Adaptive binary tree for fast SVM multiclass classification

This paper presents an adaptive binary tree (ABT) to reduce the test computational complexity of multiclass support vector machine (SVM). It achieves a fast classification by: (1) reducing the number of binary SVMs for one classification by using separating planes of some binary SVMs to discriminate other binary problems; (2) selecting the binary SVMs with the fewest average number of support vectors (SVs). The average number of SVs is proposed to denote the computational complexity to exclude one class. Compared with five well-known methods, experiments on many benchmark data sets demonstrate our method can speed up the test phase while remain the high accuracy of SVMs.     

Boundary Detection in Particle‐based Fluids

This paper presents a novel method to detect free‐surfaces on particle‐based volume representation. In contrast to most particle‐based free‐surface detection methods, which perform the surface identification based on physical and geometrical properties derived from the underlying fluid flow simulation, the proposed approach only demands the spatial location of the particles to properly recognize surface particles, avoiding even the use of kernels. Boundary particles are identified through a Hidden Point Removal (HPR) operator used for visibility test. Our method is very simple, fast, easy to implement and robust to changes in the distribution of particles, even when facing large deformation of the free‐surface. A set of comparisons against state‐of‐the‐art boundary detection methods show the effectiveness of our approach. The good performance of our method is also attested in the context of fluid flow simulation involving free‐surface, mainly when using level‐sets for rendering purposes.     

Buoyancy Optimization for Computational Fabrication

This paper introduces a design and fabrication pipeline for creating floating forms. Our method optimizes for buoyant equilibrium and stability of complex 3D shapes, applying a voxel‐carving technique to control the mass distribution. The resulting objects achieve a desired floating pose defined by a user‐specified waterline height and orientation. In order to enlarge the feasible design space, we explore novel ways to load the interior of a design using prefabricated components and casting techniques. 3D printing is employed for high‐precision fabrication. For larger scale designs we introduce a method for stacking lasercut planar pieces to create 3D objects in a quick and economic manner. We demonstrate fabricated designs of complex shape in a variety of floating poses.     

Space‐Time Co‐Segmentation of Articulated Point Cloud Sequences

Consistent segmentation is to the center of many applications based on dynamic geometric data. Directly segmenting a raw 3D point cloud sequence is a challenging task due to the low data quality and large inter‐frame variation across the whole sequence. We propose a local‐to‐global approach to co‐segment point cloud sequences of articulated objects into near‐rigid moving parts. Our method starts from a per‐frame point clustering, derived from a robust voting‐based trajectory analysis. The local segments are then progressively propagated to the neighboring frames with a cut propagation operation, and further merged through all frames using a novel space‐time segment grouping technqiue, leading to a globally consistent and compact segmentation of the entire articulated point cloud sequence. Such progressive propagating and merging, in both space and time dimensions, makes our co‐segmentation algorithm especially robust in handling noise, occlusions and pose/view variations that are usually associated with raw scan data.     

A Hierarchical Approach for Regular Centroidal Voronoi Tessellations

In this paper, we consider Centroidal Voronoi Tessellations (CVTs) and study their regularity. CVTs are geometric structures that enable regular tessellations of geometric objects and are widely used in shape modelling and analysis. While several efficient iterative schemes, with defined local convergence properties, have been proposed to compute CVTs, little attention has been paid to the evaluation of the resulting cell decompositions. In this paper, we propose a regularity criterion that allows us to evaluate and compare CVTs independently of their sizes and of their cell numbers. This criterion allows us to compare CVTs on a common basis. It builds on earlier theoretical work showing that second moments of cells converge to a lower bound when optimizing CVTs. In addition to proposing a regularity criterion, this paper also considers computational strategies to determine regular CVTs. We introduce a hierarchical framework that propagates regularity over decomposition levels and hence provides CVTs with provably better regularities than existing methods. We illustrate these principles with a wide range of experiments on synthetic and real models.     

