Online distance learning emerged as a prominent means of education during the pandemic and is expected to continue as a long-lasting trend, enabling access to top education resources without the constraints of physical distance. However, conferencing software predominantly used for synchronous online teaching and learning is not suitable or sufficient for young students and teachers. The learning experiences of these students heavily rely on hands-on activities and interactions with peers and teachers that are challenging to replicate. Additionally, teachers face difficulties in effectively monitoring student progress. To address these challenges, we propose a Synchronous Accessible Immersive Online Learning System (SAILS). It offers an immersive and interactive platform for young learners by integrating real-life school activities with a virtual learning environment. Using the system, teachers can easily organize classes, assess students' work. We evaluated the effectiveness of SAILS through a user study involving 40 young learners from a kindergarten and several primary schools, along with their teachers. The results demonstrated a strong preference for our system among the participants, highlighting its ability to provide a more immersive and engaging online learning experience.

Human pose estimation in videos has wide-ranging practical applications across various fields, many of which require fast inference on resource-scarce devices, necessitating the development of efficient and accurate algorithms. Previous works have demonstrated the feasibility of exploiting motion continuity to conduct pose estimation using sparsely sampled frames with transformer-based models. However, these methods only consider the temporal relation while neglecting spatial attention, and the complexity of dot product self-attention calculations in transformers are quadratically proportional to the embedding size. To address these limitations, we propose MixSynthFormer, a transformer encoder-like model with MLP-based mixed synthetic attention. By mixing synthesized spatial and temporal attentions, our model incorporates inter-joint and inter-frame importance and can accurately estimate human poses in an entire video sequence from sparsely sampled frames. Additionally, the flexible design of our model makes it versatile for other motion synthesis tasks. Our extensive experiments on 2D/3D pose estimation, body mesh recovery, and motion prediction validate the effectiveness and efficiency of MixSynthFormer. The code is available at https://github.com/ireneesun/MixSynthFormer.git

We introduce Point2Skeleton, an unsupervised method to learn skeletal representations from point clouds. Existing skeletonization methods are limited to tubular shapes and the stringent requirement of watertight input, while our method aims to produce more generalized skeletal representations for complex structures and handle point clouds. Our key idea is to use the insights of the medial axis transform (MAT) to capture the intrinsic geometric and topological natures of the original input points. We first predict a set of skeletal points by learning a geometric transformation, and then analyze the connectivity of the skeletal points to form skeletal mesh structures. Extensive evaluations and comparisons show our method has superior performance and robustness. The learned skeletal representation will benefit several unsupervised tasks for point clouds, such as surface reconstruction and segmentation.

The availability of commodity 3D extruder pen allows direct drawing of 3D wire sculptures for novice users, enabling many novel applications such as intuitive spatial intelligence development for school students. However, the lack of spatial and structural cues among individual pen strokes makes the 3D drawing process challenging, which often leads to highly distorted and even incomplete wire sculptures. We present a mixed reality system, called `WireDraw', to immersively guide the 3D drawing for easy wire sculpturing. The system design is based on novel 3D drawing principles and the subsequent optimization, making the stroke sequence of the wire model drawable and easy to draw. On-the-fly edits on unsatisfactory strokes are also allowed for creative design. We demonstrate the effectiveness of our system by testing on a variety of wire models and a user study. The results show that the visual guidance provided by our system is extremely helpful for drawing high-quality wire sculptures.

The medial axis transform has long been known as an intrinsic shape representation supporting a variety of shape analysis and synthesis tasks. However, for a given shape, it is hard to obtain its faithful, concise and stable medial axis, which hinders the application of the medial axis. In this paper, we introduce the medial mesh, a new discrete representation of the medial axis. A medial mesh is a 2D simplicial complex coupled with a radius function that provides a piecewise linear approximation to the medial axis. We further present an effective algorithm for computing a concise and stable medial mesh for a given shape. Our algorithm is quantitatively driven by a shape approximation error metric, and progressively simplifies an initial medial mesh by iteratively contracting edges until the approximation error reaches a predefined threshold. We further demonstrate the superior efficiency and accuracy of our method over existing methods for medial axis simplification.

