460 research outputs found
A Minimalist Approach to Type-Agnostic Detection of Quadrics in Point Clouds
This paper proposes a segmentation-free, automatic and efficient procedure to
detect general geometric quadric forms in point clouds, where clutter and
occlusions are inevitable. Our everyday world is dominated by man-made objects
which are designed using 3D primitives (such as planes, cones, spheres,
cylinders, etc.). These objects are also omnipresent in industrial
environments. This gives rise to the possibility of abstracting 3D scenes
through primitives, thereby positions these geometric forms as an integral part
of perception and high level 3D scene understanding.
As opposed to state-of-the-art, where a tailored algorithm treats each
primitive type separately, we propose to encapsulate all types in a single
robust detection procedure. At the center of our approach lies a closed form 3D
quadric fit, operating in both primal & dual spaces and requiring as low as 4
oriented-points. Around this fit, we design a novel, local null-space voting
strategy to reduce the 4-point case to 3. Voting is coupled with the famous
RANSAC and makes our algorithm orders of magnitude faster than its conventional
counterparts. This is the first method capable of performing a generic
cross-type multi-object primitive detection in difficult scenes. Results on
synthetic and real datasets support the validity of our method.Comment: Accepted for publication at CVPR 201
Signature Sequence of Intersection Curve of Two Quadrics for Exact Morphological Classification
We present an efficient method for classifying the morphology of the
intersection curve of two quadrics (QSIC) in PR3, 3D real projective space;
here, the term morphology is used in a broad sense to mean the shape,
topological, and algebraic properties of a QSIC, including singularity,
reducibility, the number of connected components, and the degree of each
irreducible component, etc. There are in total 35 different QSIC morphologies
with non-degenerate quadric pencils. For each of these 35 QSIC morphologies,
through a detailed study of the eigenvalue curve and the index function jump we
establish a characterizing algebraic condition expressed in terms of the Segre
characteristics and the signature sequence of a quadric pencil. We show how to
compute a signature sequence with rational arithmetic so as to determine the
morphology of the intersection curve of any two given quadrics. Two immediate
applications of our results are the robust topological classification of QSIC
in computing B-rep surface representation in solid modeling and the derivation
of algebraic conditions for collision detection of quadric primitives
Generic Primitive Detection in Point Clouds Using Novel Minimal Quadric Fits
We present a novel and effective method for detecting 3D primitives in
cluttered, unorganized point clouds, without axillary segmentation or type
specification. We consider the quadric surfaces for encapsulating the basic
building blocks of our environments - planes, spheres, ellipsoids, cones or
cylinders, in a unified fashion. Moreover, quadrics allow us to model higher
degree of freedom shapes, such as hyperboloids or paraboloids that could be
used in non-rigid settings.
We begin by contributing two novel quadric fits targeting 3D point sets that
are endowed with tangent space information. Based upon the idea of aligning the
quadric gradients with the surface normals, our first formulation is exact and
requires as low as four oriented points. The second fit approximates the first,
and reduces the computational effort. We theoretically analyze these fits with
rigor, and give algebraic and geometric arguments. Next, by re-parameterizing
the solution, we devise a new local Hough voting scheme on the null-space
coefficients that is combined with RANSAC, reducing the complexity from
to (three points). To the best of our knowledge, this is the
first method capable of performing a generic cross-type multi-object primitive
detection in difficult scenes without segmentation. Our extensive qualitative
and quantitative results show that our method is efficient and flexible, as
well as being accurate.Comment: Submitted to IEEE Transactions on Pattern Analysis and Machine
Intelligence (T-PAMI). arXiv admin note: substantial text overlap with
arXiv:1803.0719
Implicitization of rational surfaces using toric varieties
A parameterized surface can be represented as a projection from a certain
toric surface. This generalizes the classical homogeneous and bihomogeneous
parameterizations. We extend to the toric case two methods for computing the
implicit equation of such a rational parameterized surface. The first approach
uses resultant matrices and gives an exact determinantal formula for the
implicit equation if the parameterization has no base points. In the case the
base points are isolated local complete intersections, we show that the
implicit equation can still be recovered by computing any non-zero maximal
minor of this matrix.
The second method is the toric extension of the method of moving surfaces,
and involves finding linear and quadratic relations (syzygies) among the input
polynomials. When there are no base points, we show that these can be put
together into a square matrix whose determinant is the implicit equation. Its
extension to the case where there are base points is also explored.Comment: 28 pages, 1 figure. Numerous major revisions. New proof of method of
moving surfaces. Paper accepted and to appear in Journal of Algebr
Surface and Volumetric Segmentation of Complex 3-D Objects Using Parametric Shape Models
The problem of part definition, description, and decomposition is central to the shape recognition systems. In this dissertation, we develop an integrated framework for segmenting dense range data of complex 3-D scenes into their constituent parts in terms of surface and volumetric primitives. Unlike previous approaches, we use geometric properties derived from surface, as well as volumetric models, to recover structured descriptions of complex objects without a priori domain knowledge or stored models.
To recover shape descriptions, we use bi-quadric models for surface representation and superquadric models for object-centered volumetric representation. The surface segmentation uses a novel approach of searching for the best piecewise description of the image in terms of bi-quadric (z = f(x,y)) models. It is used to generate the region adjacency graphs, to localize surface discontinuities, and to derive global shape properties of the surfaces. A superquadric model is recovered for the entire data set and residuals are computed to evaluate the fit. The goodness-of-fit value based on the inside-outside function, and the mean-squared distance of data from the model provide quantitative evaluation of the model. The qualitative evaluation criteria check the local consistency of the model in the form of residual maps of overestimated and underestimated data regions.
