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This paper describes a fast algorithm for scattered data interpolation and approximation. Multilevel B-splines are introduced to compute a C 2-continuous surface through a set of irregularly spaced points. The algorithm makes use of a coarse-tofine hierarchy of control lattices to generate a sequence of bicubic B-spline functions whose sum approaches the desired interpolation function. Large performance gains are realized by using B-spline refinement to reduce the sum of these functions into one equivalent B-spline function. Experimental results demonstrate that high-fidelity reconstruction is possible from a selected set of sparse and irregular samples.

This paper presents a technique for adapting existing motion of a human-like character to have the desired features that are specified by a set of constraints. This problem can be typically formulated as a spacetime constraint problem. Our approach combines a hierarchical curve fitting technique with a new inverse kinematics solver. Using the kinematics solver, we can adjust the configuration of an articulated figure to meet the constraints in each frame. Through the fitting technique, the motion displacement of every joint at each constrained frame is interpolated and thus smoothly propagated to frames. We are able to adaptively add motion details to satisfy the constraints within a specified tolerance by adopting a multilevel Bspline representation which also provides a speedup for the interpolation. The performance of our system is further enhanced by the new inverse kinematics solver. We present a closed-form solution to compute the joint angles of a limb linkage. This analytical method greatly reduces the burden of a numerical optimization to find the solutions for full degrees of freedom of a human-like articulated figure. We demonstrate that the technique can be used for retargetting a motion to compensate for geometric variations caused by both characters and environments. Furthermore, we can also use this technique for directly manipulating a motion clip through a graphical interface.

We report high-performance flexible nanogenerators (NGs) based on a composite thin film, composed of hemispherically aggregated BaTiO3 nanoparticles (NPs) and poly(vinylidene fluoride-co-hexafluoropropene) P(VDF-HFP). The hemispherical BTO-P(VDF-HFP) clusters were realized by a solvent evaporation method, which greatly enhanced piezoelectric power generation. The flexible NGs exhibit high electrical output up to ∼75 V and ∼15 μA at the applied force normal to the surface, indicating the important role of hemispherical BTO clusters. Besides, the durability and reproducibility of the NGs were tested by cyclic measurement under bending stage, generating the output of ∼5 V and ∼750 nA. The approach we introduce here is simple, cost-effective, and well-suited for large-scale high-performance flexible NG fabrication.

Computer puppetry maps the movements of a performer to an animated character in real-time. In this article, we provide a comprehensive solution to the problem of transferring the observations of the motion capture sensors to an animated character whose size and proportion may be different from the performer's. Our goal is to map as many of the important aspects of the motion to the target character as possible, while meeting the online, real-time demands of computer puppetry. We adopt a Kalman filter scheme that addresses motion capture noise issues in this setting. We provide the notion of dynamic importance of an end-effector that allows us to determine what aspects of the performance must be kept in the resulting motion. We introduce a novel inverse kinematics solver that realizes these important aspects within tight real-time constraints. Our approach is demonstrated by its application to broadcast television performances.

Patterns of brain atrophy measured by magnetic resonance structural imaging have been utilized as significant biomarkers for diagnosis of Alzheimer’s disease (AD). However, brain atrophy is variable across patients and is non-specific for AD in general. Thus, automatic methods for AD classification require a large number of structural data due to complex and variable patterns of brain atrophy. In this paper, we propose an incremental method for AD classification using cortical thickness data. We represent the cortical thickness data of a subject in terms of their spatial frequency components, employing the manifold harmonic transform. The basis functions for this transform are obtained from the eigenfunctions of the Laplace-Beltrami operator, which are dependent only on the geometry of a cortical surface but not on the cortical thickness defined on it. This facilitates individual subject classification based on incremental learning. In general, methods based on region-wise features poorly reflect the detailed spatial variation of cortical thickness, and those based on vertex-wise features are sensitive to noise. Adopting a vertex-wise cortical thickness representation, our method can still achieve robustness to noise by filtering out high frequency components of the cortical thickness data while reflecting their spatial variation. This compromise leads to high accuracy in AD classification. We utilized MR volumes provided by Alzheimer’s Disease Neuroimaging Initiative (ADNI) to validate the performance of the method. Our method discriminated AD patients from Healthy Control (HC) subjects with 82% sensitivity and 93% specificity. It also discriminated Mild Cognitive Impairment (MCI) patients, who converted to AD within 18 month, from non-converted MCI subjects with 63% sensitivity and 76% specificity. Moreover, it showed that the entorhinal cortex was the most discriminative region for classification, which is consistent with previous pathological findings. In comparison with other classification methods, our method demonstrated high classification performance in the both categories, which supports the discriminative power of our method in both AD diagnosis and AD prediction.

This paper proposes a new class of unit quaternion curves in SO ( 3 ) . A general method is developed that transforms a curve in R 3 (defined as a weighted sum of basis functions) into its unit quaternion analogue in SO ( 3 ) . Applying the method to well-known spline curves (such as Bézier, Hermite, and B-spline curves), we are able to construct various unit quaternion curves which share many important differential properties with their original curves.Many of our naive common beliefs in geometry break down even in the simple non-Euclidean space S 3 or SO ( 3 ) . For example, the de Casteljau type construction of cubic B-spline quaternion curves does not preserve C 2 -continuity [10]. Through the use of decomposition into simple primitive quaternion curves, our quaternion curves preserve most of the algebraic and differential properties of the original spline curves.

CH3NH3PbI3(MAPbI3) perovskite thin films were applied for piezoelectric generators under various applied pressures, poling field conditions, and switching polarity test.