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Efficient Intersection of Three Quadrics and Applications in Computer Vision

Zuzana Kukelova, Jan Heller, Andrew Fitzgibbon
2016 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)  
In this paper, we present a new algorithm for finding all intersections of three quadrics.  ...  The proposed method is algebraic in nature and it is considerably more efficient than the Gröbner basis and resultant-based solutions previously used in computer vision applications.  ...  Resultant [13, 32, 8] GB [30, 20] E3Q3 # of ops >100000 ∼11846 1811 3Q3 in computer vision The problem of finding the intersection of three quadrics has already appeared in several computer vision  ... 
doi:10.1109/cvpr.2016.199 dblp:conf/cvpr/KukelovaHF16 fatcat:sy4p56gjcrfpvditm3uqvlive4

Efficient distance estimation for fitting implicit quadric surfaces

Angel D. Sappa, Mohammad Rouhani
2009 2009 16th IEEE International Conference on Image Processing (ICIP)  
Surfaces fitted by using the proposed geometric distance estimation and state of the art metrics are presented to show the viability of the proposed approach.  ...  Comparisons of the proposed metric with previous approaches are provided to show both improvements in CPU time as well as in the accuracy of the obtained results.  ...  In the context of 3D computer vision the quadric surface fitting has been an active research topic during the last two decades [1, 7] .  ... 
doi:10.1109/icip.2009.5414072 dblp:conf/icip/SappaR09 fatcat:g6ueedxgunc5vnsnicpsimgnwe

The invariant representations of a quadric cone and a twisted cubic

Y.H. Wu, Z.Y. Hu
2003 IEEE Transactions on Pattern Analysis and Machine Intelligence  
Finally, we exemplify some applications of our proposed invariant representations in the fields of computer vision and automated geometric theorem proving.  ...  Up to now, the shortest invariant representation of a quadric has 138 summands and there has been no invariant representation of a twisted cubic in 3D projective space, which limit to some extent the applications  ...  Maybank for his kind provision of reprints. This work was supported by the Natural  ... 
doi:10.1109/tpami.2003.1233907 fatcat:4hjmdacconc2dhw4xhoqubpxsy

Degeneracy of the Intersection of Three Quadrics

André Wagner
2018 Journal of Mathematical Imaging and Vision  
the intersection of three quadrics in P 3 .  ...  This generalizes a multiple results of the degeneracies of the 8-point algorithm. We give an algorithm that improves the 7-and 8-point algorithm in such a pathological situation.  ...  Acknowledgements We would like to thank Michael Joswig for his guidance and Fredrik Kahl for our correspondences about critical configurations.  ... 
doi:10.1007/s10851-018-0841-x fatcat:r5zspq5ydjgxtlb3rh75kghnda

Generic Primitive Detection in Point Clouds Using Novel Minimal Quadric Fits [article]

Tolga Birdal and Benjamin Busam and Nassir Navab and Slobodan Ilic and Peter Sturm
2019 arXiv   pre-print
Moreover, quadrics allow us to model higher degree of freedom shapes, such as hyperboloids or paraboloids that could be used in non-rigid settings.  ...  Our extensive qualitative and quantitative results show that our method is efficient and flexible, as well as being accurate.  ...  ACKNOWLEDGMENTS The authors would like to thank Bertram Drost and Maximilian Baust for fruitful discussions.  ... 
arXiv:1901.01255v1 fatcat:m6vbmsrlpzdurmqquknfdascrm

Camera autocalibration using Plucker coordinates

J.I. Ronda, G. Gallego, A. Valdes
2005 IEEE International Conference on Image Processing 2005  
We present new results on the Absolute Line Quadric (ALQ), the geometric object representing the set of lines that intersect the absolute conic.  ...  We include new techniques for the obtainment of the Euclidean structure that lead to an efficient algorithm for the autocalibration of cameras with varying parameters.  ...  The first one was introduced in the computer vision literature in [7] and is known as the dual absolute quadric (DAQ).  ... 
doi:10.1109/icip.2005.1530513 dblp:conf/icip/RondaGV05 fatcat:vkmzdu64cnhkzhaecobyvspevi

G1 interpolation using piecewise quadric and cubic surfaces

Chandrajit L. Bajaj, Leonard A. Ferrari, Rui J. P. de Figueiredo
1990 Curves and Surfaces in Computer Vision and Graphics  
Algorithms are presented for constructing G t continuous meshes of degree two (quadric) and degree three (cubic) implicitly defined, piecewise algebraic surfaces, which exactly fit any given collection  ...  A combination of techniques are used from computational algebraic geometry and numerical approximation theory which reduces the problem to solving coupled systems of linear equations and low degree, polynomial  ...  Introduction Interpolation provides an efficient way of generating G 1 continuous meshes of surface patches, necessary for the construction of accurate computer models of solid physical objects [2] .  ... 
doi:10.1117/12.19736 fatcat:64kdqd4m65gfjorjr7m7ltv3ye

