and AR have relatively primitive interaction feedback mechanisms. This study proposes an innovative teaching model that uses real-time monocular vision and mixed reality technology. First, we introduce an improved hand-posture reconstruction method to achieve sign language semantic retention and real-time feedback. Second, a ternary system evaluation algorithm is proposed for a comprehensive assessment, maintaining good consistency with experts in sign language. Furthermore, we use mixed reality technology to construct a scenario-based 3D sign language classroom and explore the user experience of scenario teaching. Overall, this paper presents a novel teaching method that provides an immersive learning experience, advanced posture reconstruction, and precise feedback, achieving positive feedback on user experience and learning effectiveness.

Abstract Due to the widespread applications of curves on n‐dimensional spheres, fitting curves on n‐dimensional spheres has received increasing attention in recent years. However, due to the non‐Euclidean nature of spheres, curve fitting methods on n‐dimensional spheres often struggle to balance fitting accuracy and curve fairness. In this paper, we propose a new fitting framework, GLS‐PIA, for parameterized point sets on n‐dimensional spheres to address the challenge. Meanwhile, we provide the proof of the method. Firstly, we propose a progressive iterative approximation method based on geodesic least squares which can directly optimize the geodesic least squares loss on the n‐sphere, improving the accuracy of the fitting. Additionally, we use an error allocation method based on contribution coefficients to ensure the fairness of the fitting curve. Secondly, we propose an adaptive knot placement method based on geodesic difference to estimate a more reasonable distribution of control points in the parameter domain, placing more control points in areas with greater detail. This enables B‐spline curves to capture more details with a limited number of control points. Experimental results demonstrate that our framework achieves outstanding performance, especially in handling imbalanced data points. (In this paper, “sphere” refers to n‐sphere (n≥ 2) unless otherwise specified.)

Abstract Due to the widespread applications of 2‐dimensional spherical designs, there has been an increasing requirement of modeling on the 𝕊2 manifold in recent years. Due to the non‐Euclidean nature of the sphere, it has some challenges to find a method to represent 2D regions on 𝕊2 manifold. In this paper, a skeleton‐based representation method of regions on 𝕊2, disk B‐spline(DBSC) on 𝕊2 is proposed. Firstly, we give the definition and basic algorithms of DBSC on 𝕊2. Then we provide the calculation method of DBSC on 𝕊2, which includes calculating the boundary points, internal points and their corresponding derivatives. Based on that, we give some modeling methods of DBSC on 𝕊2, including approximation, deformation. In the end, some stunning application examples of DBSC on 𝕊2 are shown. This work lays a theoretical foundation for further applications of DBSC on 𝕊2.

High-quality image generation is an important topic in digital visualization. As a sub-topic of the research, color transfer is to produce a high-quality image with ideal color scheme learned from the reference one. In this article, we investigate the mainstream methods of color transfer to provide a survey that introduces the related theories and frameworks. Such methods can be divided into three categories: statistical color transfer, semantic-based color transfer, and color transfer for special target. For these mainstream technical routes, we discuss the related research background, technical details, and representative methods. We also exhibit some new trends of the topic according to recent progress. Based on the comparisons, we discuss the unsolved issues of color transfer and potential solutions in future work.

As a significant geometric feature of 3D point clouds, sharp features play an important role in shape analysis, 3D reconstruction, registration, localization, etc. Current sharp feature detection methods are still sensitive to the quality of the input point cloud, and the detection performance is affected by random noisy points and non-uniform densities. In this paper, using the prior knowledge of geometric features, we propose a Multi-scale Laplace Network (MSL-Net), a new deep-learning-based method based on an intrinsic neighbor shape descriptor, to detect sharp features from 3D point clouds. First, we establish a discrete intrinsic neighborhood of the point cloud based on the Laplacian graph, which reduces the error of local implicit surface estimation. Then, we design a new intrinsic shape descriptor based on the intrinsic neighborhood, combined with enhanced normal extraction and cosine-based field estimation function. Finally, we present the backbone of MSL-Net based on the intrinsic shape descriptor. Benefiting from the intrinsic neighborhood and shape descriptor, our MSL-Net has simple architecture and is capable of establishing accurate feature prediction that satisfies the manifold distribution while avoiding complex intrinsic metric calculations. Extensive experimental results demonstrate that with the multi-scale structure, MSL-Net has a strong analytical ability for local perturbations of point clouds. Compared with state-of-the-art methods, our MSL-Net is more robust and accurate.