Pairwise Registration by Local Orientation Cues

Inspired by recent work on robust and fast computation of 3D Local Reference Frames (LRFs), we propose a novel pipeline for coarse registration of 3D point clouds. Key to the method are: (i) the observation that any two corresponding points endowed with an LRF provide a hypothesis on the rigid motion between two views, (ii) the intuition that feature points can be matched based solely on cues directly derived from the computation of the LRF, (iii) a feature detection approach relying on a saliency criterion which captures the ability to establish an LRF repeatably. Unlike related work in literature, we also propose a comprehensive experimental evaluation based on diverse kinds of data (such as those acquired by laser scanners, Kinect and stereo cameras) as well as on quantitative comparison with respect to other methods. We also address the issue of setting the many parameters that characterize coarse registration pipelines fairly and realistically. The experimental evaluation vouches that our method can handle effectively data acquired by different sensors and is remarkably fast.     

Advection‐Based Function Matching on Surfaces

A tangent vector field on a surface is the generator of a smooth family of maps from the surface to itself, known as the flow. Given a scalar function on the surface, it can be transported, or advected, by composing it with a vector field's flow. Such transport is exhibited by many physical phenomena, e.g., in fluid dynamics. In this paper, we are interested in the inverse problem: given source and target functions, compute a vector field whose flow advects the source to the target. We propose a method for addressing this problem, by minimizing an energy given by the advection constraint together with a regularizing term for the vector field. Our approach is inspired by a similar method in computational anatomy, known as LDDMM, yet leverages the recent framework of functional vector fields for discretizing the advection and the flow as operators on scalar functions. The latter allows us to efficiently generalize LDDMM to curved surfaces, without explicitly computing the flow lines of the vector field we are optimizing for. We show two approaches for the solution: using linear advection with multiple vector fields, and using non‐linear advection with a single vector field. We additionally derive an approximated gradient of the corresponding energy, which is based on a novel vector field transport operator. Finally, we demonstrate applications of our machinery to intrinsic symmetry analysis, function interpolation and map improvement.     

An Interactive Design System of Free‐Formed Bamboo‐Copters

We present an interactive design system for designing free‐formed bamboo‐copters, where novices can easily design free‐formed, even asymmetric bamboo‐copters that successfully fly. The designed bamboo‐copters can be fabricated using digital fabrication equipment, such as a laser cutter. Our system provides two useful functions for facilitating this design activity. First, it visualizes a simulated flight trajectory of the current bamboo‐copter design, which is updated in real time during the user's editing. Second, it provides an optimization function that automatically tweaks the current bamboo‐copter design such that the spin quality—how stably it spins—and the flight quality—how high and long it flies—are enhanced. To enable these functions, we present non‐trivial extensions over existing techniques for designing free‐formed model airplanes [ UKSI14 ], including a wing discretization method tailored to free‐formed bamboo‐copters and an optimization scheme for achieving stable bamboo‐copters considering both spin and flight qualities.     

Data‐Driven Bending Elasticity Design by Shell Thickness

We present a method to design the deformation behavior of 3D printed models by an interactive tool, where the variation of bending elasticity at different regions of a model is realized by a change in shell thickness. Given a soft material to be used in 3D printing, we propose an experimental setup to acquire the bending behavior of this material on tubes with different diameters and thicknesses. The relationship between shell thickness and bending elasticity is stored in an echo state network using the acquired dataset. With the help of the network, an interactive design tool is developed to generate non‐uniformly hollowed models to achieve desired bending behaviors. The effectiveness of this method is verified on models fabricated by different 3D printers by studying whether their physical deformation can match the designed target shape.     

Using hash tables to manage the time-storage complexity in a point location problem: Application to explicit model predictive control

The online computational burden of linear model predictive control (MPC) can be moved offline by using multi-parametric programming, so-called explicit MPC. The solution to the explicit MPC problem is a piecewise affine (PWA) state feedback function defined over a polyhedral subdivision of the set of feasible states. The online evaluation of such a control law needs to determine the polyhedral region in which the current state lies. This procedure is called point location; its computational complexity is challenging, and determines the minimum possible sampling time of the system. A new flexible algorithm is proposed which enables the designer to trade off between time and storage complexities. Utilizing the concept of hash tables and the associated hash functions, the proposed method solves an aggregated point location problem that overcomes prohibitive complexity growth with the number of polyhedral regions, while the storage–processing trade-off can be optimized via scaling parameters. The flexibility and power of this approach is supported by several numerical examples.