In this paper, we propose a novel edge prior for image interpolation which assumes that the variation of image intensity away from an edge is locally similar along the edge. Based on this edge prior, our method first approximates the gradient of the HR image which is then refined by diffusion. The unknown HR pixels are estimated by a weighted average of their neighbouring LR samples, with the weights being determined with respect to the gradient. This new approach performs significantly better than several representative edge-directed image interpolation methods in terms of PSNR and SSIM, as well as subjective visual quality in most of our test cases. Annoying artifacts (such as blurring, jaggies, ringing, etc.) are also greatly suppressed.

Abstract Shape analysis finds many important applications in shape understanding, matching and retrieval. Among the various shape analysis methods, spectral shape analysis aims to study the spectrum of the Laplace–Beltrami operator of some well‐designed shape‐dependent equations and obtain a spectral shape descriptor that can in turn be used for shape analysis purposes. The success of such approaches depends greatly on the discriminating power of a shape descriptor. On the other hand, the medial axis of a shape is widely known for its complete shape representation. It is sensitive to small perturbation of the boundary of a shape which often poses difficulty in its effective use for shape analysis. In this paper, we propose a new spectral shape descriptor, called the medial axis spectrum for 2D shapes, which directly applies spectral analysis to the medial axes of the shapes. We extend the Laplace–Beltrami operator onto the medial axis, and take the solution to an extended Laplacian eigenvalue problem defined on the axis as the medial axis spectrum. The medial axis spectrum is robust in the presence of shape boundary noise, and is invariant under rigid transformations, uniform scaling and isometry of the medial axis. We demonstrate these benefits of such a medial axis spectrum representation through extensive experiments. The medial axis spectrum is further used for 2D shape retrieval, and its superiority over previous work is shown by comparison.

We present a new method for modeling discrete constant mean curvature (CMC) surfaces, which arise frequently in nature and are highly demanded in architecture and other engineering applications. Our method is based on a novel use of the CVT ( centroidal Voronoi tessellation ) optimization framework. We devise a CVT-CMC energy function defined as a combination of an extended CVT energy and a volume functional. We show that minimizing the CVT-CMC energy is asymptotically equivalent to minimizing mesh surface area with a fixed volume, thus defining a discrete CMC surface. The CVT term in the energy function ensures high mesh quality throughout the evolution of a CMC surface in an interactive design process for form finding. Our method is capable of modeling CMC surfaces with fixed or free boundaries and is robust with respect to input mesh quality and topology changes. Experiments show that the new method generates discrete CMC surfaces of improved mesh quality over existing methods.

Blue noise point sampling is one of the core algorithms in computer graphics. In this paper, we present a new and versatile variational framework for generating point distributions with high-quality blue noise characteristics while precisely adapting to given density functions. Different from previous approaches based on discrete settings of capacity-constrained Voronoi tessellation, we cast the blue noise sampling generation as a variational problem with continuous settings. Based on an accurate evaluation of the gradient of an energy function, an efficient optimization is developed which delivers significantly faster performance than the previous optimization-based methods. Our framework can easily be extended to generating blue noise point samples on manifold surfaces and for multi-class sampling. The optimization formulation also allows us to naturally deal with dynamic domains, such as deformable surfaces, and to yield blue noise samplings with temporal coherence. We present experimental results to validate the efficacy of our variational framework. Finally, we show a variety of applications of the proposed methods, including nonphotorealistic image stippling, color stippling, and blue noise sampling on deformable surfaces.

Maximal clearance is an important property that is highly desirable in multi-agent motion planning. However, it is also inherently difficult to attain. We propose a novel approach to achieve maximal clearance by exploiting the ability of evenly distributing a set of points by a centroidal Voronoi tessellation (CVT). We adapt the CVT framework to multi agent motion planning by adding an extra time dimension and optimize the trajectories of the agents in the augmented domain. As an optimization framework, our method can work naturally on complex regions. We demonstrate the effectiveness of our algorithm in achieving maximal clearance in motion planning with some examples.