Magnetic resonance imaging (MRI) scans often suffer from noise and low-resolution (LR), which affect the diagnosis and treatment results obtained for patients. LR images and noise come together with MRI, and the existing methods solve image super-resolution (SR) reconstruction and denoising tasks in a step-by-step manner, which influences the overall real distribution of the MRI data. In this paper, we present a simultaneous SR and denoising algorithm based on a stochastic normalizing flow (SNF), named the MR image SR and denoising model based on an SNF (SRDSNF). SRDSNF adds the encoded information of the input image as the conditional information to each reverse step of the stochastic normalizing flow, which realizes a consistent description of the spatial distribution between the reconstruction result and the input image. We introduce rangenull space decomposition and subsequence sampling strategies to enhance the consistency of the input and output data and increase the generation speed of the model. Simultaneous SR and denoising tasks experiment is carried out using the BrainWeb and NFBS datasets. The experimental results show that good SR and denoising results are obtained with fewer sampling steps, these results are consistent with the ground truths, and the structural similarity and peak signal-to-noise ratio of the results are also higher than those of the comparison methods. The proposed method demonstrates potential clinical promise.

We present an effective spectral matching method based on a shape association graph for finding region correspondences between two cel animation keyframes. We formulate the correspondence problem as an adapted quadratic assignment problem, which comprehensively considers both the intrinsic geometric and topology of regions to find the globally optimal correspondence. To simultaneously represent the geometric and topological similarities between regions, we propose a shape association graph (SAG), whose node attributes indicate the geometric distance between regions, and whose edge attributes indicate the topological distance between combined region pairs. We convert topological distance to geometric distance between geometric objects with topological features of the pairs, and introduce Kendall shape space to calculate the intrinsic geometric distance. By utilizing the spectral properties of the affinity matrix induced by the SAG, our approach can efficiently extract globally optimal region correspondences, even if shapes have inconsistent topology and severe deformation. It is also robust to shapes undergoing similarity transformations, and compatible with parallel computing techniques.

Image denoising is an important topic in the digital image processing field. This paper theoretically studies the validity of the classical non-local mean filter (NLM) for removing Gaussian noise from a novel statistic perspective. By regarding the restored image as an estimator of the clear image from the statistical view, we gradually analyse the unbiasedness and effectiveness of the restored value obtained by the NLM filter. Then, we propose an improved NLM algorithm called the clustering-based NLM filter (CNLM) that derived from the conditions obtained through the theoretical analysis. The proposed filter attempts to restore an ideal value using the approximately constant intensities obtained by the image clustering process. Here, we adopt a mixed probability model on a prefiltered image to generate an estimator of the ideal clustered components. The experimental results show that our algorithm obtains considerable improvement in peak signal-to-noise ratio (PSNR) values and visual results when removing Gaussian noise. On the other hand, the considerable practical performance of our filter shows that our method is theoretically acceptable as it can effectively estimates ideal images.

Craniofacial reconstruction is fundamental in resolving forensic cases. It is rather challenging due to the complex topology of the craniofacial model and the ambiguous relationship between a skull and the corresponding face. In this paper, we propose a novel approach for 3D craniofacial reconstruction by utilizing Conditional Generative Adversarial Networks (CGAN) based on craniofacial depth map. More specifically, we treat craniofacial reconstruction as a mapping problem from skull to face. We represent 3D cran- iofacial shapes with depth maps, which include most craniofacial features for identification purposes and are easy to generate and apply to neural networks. We designed an end-to-end neural networks model based on CGAN then trained the model with paired craniofacial data to automatically learn the complex nonlinear relationship between skull and face. By introducing body mass index classes(BMIC) into CGAN, we can realize objective reconstruction of 3D facial geometry according to its skull, which is a complicated 3D shape generation task with different topologies. Through comparative experiments, our method shows accuracy and verisimilitude in craniofacial reconstruction results.

This paper presents an example-guided facial reconstruction method for creating a 3D refined human face model from sparse landmarks, with a given example dataset. It is challenging to rapidly and accurately generate a high-precision 3D face model from raw scan data with a simple setup and processing. The main roadblock is that existing 3D face databases are far from adequate to describe the full variability of faces. To address these problems, we analyse the characteristics of examples from a relatively small sample set for more reliable reconstruction knowledge, as well as a new landmark marking method to simplify the description of human face shape. Principal component analysis is used to extract the feature patterns from samples and simplify data representation. Then the 3D face model and the landmarks are correlated via a mapping matrix. An effective mapping algorithm is devised to learn the transformation relation from landmarks to 3D face shapes. Compared with existing methods, the proposed method can generate a high-precision 3D face model from sparse landmarks more accurately. The application and extensive experimental evaluations on the Chinese craniofacial database and FaceWarehouse database show that our method can achieve high accuracy, effectiveness and robustness in 3D face reconstruction.

