624 research outputs found
Autocalibration with the Minimum Number of Cameras with Known Pixel Shape
In 3D reconstruction, the recovery of the calibration parameters of the
cameras is paramount since it provides metric information about the observed
scene, e.g., measures of angles and ratios of distances. Autocalibration
enables the estimation of the camera parameters without using a calibration
device, but by enforcing simple constraints on the camera parameters. In the
absence of information about the internal camera parameters such as the focal
length and the principal point, the knowledge of the camera pixel shape is
usually the only available constraint. Given a projective reconstruction of a
rigid scene, we address the problem of the autocalibration of a minimal set of
cameras with known pixel shape and otherwise arbitrarily varying intrinsic and
extrinsic parameters. We propose an algorithm that only requires 5 cameras (the
theoretical minimum), thus halving the number of cameras required by previous
algorithms based on the same constraint. To this purpose, we introduce as our
basic geometric tool the six-line conic variety (SLCV), consisting in the set
of planes intersecting six given lines of 3D space in points of a conic. We
show that the set of solutions of the Euclidean upgrading problem for three
cameras with known pixel shape can be parameterized in a computationally
efficient way. This parameterization is then used to solve autocalibration from
five or more cameras, reducing the three-dimensional search space to a
two-dimensional one. We provide experiments with real images showing the good
performance of the technique.Comment: 19 pages, 14 figures, 7 tables, J. Math. Imaging Vi
Darboux cyclides and webs from circles
Motivated by potential applications in architecture, we study Darboux
cyclides. These algebraic surfaces of order a most 4 are a superset of Dupin
cyclides and quadrics, and they carry up to six real families of circles.
Revisiting the classical approach to these surfaces based on the spherical
model of 3D Moebius geometry, we provide computational tools for the
identification of circle families on a given cyclide and for the direct design
of those. In particular, we show that certain triples of circle families may be
arranged as so-called hexagonal webs, and we provide a complete classification
of all possible hexagonal webs of circles on Darboux cyclides.Comment: 34 pages, 20 figure
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
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ALPHA_I, Remote Manufacturing, and Solid Freeform Fabrication
Alpha_l is a nonuniform rational B-spline (NURBs) based solid modeling system that
has been developed at the University of Utah over the past 10 years. In addition to being
useful in modeling objects that are described by simple rotation and extrusion operations,
the real power of Alpha_l is demonstrated in the modeling of complex parts with sculptured
surfaces. For the past several years, a major research thrust has been to use Alpha_l to
semi-automatically generate process plan information and numerical control code to manufacture
mechanical parts directly from the models. A long term goal is to support an on-line
remote manufacturing facility for producing prototype parts. Recently, a 3D Systems stereo
lithography machine has been added to the advanced manufacturing laboratory. The stereo
lithography process and other SFF techniques are of particular interest for supporting a
remote manufacturing facility in that these processes are inherently much safer than numerically
controlled machining. Special Alpha_l interfaces including a new slicing algorithm
are being developed for the SFF machine use. By generating a SFF part directly from
its NURBs description, Alpha_l should facilitate the manufacture of complex parts while
providing smoother surfaces.Mechanical Engineerin
Recognition of Quadric Surfaces From Range Data: An Analytical Approach
In this dissertation, a new technique based on analytic geometry for the recognition and description of three-dimensional quadric surfaces from range images is presented. Beginning with the explicit representation of quadrics, a set of ten coefficients are determined for various three-dimensional surfaces. For each quadric surface, a unique set of two-dimensional curves which serve as a feature set is obtained from the various angles at which the object is intersected with a plane. Based on a discriminant method, each of the curves is classified as a parabola, circle, ellipse, hyperbola, or a line. Each quadric surface is shown to be uniquely characterized by a set of these two-dimensional curves, thus allowing discrimination from the others.
Before the recognition process can be implemented, the range data have to undergo a set of pre-processing operations, thereby making it more presentable to classification algorithms. One such pre-processing step is to study the effect of median filtering on raw range images. Utilizing a variety of surface curvature techniques, reliable sets of image data that approximate the shape of a quadric surface are determined. Since the initial orientation of the surfaces is unknown, a new technique is developed wherein all the rotation parameters are determined and subsequently eliminated. This approach enables us to position the quadric surfaces in a desired coordinate system.
Experiments were conducted on raw range images of spheres, cylinders, and cones. Experiments were also performed on simulated data for surfaces such as hyperboloids of one and two sheets, elliptical and hyperbolic paraboloids, elliptical and hyperbolic cylinders, ellipsoids and the quadric cones. Both the real and simulated data yielded excellent results. Our approach is found to be more accurate and computationally inexpensive as compared to traditional approaches, such as the three-dimensional discriminant approach which involves evaluation of the rank of a matrix.
Finally, we have proposed one other new approach, which involves the formulation of a mapping between the explicit and implicit forms of representing quadric surfaces. This approach, when fully realized, will yield a three-dimensional discriminant, which will recognize quadric surfaces based upon their component surface patches. This approach is faster than prior approaches and at the same time is invariant to pose and orientation of the surfaces in three-dimensional space
A new method for recognizing quadric surfaces from range data and its application to telerobotics and automation, final phase
In the final phase of the proposed research a complete top to down three dimensional object recognition scheme has been proposed. The various three dimensional objects included spheres, cones, cylinders, ellipsoids, paraboloids, and hyperboloids. Utilizing a newly developed blob determination technique, a given range scene with several non-cluttered quadric surfaces is segmented. Next, using the earlier (phase 1) developed alignment scheme, each of the segmented objects are then aligned in a desired coordinate system. For each of the quadric surfaces based upon their intersections with certain pre-determined planes, a set of distinct features (curves) are obtained. A database with entities such as the equations of the planes and angular bounds of these planes has been created for each of the quadric surfaces. Real range data of spheres, cones, cylinders, and parallelpipeds have been utilized for the recognition process. The developed algorithm gave excellent results for the real data as well as for several sets of simulated range data
A graph-spectral approach to shape-from-shading
In this paper, we explore how graph-spectral methods can be used to develop a new shape-from-shading algorithm. We characterize the field of surface normals using a weight matrix whose elements are computed from the sectional curvature between different image locations and penalize large changes in surface normal direction. Modeling the blocks of the weight matrix as distinct surface patches, we use a graph seriation method to find a surface integration path that maximizes the sum of curvature-dependent weights and that can be used for the purposes of height reconstruction. To smooth the reconstructed surface, we fit quadrics to the height data for each patch. The smoothed surface normal directions are updated ensuring compliance with Lambert's law. The processes of height recovery and surface normal adjustment are interleaved and iterated until a stable surface is obtained. We provide results on synthetic and real-world imagery
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Body surface imaging
An embodiment of the invention may provide a portable, inexpensive two-view 3D stereo vision imaging system, which acquires a 3D surface model and dimensions of an object. The system may comprise front-side and back-side stereo imagers which each have a projector and at least two digital cameras to image the object from different perspectives. An embodiment may include a method for reconstructing an image of a human body from the data of a two-view body scanner by obtaining a front scan image data point set and a back scan image data point set. A smooth body image may be gained by processing the data point sets using the following steps: (1) data resampling; (2) initial mesh generation; (3) mesh simplification; and (4) mesh subdivision and optimization.Board of Regents, University of Texas Syste
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