The control structure invokes the models in a systematic manner, evaluates the intermediate descriptions, and integrates them to achieve final segmentation. Superquadric and bi-quadric models are recovered in parallel to incorporate the best of the coarse-to-fine and fine-to-coarse segmentation strategies. The model evaluation criteria determine the dimensionality of the scene, and decide whether to terminate the procedure, or selectively refine the segmentation by following a global-to-local part segmentation approach. The control module generates hypotheses about superquadric models at clusters of underestimated data and performs controlled extrapolation of the part-model by shrinking the global model. As the global model shrinks and the local models grow, they are evaluated and tested for termination or further segmentation.
We present results on real range images of scenes of varying complexity, including objects with occluding parts, and scenes where surface segmentation is not sufficient to guide the volumetric segmentation. We analyze the issue of segmentation of complex scenes thoroughly by studying the effect of missing data on volumetric model recovery, generating object-centered descriptions, and presenting a complete set of criteria for the evaluation of the superquadric models. We conclude by discussing the applications of our approach in data reduction, 3-D object recognition, geometric modeling, automatic model generation. object manipulation, and active vision
Hand tracking using a quadric surface model and Bayesian filtering
Within this paper a technique for model-based 3D hand tracking is presented. A hand model is built from a set of truncated quadrics, approximating the anatomy of a real hand with few parameters. Given that the projection of a quadric onto the image plane is a conic, the contours can be generated efficiently. These model contours are used as shape templates to evaluate possible matches in the current frame. The evaluation is done within a hierarchical Bayesian filtering framework, where the posterior distribution is computed efficiently using a tree of templates. We demonstrate the effectiveness of the technique by using it for tracking 3D articulated and non-rigid hand motion from monocular video sequences in front of a cluttered background
Three dimensional extension of Bresenham’s algorithm with Voronoi diagram
Bresenham’s algorithm for plotting a two-dimensional line segment is elegant and efficient in its deployment of mid-point comparison and integer arithmetic. It is natural to investigate its three-dimensional extensions. In so doing, this paper uncovers the reason for little prior work. The concept of the mid-point in a unit interval generalizes to that of nearest neighbours involving a Voronoi diagram. Algorithmically, there are challenges. While a unit interval in two-dimension becomes a unit square in three-dimension, “squaring” the number of choices in Bresenham’s algorithm is shown to have difficulties. In this paper, the three-dimensional extension is based on the main idea of Bresenham’s algorithm of minimum distance between the line and the grid points. The structure of the Voronoi diagram is presented for grid points to which the line may be approximated. The deployment of integer arithmetic and symmetry for the three-dimensional extension of the algorithm to raise the computation efficiency are also investigated
A Survey of Methods for Converting Unstructured Data to CSG Models
The goal of this document is to survey existing methods for recovering CSG
representations from unstructured data such as 3D point-clouds or polygon
meshes. We review and discuss related topics such as the segmentation and
fitting of the input data. We cover techniques from solid modeling and CAD for
polyhedron to CSG and B-rep to CSG conversion. We look at approaches coming
from program synthesis, evolutionary techniques (such as genetic programming or
genetic algorithm), and deep learning methods. Finally, we conclude with a
discussion of techniques for the generation of computer programs representing
solids (not just CSG models) and higher-level representations (such as, for
example, the ones based on sketch and extrusion or feature based operations).Comment: 29 page
21st Century Simulation: Exploiting High Performance Computing and Data Analysis
This paper identifies, defines, and analyzes the limitations imposed on Modeling and Simulation by outmoded
paradigms in computer utilization and data analysis. The authors then discuss two emerging capabilities to
overcome these limitations: High Performance Parallel Computing and Advanced Data Analysis. First, parallel
computing, in supercomputers and Linux clusters, has proven effective by providing users an advantage in
computing power. This has been characterized as a ten-year lead over the use of single-processor computers.
Second, advanced data analysis techniques are both necessitated and enabled by this leap in computing power.
JFCOM's JESPP project is one of the few simulation initiatives to effectively embrace these concepts. The
challenges facing the defense analyst today have grown to include the need to consider operations among non-combatant
populations, to focus on impacts to civilian infrastructure, to differentiate combatants from non-combatants,
and to understand non-linear, asymmetric warfare. These requirements stretch both current
computational techniques and data analysis methodologies. In this paper, documented examples and potential
solutions will be advanced. The authors discuss the paths to successful implementation based on their experience.
Reviewed technologies include parallel computing, cluster computing, grid computing, data logging, OpsResearch,
database advances, data mining, evolutionary computing, genetic algorithms, and Monte Carlo sensitivity analyses.
The modeling and simulation community has significant potential to provide more opportunities for training and
analysis. Simulations must include increasingly sophisticated environments, better emulations of foes, and more
realistic civilian populations. Overcoming the implementation challenges will produce dramatically better insights,
for trainees and analysts. High Performance Parallel Computing and Advanced Data Analysis promise increased
understanding of future vulnerabilities to help avoid unneeded mission failures and unacceptable personnel losses.
The authors set forth road maps for rapid prototyping and adoption of advanced capabilities. They discuss the
beneficial impact of embracing these technologies, as well as risk mitigation required to ensure success
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