We present an automated treadmill featuring physiological-data-driven feedback-PhysioTreadmill, which allows its user to easily control running settings based on their physical condition and can also motivate them through real-time physiological computing. We developed a robust exercise intensity self-adaptive adjustment algorithm using physiological data processing to adjust the user's physiological state accurately. We also designed exergames with physiological-data-driven visual/audio feedback in PhysioTreadmill. With PhysioTreadmill, we can ideally increase exercise duration, and enhance exercise performance and safety. Two user studies involving 42 participants showed that PhysioTreadmill is user-friendly and can effectively extend users' training duration.

Abstract Curve extension is a useful tool in the computer‐aided design (CAD) community. A given B‐spline curve usually needs to be extended by another curve to reach one or more target points. In this work, we aim to enlarge the representation domain of the extending part to achieve the optimal extending result in the global solution space. Inspired by this, we have made three contributions. First, we use piecewise polynomial, that is, a nonuniform B‐spline, instead of one polynomial segment to extend the original curve. Compared to one polynomial segment, curves consisting of piecewise polynomial have stronger modeling ability and therefore expand the solution space of the problem. For extension to multiple target points, we are the first to directly give extension results based on all target points rather than extending to every target step by step. Third, we exploit the matrix representation of B‐splines to obtain an explicit solution for this extension problem. The detailed formula derivations and experimental results are provided to show the validity and effectiveness of our method.

Abstract In this article, we propose a novel 3D face modeling method which constructs a new 3D face model from a low‐dimensional feature space consisted of a large set of blend shapes based on the discrete shape space theory. The details of original face features are completely retained during the modeling process and a large number of new natural faces are constructed by several face samples. The optimization process of our method is independently decoupled for different facial attributes (identity, expression, and head pose), which improves the application flexibility and reduces the probability of it falling into a local optimal situation. The new facial data with new attributes are constructed based on the geodesic path search in discrete shape space with sufficient freedom and accuracy. In experiments and applications based on public databases (Helen, LFW, and CUFS), the modeling results show our method can provide high‐quality 3D face model, with enough freedom for face expression editing and natural facial expression animation from a small facial sample set.

The cover image is based on the Original Article Dynamic disk B-spline curves by Zhongke Wu et al., https://doi.org/10.1002/cav.1955.

Abstract A disk B‐spline curve (DBSC) is an extension of a B‐spline curve and is used to represent a two‐dimensional (2D) region. DBSC is a useful 2D geometric representation and is widely applied in the 2D art design area, such as computer calligraphy, 2D computer animation, and nonphotorealistic rendering. To enhance the flexibility of DBSC, in this article, we propose a physics‐based generalization of DBSC–dynamic DBSC (D‐DBSC), which extends the traditional DBSC in the time domain. We give the mathematical expression of D‐DBSC and prove its several mathematical properties. We derive the motion equations of D‐DBSC based on Lagrangian mechanics and investigate the motion equations when it is under linear geometric constraints. Last, a D‐DBSC physical simulation system based on finite difference method is presented.

We propose a novel framework for 3D facial similarity measurement and its application in facial organization. The construction of the framework is based on Kendall shape space theory. Kendall shape space is a quotient space that is constructed by shape features. In Kendall shape space, the shape features can be measured and is robust to similarity transformations. In our framework, a 3D face is represented by the facial feature landmarks model (FFLM), which can be regarded as the facial shape features. We utilize the geodesic in Kendall shape space to represent the FFLM similarity measurement, which can be regarded as the 3D facial similarity measurement. The FFLM similarity measurement is robust to facial expressions, head poses, and partial facial data. In our experiments, we compute the distance between different FFLMs in two public facial databases: FRGC2.0 and BosphorusDB. On average, we achieve a rank-one facial recognition rate of 98%. Based on the similarity results, we propose a method to construct the facial organization. The facial organization is a hierarchical structure that is achieved from the facial clustering by FFLM similarity measurement. Based on the facial organization, the performance of face searching in a large facial database can be improved obviously (about 400% improvement in experiments).

Segmenting the cerebral vessels precisely from the time-of-flight magnetic resonance angiography (TOF-MRA) images is important for the diagnosis and therapy of the cerebrovascular diseases. Since the complex structures of cerebral vessels, the current cerebrovascular segmentation algorithms based on statistical model have less accuracy for stenotic vessels and are quite time-consuming. In this paper, we propose a novel automatic cerebrovascular segmentation algorithm based on focused Multi-Gaussians (FMG) model and weighted 3D Markov Random Field. As far as our knowledge, this is the first time to adopt multi-Gaussians distributions as vascular model with the purpose of modeling the vascular tissue more accurately. Furthermore, the fitting range is narrowed to local region related to vessels in order to make the model focus on the vascular tissue and simplify the finite mixture model. To incorporate precise local character of images to the model, we design a new weighted 3D MRF by a weighted neighborhood system (W-NBS). Finally, the particle swarm optimization (PSO) algorithm of parameter estimation has been implemented parallelly based on GPUs and the execution speed was improved by about 70 times. The experimental results show that the algorithm can produce detailed segmentation results especially for stenotic vessels.