We present an accurate and efficient algorithm for continuous collision detection between two moving ellipsoids under rational Euclidean or affine motion. We start with a highly optimized implementation of interference testing between two stationary ellipsoids based on an algebraic condition described in terms of the signs of roots of the characteristic equation of two ellipsoids. Then we derive a time-dependent characteristic equation for two moving ellipsoids, which enables us to develop an efficient algorithm for computing the time intervals in which two moving ellipsoids collide. The effectiveness of our approach is demonstrated with several practical examples.

Abstract We propose a variational approach to computing an optimal segmentation of a 3D shape for computing a union of tight bounding volumes. Based on an affine invariant measure of e‐tightness, the resemblance to ellipsoid, a novel functional is formulated that governs an optimization process to obtain a partition with multiple components. Refinement of segmentation is driven by application‐specific error measures, so that the final bounding volume meets pre‐specified user requirement. We present examples to demonstrate the effectiveness of our method and show that it works well for computing ellipsoidal bounding volumes as well as oriented bounding boxes.

This paper presents a simple yet precise and efficient algorithm for collision prediction of two oriented bounding boxes under univariate (piecewise) rational motion. We present an analytic solution to the problem of finding the time of collision and the feature involved, or declaring that no collision should occur. Our solution can be applied to boxes of any size, under arbitrary rational rigid motion. The algorithm is based on the efficient examination of the Minkowski sum (MS) of the two boxes, using a spherical Gauss map dual representation, and a precise extraction of the collision time, if any, as a solution to a set of rational equations that are automatically derived

Collision detection and avoidance are important in robotics. Compared with commonly used circular disks, elliptic disks provide a more compact shape representation for robots or other vehicles confined to move in the plane. Furthermore, elliptic disks allow a simpler analytic representation than rectangular boxes, which makes it easier to perform continuous collision detection (CCD). We shall present a fast and accurate method for CCD between two moving elliptic disks, which avoids any need to sample the time domain of the motion, thus avoiding the possibility of missing collisions between time samples. Based on some new algebraic conditions on the separation of two ellipses, we reduce collision detection for two moving ellipses to the problem of detecting real roots of a univariate equation, which is the discriminant of the characteristic polynomial of the two ellipses. Several techniques are investigated for robust and accurate processing of this univariate equation for two classes of commonly used motions: planar cycloidal motions and planar rational motions. Experimental results demonstrate the efficiency, accuracy, and robustness of our method.

The study of the microstructure in cancellous bone is important in osteoporosis research. In this paper, we focus in the extraction of rod-like trabeculae in cancellous bone, whose topological and geometrical properties are known to be strongly related to bone strength. Three dimensional (3D) cancellous bone volume data obtained from micro computed tomography (micro-CT) scans is used in our analysis. Because of the complexity of the cancellous bone microstructure, the mere use of existing 3D digital topology methods is unable to yield satisfactory results for trabeculae extraction. We devise several enhancements which are specific to the identification of rod-like trabeculae. Experimental results show that the accuracy of trabeculae extraction is greatly improved. This application study may help clinicians to solve problems in future.

In this paper, we describe an exact method for detecting collision between two moving ellipsoids under pre-specified rational motions. Our method is based on an algebraic condition that determines the separation status of two static ellipsoids - the condition itself is described by the signs of roots of the characteristic equation of the two ellipsoids. To deal with moving ellipsoids, we derive a bivariate function whose zero-set possesses a special topological structure. By analyzing the zero-set of this function, we are able to tell whether or not two moving ellipsoids under pre-specified rational motions are collision-free; and if not, we can determine the intervals in which they overlap.

Volume visualization is an essential part of many computer-assisted medical applications. While general-purpose commercial visualization software can provide common functions for visualizing three-dimensional (3D) medical data, there are many occasions where specific requirements cannot be fulfilled by such software. In orthopaedic surgery involving screw insertion, surgeons must consider not only the surface topology but also the bone mineral density (BMD) distribution to ensure a high success rate of the operation. In this paper we present a new system, called VISBONE, for visualizing the 3D BMD distribution within a bone. Design issues and specific considerations required by this application are discussed.