Complete Classification and Efficient Determination of Arrangements Formed by Two Ellipsoids

Xiaohong Jia, Changhe Tu, Bernard Mourrain, Wenping Wang
2020 ACM Transactions on Graphics  
Arrangements are especially useful to collision detection, which is a key task in various applications such as computer animation, virtual reality, computer games, robotics, CAD/CAM and computational physics  ...  Specifically, we present a classification of these arrangements and propose an efficient algorithm for determining the arrangement formed by any particular pair of ellipsoids.  ...  Advanced subject project of University of Chinese Academy of Sciences (115200S001), and the Alibaba Group through Alibaba Innovative Research Program.  ... 
doi:10.1145/3388540 fatcat:4iltu7bsu5d7lcjjkzblmni6za

Page 6524 of Mathematical Reviews Vol. , Issue 98J [page]

1998 Mathematical Reviews  
As a practi- cal application, the results provide a parametric representation for the intersection curve of two quadric surfaces.  ...  (English and French summaries) {Applications of computer algebra to ballistics] Computer algebra (Saint-Louis, 1996). Theoret. Comput. Sci. 187 (1997), no. 1-2, 263-284.  ... 

Qualitative primitive identification using fuzzy clustering and invariant approach

Y.Y. Cai, H.T. Loh, A.Y.C. Nee
1996 Image and Vision Computing  
Finally, the extracted quadric shells are localised in terms of quadric centre(s), quadric directions, and any axes of revolution.  ...  Once the best-fitting quadric shells have been recovered, five types of invariants are used to classify the qualitative shapes and represent the geometric parameters of the shapes.  ...  Krishnapuram of the University of Missouri and Professor M. Shiraishi of Ibaraki University for the helpful discussions.  ... 
doi:10.1016/0262-8856(95)01053-x fatcat:p3exu67qvracdng3f55432k3qi

Generating Smooth High-Quality Isosurfaces for Interactive Modeling and Visualization of Complex Terrains [article]

Falko Löffler, Heidrun Schumann
2012 International Symposium on Vision, Modeling, and Visualization  
The surface extraction is a variation of Dual Marching Cubes and designed as a set of well-balanced parallel computation kernels.  ...  Moreover, our extraction approach is generally applicable, for example in the field of volume visualization.  ...  We see the scope of future work by finding a generic solution which performs well on CPU and GPU architectures. We have not addressed very large volumes or level of detail, yet.  ... 
doi:10.2312/pe/vmv/vmv12/079-086 dblp:conf/vmv/LofflerS12 fatcat:ruhmm3g7l5daxd623bl7fdzuim

Towards human motion capture from a camera mounted on a mobile robot

Paulo Menezes, Frédéric Lerasle, Jorge Dias
2011 Image and Vision Computing  
Data fusion is considered both in the importance and measurement functions with some degree of adaptability depending on the current human posture and the environmental context encountered by the robot  ...  Our particle filter based HMC system is improved and extended in two ways.  ...  The computation of the set of intersections between this line and the whole set of quadrics enable us to verify if the 3D point that originated X m is in front of all the other quadrics or is hidden by  ... 
doi:10.1016/j.imavis.2011.01.003 fatcat:n3oiegt2r5hi7dupy2kz3yhjm4

Circular Laser/Camera-Based Attitude and Altitude Estimation: Minimal and Robust Solutions

Rémi Boutteau, Peter Sturm, Pascal Vasseur, Cédric Demonceaux
2017 Journal of Mathematical Imaging and Vision  
It consists of a circular laser pattern and a camera rigidly attached to the laser source.  ...  We develop a geometric modeling that allows to efficiently estimate the pose at scale of the system, relative to a reference plane onto which the pattern is projected.  ...  (If the planes are identical, the quadric is actually of rank 1 only and has three zero eigenvalues.)  ... 
doi:10.1007/s10851-017-0764-y fatcat:md7smc2xsbcwdo462vnjwjikca

Improved quadric surface impostors for large bio-molecular visualization

Pranav D. Bagur, Nithin Shivashankar, Vijay Natarajan
2012 Proceedings of the Eighth Indian Conference on Computer Vision, Graphics and Image Processing - ICVGIP '12  
The framework first produces "impostor primitives", which are simple linear element approximations of quadric objects, such as spheres, cylinders, and helices.  ...  In this paper, we present a unified framework for accelerating the rendering of various representations of these structure using GPUs.  ...  In the second stage, the fragment shader computes the intersection of the infinite cylinder and the view-ray (see Figure 5c ).  ... 
doi:10.1145/2425333.2425366 dblp:conf/icvgip/BagurSN12 fatcat:