Flexible indoor scene synthesis is a popular topic in computer graphics and virtual reality research due to its wide-ranging applications in home design, games and automated robotics training. We propose a novel approach to automatic and flexible indoor scene synthesis using an energy-based method. We regard indoor scene synthesis as a multiple-object optimization problem with furniture location and orientation according to the user's intention, as a constraint on the energy of the optimization problem. Based on the relationship of objects, the embedded aesthetic criterion, the design criterion for proper placement and human movement in a scene, we design five energy functions, the overlap constraint, pairwise constraint, wall constraint, aisle constraint, angle constraint and penalty item, are proposed. We use a multi-object particle swarm intelligence optimization method with a Markov chain Monte Carlo algorithm to solve this optimization problem and obtain a Pareto-optimal solution. 3D gestures are used as the medium of interaction between the user and the system. Our method significantly enhances the existing weighted energy optimization method by allowing a joint optimization of various energy functions. The experiments confirm that all the energy functions can converge at the same time and that the proposed method obtains results superior to those of the weighted methods. The proposed method is general which can be used to obtain layouts for various kind of rooms with different furniture.

The 3D skull is a well preserved bone under the effect of fire, humidity, temperature changes, and it is a important biological characteristic in the fields of archaeology, forensic science and anthropology. In particular, measuring the 3D skull similarity is a challenging and meaningful task. 3D skulls are geometric models with multiple holes and complex topologies. It is difficult to correctly calculate the similarity between 3D skulls because the general 3D shape similarity measurement is sensitive to boundaries. In this paper, we provide an effective pipeline for measuring the 3D skull similarity by calculating the cosine distance between the harmonic wave kernel signature (HWKS) values of 3D skulls. Based on the wave kernel signature, the HWKS is a shape descriptor which is involved the Laplace-Beltrami operator that can effectively extract geometrical and topological information from the 3D skulls. And the HWKS simultaneously describes the local and global properties of a skull compared to the wave kernel signature. In addition, our method is more flexible, and can be generalized to other 3D shapes. Several experiments show our method achieves good results and can correctly calculate the similarity between 3D skulls.

We propose a skeleton tree based method for classifying and retrieving non-rigid shapes. Firstly, based on the extracted skeletons of a non-rigid shape and geodesic distance computation, the center point in skeleton is defined and detected. Then, a skeleton tree is constructed based on the connection between the center point and other discrete points in skeleton. After that, a correspondence between the skeleton tree and the area distribution of the non-rigid shape is established. The skeleton tree features are achieved. The advantages of our method can be summarized as follows: (1) Scale-Invariant; (2) Low computational complexity; (3) Automatic topology repair. The experimental results show that our method is more accurate than existing methods.

Abstract Team formation with realistic crowd simulation behavior is a challenge in computer graphics, multiagent control, and social simulation. In this study, we propose a framework of crowd formation via hierarchical planning, which includes cooperative‐task, coordinated‐behavior, and action‐control planning. In cooperative‐task planning, we improve the grid potential field to achieve global path planning for a team. In coordinated‐behavior planning, we propose a time–space table to arrange behavior scheduling for a movement. In action‐control planning, we combine the gaze‐movement angle model and fuzzy logic control to achieve agent action. Our method has several advantages. (1) The hierarchical architecture is guaranteed to match the human decision process from high to low intelligence. (2) The agent plans his behavior only with the local information of his neighbor; the global intelligence of the group emerges from these local interactions. (3) The time–space table fully utilizes three‐dimensional information. Our method is verified using crowds of various densities, from sparse to dense, employing quantitative performance measures. The approach is independent of the simulation model and can be extended to other crowd simulation tasks.

