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.     

Non‐Rigid Puzzles

Shape correspondence is a fundamental problem in computer graphics and vision, with applications in various problems including animation, texture mapping, robotic vision, medical imaging, archaeology and many more. In settings where the shapes are allowed to undergo non‐rigid deformations and only partial views are available, the problem becomes very challenging. To this end, we present a non‐rigid multi‐part shape matching algorithm. We assume to be given a reference shape and its multiple parts undergoing a non‐rigid deformation. Each of these query parts can be additionally contaminated by clutter, may overlap with other parts, and there might be missing parts or redundant ones. Our method simultaneously solves for the segmentation of the reference model, and for a dense correspondence to (subsets of) the parts. Experimental results on synthetic as well as real scans demonstrate the effectiveness of our method in dealing with this challenging matching scenario.     

Adaptive Bas‐relief Generation from 3D Object under Illumination

Bas‐relief is designed to provide 3D perception for the viewers under illumination. For the problem of bas‐relief generation from 3D object, most existing methods ignore the influence of illumination on bas‐relief appearance. In this paper, we propose a novel method that adaptively generate bas‐reliefs with respect to illumination conditions. Given a 3D object and its target appearance, our method finds an adaptive surface that preserves the appearance of the input. We validate our approach through a variety of applications. Experimental results indicate that the proposed approach is effective in producing bas‐reliefs with desired appearance under illumination.     

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.     

梯度引导的高阶几何彩色图像去噪模型

目的 为了消除低阶彩色图像去噪模型产生视觉上不希望得到的"阶梯效应"并提高去噪过程中的边缘保持效果,提出一种黎曼几何驱动的高阶彩色图像去噪模型,并在扩散中使用一阶梯度信息引导高阶信息驱动的扩散,以改善去噪过程中的边界探测和保持能力。方法 在黎曼几何框架下,对低阶彩色图像去噪模型进行分析,并由面积微元出发得到对应的二阶微分形式,利用二阶导数矩阵的Frobenius范数构造高阶彩色图像变分能量泛函,由此得到一个彩色图像去噪的高阶扩散模型。为在扩散中保持边界,使用高斯卷积后的一阶梯度信息引导高阶扩散,得到一个多通道耦合的高阶非线性彩色图像去噪模型。分析表明,该模型在扩散时兼顾了单通道和多通道、低阶和高阶等多种信息之间的关系进行耦合去噪。结果 在实验中对不同噪声水平下的1维彩色信号、合成彩色图像和标准彩色测试图像进行去噪,并使用峰值信噪比（PSNR）与结构相似性（SSIM）作为客观评价指标,将本文结果与相关彩色图像去噪扩散模型的结果进行对比。在不同噪声水平下本文模型去噪结果的平均PSNR与相关模型相比提高了2.33%,平均SSIM提高了0.4%。结论 本文模型能够有效去除彩色图像中不同噪声水平的高斯白噪声,能较好消除视觉上的"阶梯效应",得到分片线性光滑的彩色图像,同时还能够较好保持图像边界信息。     

A Condition Number for Non‐Rigid Shape Matching

Despite the large amount of work devoted in recent years to the problem of non‐rigid shape matching, practical methods that can successfully be used for arbitrary pairs of shapes remain elusive. In this paper, we study the hardness of the problem of shape matching, and introduce the notion of the shape condition number, which captures the intuition that some shapes are inherently more difficult to match against than others. In particular, we make a connection between the symmetry of a given shape and the stability of any method used to match it while optimizing a given distortion measure. We analyze two commonly used classes of methods in deformable shape matching, and show that the stability of both types of techniques can be captured by the appropriate notion of a condition number. We also provide a practical way to estimate the shape condition number and show how it can be used to guide the selection of landmark correspondences between shapes. Thus we shed some light on the reasons why general shape matching remains difficult and provide a way to detect and mitigate such difficulties in practice.     

Discovery of Intrinsic Primitives on Triangle Meshes

The discovery of meaningful parts of a shape is required for many geometry processing applications, such as parameterization, shape correspondence, and animation. It is natural to consider primitives such as spheres, cylinders and cones as the building blocks of shapes, and thus to discover parts by fitting such primitives to a given surface. This approach, however, will break down if primitive parts have undergone almost‐isometric deformations, as is the case, for example, for articulated human models. We suggest that parts can be discovered instead by finding intrinsic primitives, which we define as parts that posses an approximate intrinsic symmetry. We employ the recently‐developed method of computing discrete approximate Killing vector fields (AKVFs) to discover intrinsic primitives by investigating the relationship between the AKVFs of a composite object and the AKVFs of its parts. We show how to leverage this relationship with a standard clustering method to extract k intrinsic primitives and remaining asymmetric parts of a shape for a given k. We demonstrate the value of this approach for identifying the prominent symmetry generators of the parts of a given shape. Additionally, we show how our method can be modified slightly to segment an entire surface without marking asymmetric connecting regions and compare this approach to state‐of‐the‐art methods using the Princeton Segmentation Benchmark.     

Global Structure Optimization of Quadrilateral Meshes

We introduce a fully automatic algorithm which optimizes the high‐level structure of a given quadrilateral mesh to achieve a coarser quadrangular base complex. Such a topological optimization is highly desirable, since state‐of‐the‐art quadrangulation techniques lead to meshes which have an appropriate singularity distribution and an anisotropic element alignment, but usually they are still far away from the high‐level structure which is typical for carefully designed meshes manually created by specialists and used e.g. in animation or simulation. In this paper we show that the quality of the high‐level structure is negatively affected by helical configurations within the quadrilateral mesh. Consequently we present an algorithm which detects helices and is able to remove most of them by applying a novel grid preserving simplification operator (GP‐operator) which is guaranteed to maintain an all‐quadrilateral mesh. Additionally it preserves the given singularity distribution and in particular does not introduce new singularities. For each helix we construct a directed graph in which cycles through the start vertex encode operations to remove the corresponding helix. Therefore a simple graph search algorithm can be performed iteratively to remove as many helices as possible and thus improve the high‐level structure in a greedy fashion. We demonstrate the usefulness of our automatic structure optimization technique by showing several examples with varying complexity.