Gap Processing for Adaptive Maximal Poisson-Disk Sampling

In this paper, we study the generation of maximal Poisson-disk sets with varying radii. First, we present a geometric analysis of gaps in such disk sets. This analysis is the basis for maximal and adaptive sampling in Euclidean space and on manifolds. Second, we propose efficient algorithms and data structures to detect gaps and update gaps when disks are inserted, deleted, moved, or have their radius changed. We build on the concepts of the regular triangulation and the power diagram. Third, we will show how our analysis can make a contribution to the state-of-the-art in surface remeshing.Comment: 16 pages. ACM Transactions on Graphics, 201

Practical Distance Functions for Path-Planning in Planar Domains

Path planning is an important problem in robotics. One way to plan a path between two points $x,y$ within a (not necessarily simply-connected) planar domain $\Omega$, is to define a non-negative distance function $d(x,y)$ on $\Omega\times\Omega$ such that following the (descending) gradient of this distance function traces such a path. This presents two equally important challenges: A mathematical challenge -- to define $d$ such that $d(x,y)$ has a single minimum for any fixed $y$ (and this is when $x=y$), since a local minimum is in effect a "dead end", A computational challenge -- to define $d$ such that it may be computed efficiently. In this paper, given a description of $\Omega$, we show how to assign coordinates to each point of $\Omega$ and define a family of distance functions between points using these coordinates, such that both the mathematical and the computational challenges are met. This is done using the concepts of \emph{harmonic measure} and \emph{$f$-divergences}. In practice, path planning is done on a discrete network defined on a finite set of \emph{sites} sampled from $\Omega$, so any method that works well on the continuous domain must be adapted so that it still works well on the discrete domain. Given a set of sites sampled from $\Omega$, we show how to define a network connecting these sites such that a \emph{greedy routing} algorithm (which is the discrete equivalent of continuous gradient descent) based on the distance function mentioned above is guaranteed to generate a path in the network between any two such sites. In many cases, this network is close to a (desirable) planar graph, especially if the set of sites is dense

Image Sampling with Quasicrystals

We investigate the use of quasicrystals in image sampling. Quasicrystals produce space-filling, non-periodic point sets that are uniformly discrete and relatively dense, thereby ensuring the sample sites are evenly spread out throughout the sampled image. Their self-similar structure can be attractive for creating sampling patterns endowed with a decorative symmetry. We present a brief general overview of the algebraic theory of cut-and-project quasicrystals based on the geometry of the golden ratio. To assess the practical utility of quasicrystal sampling, we evaluate the visual effects of a variety of non-adaptive image sampling strategies on photorealistic image reconstruction and non-photorealistic image rendering used in multiresolution image representations. For computer visualization of point sets used in image sampling, we introduce a mosaic rendering technique.Comment: For a full resolution version of this paper, along with supplementary materials, please visit at http://www.Eyemaginary.com/Portfolio/Publications.htm

Active Image-based Modeling with a Toy Drone

Image-based modeling techniques can now generate photo-realistic 3D models from images. But it is up to users to provide high quality images with good coverage and view overlap, which makes the data capturing process tedious and time consuming. We seek to automate data capturing for image-based modeling. The core of our system is an iterative linear method to solve the multi-view stereo (MVS) problem quickly and plan the Next-Best-View (NBV) effectively. Our fast MVS algorithm enables online model reconstruction and quality assessment to determine the NBVs on the fly. We test our system with a toy unmanned aerial vehicle (UAV) in simulated, indoor and outdoor experiments. Results show that our system improves the efficiency of data acquisition and ensures the completeness of the final model.Comment: To be published on International Conference on Robotics and Automation 2018, Brisbane, Australia. Project Page: https://huangrui815.github.io/active-image-based-modeling/ The author's personal page: http://www.sfu.ca/~rha55

Leverage of lidar point cloud for segmentation and shape reconstruction

Develop a method of annotating 3d sparse data (point cloud) in an efficient way with the help of deep neural network models and user corrections. Take the approach of human-in-the-loop to refine a AI generated fine annotation of the data. Focus on the task of self-driving cars and lidar sensor observations. The model generates a denser representation of the data and refines it by leveraging interactive human 2d annotations.Outgoin

Échantillonnage basé sur les Tuiles de Penrose et applications en infographie

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal

Multisource Point Clouds, Point Simplification and Surface Reconstruction

As data acquisition technology continues to advance, the improvement and upgrade of the algorithms for surface reconstruction are required. In this paper, we utilized multiple terrestrial Light Detection And Ranging (Lidar) systems to acquire point clouds with different levels of complexity, namely dynamic and rigid targets for surface reconstruction. We propose a robust and effective method to obtain simplified and uniform resample points for surface reconstruction. The method was evaluated. A point reduction of up to 99.371% with a standard deviation of 0.2 cm was achieved. In addition, well-known surface reconstruction methods, i.e., Alpha shapes, Screened Poisson reconstruction (SPR), the Crust, and Algebraic point set surfaces (APSS Marching Cubes), were utilized for object reconstruction. We evaluated the benefits in exploiting simplified and uniform points, as well as different density points, for surface reconstruction. These reconstruction methods and their capacities in handling data imperfections were analyzed and discussed. The findings are that (i) the capacity of surface reconstruction in dealing with diverse objects needs to be improved; (ii) when the number of points reaches the level of millions (e.g., approximately five million points in our data), point simplification is necessary, as otherwise, the reconstruction methods might fail; (iii) for some reconstruction methods, the number of input points is proportional to the number of output meshes; but a few methods are in the opposite; (iv) all reconstruction methods are beneficial from the reduction of running time; and (v) a balance between the geometric details and the level of smoothing is needed. Some methods produce detailed and accurate geometry, but their capacity to deal with data imperfection is poor, while some other methods exhibit the opposite characteristics

Learning quadrangulated patches for 3D shape parameterization and completion

We propose a novel 3D shape parameterization by surface patches, that are oriented by 3D mesh quadrangulation of the shape. By encoding 3D surface detail on local patches, we learn a patch dictionary that identifies principal surface features of the shape. Unlike previous methods, we are able to encode surface patches of variable size as determined by the user. We propose novel methods for dictionary learning and patch reconstruction based on the query of a noisy input patch with holes. We evaluate the patch dictionary towards various applications in 3D shape inpainting, denoising and compression. Our method is able to predict missing vertices and inpaint moderately sized holes. We demonstrate a complete pipeline for reconstructing the 3D mesh from the patch encoding. We validate our shape parameterization and reconstruction methods on both synthetic shapes and real world scans. We show that our patch dictionary performs successful shape completion of complicated surface textures.Comment: To be presented at International Conference on 3D Vision 2017, 201