Facial expression editing in face sketch is an important and challenging problem in computer vision community as facial animation and modeling. For criminal investigation and portrait drawing, automatic expression editing tools for face sketch improve work efficiency obviously and reduce professional requirements for users. In this paper, we propose a novel method for facial expression editing in face sketch using shape space theory. The new facial expressions in the sketch images can be regenerated automatically. The method includes two components: 1) face sketch modeling; 2) expression editing. The face sketch modeling constructs 3D face sketch data from 3D facial database to match the 2D face sketch. Using facial landmarks, the "shape" of the face sketch is represented in shape space. The shape space is a manifold space which removes the rigid transform group. In shape space, the accurate 3D face sketch model is obtained which is consistent to the original 2D face sketch. For expression editing, we change the parameters of 3D face sketch model in the shape space to obtain new expressions. The expression transfer in 3D face sketch model can be mapped into the 2D face sketch. The advantages of our method are: full-automatic in modeling process; no requirements of drawing skills to user and friendly interaction; robustness to head poses and different scales. In experiments, we use the 3D facial database, FaceWareHouse, to construct the 3D face sketch model and use face sketch images from database: CUHK Face sketch Database (CUFS) to show the performance of expression editing. Experimental results demonstrate that our method can effectively edit facial expressions in face sketch with high consistency and fidelity.

Scattered data fitting is always a challenging problem in the fields of geometric modeling and computer aided design. As the skeleton based three-dimensional solid model representation, the Ball B-Spline Curve is suitable to fit the tubular scattered data points. We study the problem of fitting the scattered data points with Ball B-spline curves (BBSCs) and propose the corresponding fitting algorithm based on the Particle Swarm Optimization (PSO) algorithm. In this process, we face three critical and difficult sub problems: (1) parameterization of the data points, (2) determination of the knot vector and (3) calculation of the control radii. All of them are multidimensional and nonlinear, especially the calculation of the parametric values. The parallelism of the PSO algorithm provides a high optimization, which is more suitable for solving nonlinear, nondifferentiable and multi-modal optimization problems. So we use it to solve the scattered data fitting problem. The PSO is applied in three steps to solve them. Firstly, we determine the parametric values of the data points with PSO. Then we compute the knot vector based on the parametric values of the data points. At last, we get the radius function. The experiments on the shell surface, the crescent surface and the real-world models verify the accuracy and flexibility of the method. The research can be widely used in the computer aided design, animation and model analysis.

The analysis of cerebrovascular shape is important for the diagnose and pathologic identification. But as the limitation of the segmentation algorithm, the complete cerebrovascular volume data are difficult to obtain. So the triangle mesh of the vessel model generated for the medical images may appear many gaps. In the paper, we present a extension algorithm for Ball B-Spline curve with G2 continuity to repair the cerebrovascular structure from time-of-flight (TOF) magnetic resonance angiography (MRA) data. Ball B-Spline curve has its distinct advantages in representing a 3D tube like organs. A ball Bezier segment is used to construct the extending part and G2-continuity is applied to describe the smoothness at the joints. Fairness of the extending ball Bezier curve segment is achieved by minimizing energy objective functions for the center curve and the radius function separately. New control balls are computed by unclamping algorithm to represent the whole extended ball B-Spline curve. The experimental results demonstrate the effectiveness of our algorithm. The final results show that the proposed method provides good blending result, especially for those blood vessels of small size.

Chinese calligraphy art is of significant importance in Chinese traditional culture, and meanwhile, the way to carry it forward in our information era is a critical issue. Thus, aiming at making a progress of the problem mentioned above, we present a novel method of writing Chinese calligraphy on arbitrary surfaces (triangle mesh). In this paper, Gong Qi calligraphy (i.e. Qi fonts) is chosen as test samples in the reason that it is one of the most famous calligraphy in China for its liquid structure and concise strokes. This paper consists of following four steps. Firstly, each character is decomposed to strokes, and we use the dynamic balance of bouncing disks approach to achieve the strokes' centerlines and corresponding radii which will be applied in vectorizing the strokes of characters through Disk B-Spline Curves. Secondly, both a fast geodesic algorithm and an exponential map method are employed which the former is to calculate the geodesic distance between every two vertexes of the character mapped region, while the latter is to obtain the geodesic coordinates corresponding to every vertexes of the triangle meshes in 3D, namely the geodesic triangulation. Thirdly, 3D points coordinates on surfaces, correspond to vectored character in tangent plane, are acquired on the basis of geodesic triangulation, thereby the character is able to be written on the surfaces. At last, some experiments are accomplished to test and verify the accuracy and efficiency of our method.

