Given a collection of points in $\mathbb {R}^{3}$R3, KD-Tree and R-Tree are well-known nearest neighbor search (NNS) algorithms that rely on spatial partitioning and indexing techniques. However, when the query point is far from the data points or the data points inherently represent a 2-manifold surface, their query performance may degrade. To address this, we propose a novel dynamic programming technique that precomputes a Directed Acyclic Graph (DAG) to encode the proximity structure between data points. More specifically, the DAG captures how the proximity structure evolves during the incremental construction of the Voronoi diagram of the data points. Experimental results demonstrate that our method achieves a speed increase of 1-10x. Furthermore, our algorithm demonstrates significant practical value in diverse applications. We validated its effectiveness through extensive testing in four key applications: Point-to-Mesh Distance Queries, Iterative Closest Point (ICP) Registration, Density Peak Clustering, and Point-to-Segments Distance Queries. A particularly notable feature of our approach is its unique ability to efficiently identify the nearest neighbor among the first $k$k points in the point cloud, a capability that enables substantial acceleration in low-dimensional applications like Density Peak Clustering. As a natural extension of our incremental construction process, our method can also be readily adapted for farthest-point sampling tasks. These experimental results across multiple domains underscore the broad applicability and practical importance of our approach.

Anomaly detection plays a vital role in monitoring industrial processes. Despite the extensive development of deep anomaly detection approaches, many assume uniform sampling rates for process variables, yet multirate phenomena are common in practice. The resultant large-scale missing data and varying dynamics of variables with different sampling rates pose a challenge to conventional anomaly detection methods. To this end, this paper developed a SAmpling-Rate-aware sequential Knowledge trAnsfer (SARKA) model for detecting the anomalies in multirate industrial processes. First, the raw multirate dataset is chunked into multiple data blocks, such that samples in each block correspond to a specific sampling rate and can be more readily processed by deep neural networks. Then, a Sampling-rate aware Slow Variational Auto-Encoder (S2VAE) model is developed, in which a sampling-rate-aware slowness principle is devised and integrated to enable both data block- and instance-wise personalized dynamic features characterization. Besides, to alleviate the scarce sample problem in the low-sampling-rate data block due to the multirate phenomena, a Sequential Knowledge Transfer (SKT) strategy is devised to convey the knowledge from the high-rate data to facilitate low-rate data modeling and improve the overall monitoring performance. Experimental results from a real-world coal mill in a thermal power plant multirate process demonstrate the effectiveness of the proposed method.Note to Practitioners—Due to the challenges resulting from large-scale missing data and complex varying dynamics, multirate process anomaly detection is a crucial task in modern industries. To tackle the challenge, this paper presents SARKA, which consists of two modules, i.e., S2VAE and SKT. Among them, S2VAE serves as the base model, which integrates a novel devised slowness principle under the probabilistic framework for improved sampling-rate-aware dynamic features characterization. Besides, SKT is elaborated to bridge the multiple S2VAE base models by conveying the modeling knowledge from those high-rate data to low-rate data, as the amount of the low-rate data is generally scarce to train a valid base model. Therefore, the base model can sufficiently capture both the static and dynamic features of the multirate process, and the SKT further enhances the modeling of the low-rate data, yielding improved performance on the overall multirate process.

In this paper, we propose an approximate Voronoi base domain method to address constrained texture mapping problem. In particular, we generate approximate Voronoi base domains on the input texture image plane and planar embedding of mesh surface. Then, we propose to leverage the triangulations of constraint points on both sides, and yield the same topology for the two approximate Voronoi base domains. Based on the equivalent topology, we are able to employ generalized barycentric coordinates between pairwise Voronoi cells of the two approximate Voronoi base domains. The proposed method is highly efficient, and it allows to edit constraints in real time. Experimental results show the improved effectiveness and robustness of the proposed method for constraint texture mapping.

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 Updating a Delaunay triangulation when data points are slightly moved is the bottleneck of computation time in variational methods for mesh generation and remeshing. Utilizing the connectivity coherence between two consecutive Delaunay triangulations for computation speedup is the key to solving this problem. Our contribution is an effective filtering technique that confirms most bi‐cells whose Delaunay connectivities remain unchanged after the points are perturbed. Based on bi‐cell flipping, we present an efficient algorithm for updating two‐dimensional and three‐dimensional Delaunay triangulations of dynamic point sets. Experimental results show that our algorithm outperforms previous methods.

We present new results on classifying the morphology of the nonsingular intersection curve of two quadrics by studying the roots of the characteristic equation, or the discriminant, of the pencil spanned by the two quadrics. The morphology of a nonsingular algebraic curve means the structural (or topological) information about the curve, such as the number of disjoint connected components of the curve in P/spl Ropf//sup 3/ (the 3D real projective space), and whether a particular component is a compact set in any affine realization of P/spl Ropf//sup 3/. For example, we show that two quadrics intersect along a nonsingular space quartic curve in P/spl Ropf//sup 3/ with one connected component if and only if their characteristic equation has two distinct real roots and a pair of complex conjugate roots. Since the number of the real roots of the characteristic equation can be counted robustly with exact arithmetic, our results can be used to obtain structural information reliably before computing the parameterization of the intersection curve; thus errors in the subsequent computation that is most likely done using floating point arithmetic will not lead to erroneous topological classification of the intersection curve. The key technique used to prove our results is to reduce two quadrics into simple forms using a projective transformation, a technique equivalent to the simultaneous block diagonalization of two real symmetric matrices, a topic that has been studied in matrix algebra.

This paper discusses the problem of constructing C 2 quartic spline surface interpolation. Decreasing the continuity of the quartic spline to C 2 offers additional freedom degrees that can be used to adjust the precision and the shape of the interpolation surface. An approach to determining the freedom degrees is given, the continuity equations for constructing C 2 quartic spline curve are discussed, and a new method for constructing C 2 quartic spline surface is presented. The advantages of the new method are that the equations that the surface has to satisfy are strictly row diagonally dominant, and the discontinuous points of the surface are at the given data points. The constructed surface has the precision of quartic polynomial. The comparison of the interpolation precision of the new method with cubic and quartic spline methods is included.