With the development of computer techniques and computer graphics, computer aided design (CAD) technology has been applied widely in the textile printing industry. There are many good methods for simulating weft knitted fabric, however, no work on knitted fabric had been performed using ball B-spline curves. In this paper, we have proposed a novel algorithm based on ball B-spline curves and Hooke's Law for modelling weft knitted fabric in 3D. Ball B-spline curves are based on B-spline curves that use data balls instead of data points. By changing the position and the radius of balls of the ball B-spline curves, we can change the thickness and position of the yarn. The loop is the basic unit of knitted fabric, it requires 7 data points to be represented by a ball B-spline curve, and the model is notably fast. At the same time, the model maintains both its accuracy and the geometrical and topological features of the fabric. With VC++ and Open GL, we added texture and light to simulate different patterns of weft knitted fabric in 3D, including stockinette knit, garter knit, 2-2 rib knit, wing knit, heart knit and stripe knit. Because of the nested structure of knitted fabric, each data point of each loop has changes in a different way when a force is applied to the knitted fabric. The deformation and force on the knitted fabric is modelled using Hooke's Law, which results in a more realistic and faster simulation. We use the parameterization method, and the parameters, such as the radius of ball, the height of a loop, the number of courses, the number of wales and the magnitude of the force, are easy to change. This method is a new means of naturally building and simulating weft knitted fabric in a CAD system.

In the field of computer graphics and human simulation, hair simulation is one of the most challenging physics and rendering problem. This paper presents a curly hair modeling utilizing the Nelder-Mead method and being based on the ball B-Spline Curves (BBSCs). The ball B-Spline Curves (BBSCs) is used to reconstruct hair model and the Nelder-Mead method is for calculating the equilibrium shape of each hair. The main advantages of our method used in this experiment are: (1) We construct hair model for each individual hair. (2) It can provide a wide range of curly hair types with the BBSCs for its good properties that it is flexible for modifying, editing and deforming. (3) The method can obtain efficient curly hair type because of the fast calculation and easy implementation of Nelder-Mead method. The hypothesis in this paper is supported by several credible evidences and the model can be widely used in the similar systems (e.g. Fabrics, green fields).

We present an automatic statistical intensity-based approach to extract the 3D cerebrovascular structure from time-of flight (TOF) magnetic resonance angiography (MRA) data. We use the finite mixture model (FMM) to fit the intensity histogram of the brain image sequence, where the cerebral vascular structure is modeled by a Gaussian distribution function and the other low intensity tissues are modeled by Gaussian and Rayleigh distribution functions. To estimate the parameters of the FMM, we propose an improved particle swarm optimization (PSO) algorithm, which has a disturbing term in speeding updating the formula of PSO to ensure its convergence. We also use the ring shape topology of the particles neighborhood to improve the performance of the algorithm. Computational results on 34 test data show that the proposed method provides accurate segmentation, especially for those blood vessels of small sizes.

Surveillance means is a system that monitors the behavior, activities, or other changing information, usually it is used to recognize the people for the purpose of security issues in society. This paper aims to propose a novel approach based on sensor data acquired by an optical system for the purpose of human identification. Three joints of the human body, such as the hip, knee, and ankle joint have been selected by the amount of gait movement in this algorithm. By extracting suitable 3D static and dynamic joints feature from data. The method applies the PBC (Parametric Bézier Curve) technique on the extracted features in order to derive the strong correlation between joint movements. The curve control points are used to construct the triangles of each walking pose of human. The geometric function and statistical methods on the triangles are used here to compute the gait signature and analysis of this signature and find the maximum unique relationship among the human gait during the walk, and use it as to classify the human identification. The experimental results demonstrate that this method is more accurate and reliable.

Non-rigid 3D shape correspondence is a fundamental and challenging problem. Isometric correspondence is an important topic because of its wide applications. But it is a NP hard problem if you detect the mapping directly. In this paper, we propose a novel approach to find the correspondence between two (nearly) isometric shapes. Our method is based on the geodesic structure of the shape and minimum cost flow. Firstly, several pre-computed base vertices are initialized for embedding the shapes into Euclidian space, which is constructed by the geodesic distances. Then we construct a network flow with the points of the two shapes and another two virtual points, source point and sink point. The arcs of the network flow are the edges between each point on two shapes. And the L2distances in the k dimensional Euclidian embedding space are taken as the arc costs and a capacity value is added on each point in the above network flow. At last we solve the correspondence problem as a minimum cost max flow problem (MCFP) with shortest path faster algorithm (SPFA). Experiments show that our method is accurate and efficient.

The process of making skeleton for character animation is a long-winded task requiring manual tweaking. This paper presents a novel method to generate an automatic robust animated skeleton from 3D human geometric model. First, our method contracts the mesh by applying Laplacian-based mesh contractions with constraints. The mesh contraction process preserves the original topology and connectivity of the mesh model. The 1D curve-skeleton is extracted from contracted mesh by applying edge contraction. Second, an automatic hierarchical joint-based skeleton (armature) has been generated, using the refined extracted curve-skeleton obtained from input mesh. Third, 3D motion data of joints are retargeted on generated skeleton through joint mapping to evaluate the accuracy of the skeleton animation. The significance of our approach is to minimize the labor-intensive process of skeleton adjustments for character animation. An automatic generated skeleton can be directly used to mesh rigging, mesh skinning and retargeting to create satisfactory character animation. Finally, experiments have been carried out to generate a plausible skeleton from mesh and create animation of that skeleton.

Touch less interaction has received considerable attention in recent years with benefit of removing the burden of physical contact. To achieve mid-air interaction, several strategies are available. However, since most of these techniques directly map the 2D WIMP GUI to 3D user interface, they lead unnatural result. In this paper, interaction gestures and tools for exploring volume dataset are designed to perform the similar tasks in the real world. We mainly employ the idea of focus + context based on GPU volume ray casting by trapezoid-shaped transfer function when designing interaction tools. User studies are conducted to demonstrate the usability and intuitiveness of our method. The experimental results show a significant advantage in completion time after a short period of training.

In shape analysis, scaling factors have a great influence on the results of non-rigid shape retrieval and comparison. In order to eliminate the scale ambiguity in shape acquisition and other cases, a method with scale-invariant property is required for shape analysis. The mapping method previously proposed only preserves geodesic distances between pair wise points. In this paper, a Scale-invariant Heat Kernel Mapping (SIHKM) method is introduced, which bases on the Scale-invariant Heat Kernel (SIHK) that handles various types of 3D shapes with different kinds of scaling transformations. SIHK is the generalization of the Heat Kernel and related to the heat diffusion behavior on shape. By using the SIHK, we retrieve intrinsic information from the scaled shapes while ignoring the impact of their scaling. SIHKM method maintains the heat kernel between two corresponding points on the shape with scaling deformations, including scaling transformation only, isometric deformation and scaling, and local scaling on shapes. The proof of the theory and experiments are given in this work. The experiments are performed on the TOSCA dataset, which show that our proposed method achieves good robustness and effectiveness to scaled shape analysis.

Skull identification is an important subject for research in forensic medicine. Current research can be divided into two categories: 1) craniofacial superimposition and 2) craniofacial reconstruction. Both categories rely essentially on the accurate extraction and representation of the intrinsic relationship between the skull and face in terms of the morphology, which still remain unsolved. They have high uncertainty and a low identification capability. This paper proposes a novel skull identification method that matches an unknown skull with enrolled 3D faces, in which the mapping between the skull and face is obtained using canonical correlation analysis. Unlike existing techniques, this method needs no accurate relationship between the skull and face, and measures only the correlation between them. In order to measure the correlation more reliably and improve the identification capability of the correlation analysis model, a region fusion strategy is adopted. Experimental results validate the proposed method, and show that the region-based method can significantly boost the matching accuracy. The correct identification rate reaches 94% when using a CT data set. This paper can provide a theory support for research on craniofacial superimposition and craniofacial reconstruction.

Curve blending is an essential task in geometric modeling, while a ball B-spline curve (BBSC) has its advantages in representing freeform tubular objects. This paper proposes a blending algorithm for ball B-Spline curve with G2 continuity, which is used to describe the smoothness of the joint point. An original BBSC is extended smoothly to join another one, such that no additional blending curve is created and the two original curves are not changed. The shape of the extended curve is then determined by minimizing strain energy. The corresponding scalar function of the control balls is determined through applying G2-continuity conditions to the scalar function. In order to ensure the radii of the control balls are positive, we make a decision about the range of the G2-continuity parameter and then determine it by minimizing the strain energy in the affected area. The experiment results demonstrate our method for blending BBSC is effective. Moreover, some G2 blending results of the BBSC in simulating the tubular objects are given.

Curve extension is a useful function in CAD systems. Disk B-Spline curve has its distinct advantages in representing a 2D region. This paper presents an algorithm for extending the disk B-Spline curve. A disk Bezier segment is used to construct the extending part and G2-continuity can be used to describe the smoothness of the joint disk. Fairness of the extending disk Bezier segment is achieved by minimizing an energy objective function. New control disks are computed by unclamping algorithm to represent the whole extended disk B-Spline curve. The experimental results demonstrate the effectiveness of our method.

Curve extension is a useful function in shape modeling for cyber worlds, while a ball B-spline curve (BBSC) has its advantages in representing freeform tubular objects. In this paper, an extension algorithm for ball B-Spline curve with G2-continuity is investigated. We apply the extending method of B-Spline curves to the center curve of BBSC through generalizing a minimal strain energy method from 2D to 3D. And the initial value of G2-continuity parameter was selected by minimizing the approximate energy function which is a problem with O(1) time complexity. The corresponding scalar function of control balls is determined through applying G2-continuity condition to scalar function. In order to ensure the radii of the control balls are positive, we make a decision about the range of the G2-continuity parameter and then determine it by minimizing the strain energy in the affected area. Some experiments for comparing our method with other methods are given. The results show our method for extending BBSC is effective.

The self-organizing behavior of a group emerges from the interaction of many individuals. According to this characteristic, the agent-based simulation method is investigated to implement these autonomous fish to create group motion. Here simulating cluster motion, avoidance, and escape of the fish school, and efficient aggregate algorithms are investigated. Moreover, rendering efficiency is improved by taking the advantage of a 3D engine.

Abstract In this paper, we propose a framework for modeling lower‐level pedestrian navigational behaviors. We aim not only to generate realistic simulation results but also to make our framework flexible and extendible, and easy to use for model developers. A divide‐and‐conquer methodology is first adopted to divide the complex navigational behaviors into three levels, which allows us to focus on the intermediate level. We then propose a pattern‐based framework for modeling pedestrian navigational behavior at this level. In our framework, spatial‐temporal patterns are used to represent the situational perception, and a pattern‐matching mechanism is proposed to model the navigational choices of individual pedestrians. To demonstrate the effectiveness of our framework, a computational model is constructed to simulate pedestrian behaviors in a corridor with medium to relatively high density of pedestrians. Simulation results with this model are summarized in this paper. Copyright © 2010 John Wiley & Sons, Ltd.

In this paper we propose a new algorithm of face clustering on triangle meshes, we call it balanced hierarchical face clustering (BHFC for short). Given a triangle mesh model, the algorithm iteratively generates a binary tree of face clusters on it. Each cluster consists of a set of connected faces. At every iteration, two connected clusters are chosen according to these rules we define, and they are merged into a new cluster. For each iteration there are two steps. In the first step, a set of cluster pair candidates is determined. In the second step, a single pair in the candidate set is chosen to merge. After the iteration, a hierarchical structure of clusters is constructed. The hierarchical structure is balanced, which avoids extreme size clusters appearing in the clustered result.

Matching is a central problem in pattern recognition and computer vision, its applications includes object detection and tracking. HCMA (hierarchical chamfer matching) is a classical image matching algorithm, which utilizes the edge information to match the images robustly and the multi-resolution pyramid to accelerate the matching process. However, for images with cluttered background and high resolution, HCMA is relatively computationally expensive, which has impeded its success in practical applications, especially in real-time applications. In this paper, an improved hierarchical chamfer matching algorithm is proposed to reduce its computational cost without degrading its matching quality. According to the experimental results, the proposed improvements are able to save 75% ~ 95% of the computational time, without causing any false matching.

This paper proposes a new skeleton based parametric representation of freeform shell-like solid objects — Ball B-Spline Surfaces (BBSSs) and their fundamental properties and algorithms. BBSSs are generalizations of ball B-Spline curve from one parameter variable to two parameter variables. BBSSs directly define objects in B-Spline form, unlike a procedure method like sweeping. BBSSs describe not only every point inside 3D solid objects, but also provides their center surface (skeleton). So the representation is more flexible for modeling, manipulation and deformation.

This paper proposes a parametric solid representation of freeform tubular objects - Ball B-Spline Curves (BBSCs), which are skeleton based parametric solid model. Their fundamental properties, algorithms and modeling methods are investigated. BBSC directly defines objects in B-Spline function form (not a procedure method, like sweeping), that uses control ball instead of control point in B-Spline curve. BBSC describes not only every point inside 3D solid objects, but also provides its center curve in B-Spline form directly. So the representation is more flexible for modeling, manipulation and deformation.

Abstract Disk B‐spline curve (DBSC) is previously proposed for drawing and animation. To generate inbetweens, linear interpolation is applied between points evenly taken in parametric domain of two DBSCs without incorporating characteristics of shape or motion, which results in distortion and unrealistic motion in animation. In this paper, more information in keyframes is extracted and utilized in inbetween generation. Points with high curvature are computed and corresponded between strokes in interpolation, which preserves features of strokes in animation. In addition, global motion of a character or its various components is estimated and interpolated as well, which retains the shapes during the motion. By applying the information to interpolation, the distortion is eliminated and smoother sequence of animation is achieved. Copyright © 2006 John Wiley & Sons, Ltd.

Abstract This paper proposes a Hierarchical Region Matching (HRM) approach for computer‐assisted auto coloring. The region‐level analysis in traditional 2D animation is expanded into several component levels with a novel hierarchization method. With the hierarchy, various region matching algorithms can be applied from the first/highest to the last/lowest component level. HRM improves the matching accuracy and may deal with matching errors caused by occlusion, thus making the matching more robust, as verified by the results. Copyright © 2005 John Wiley & Sons, Ltd.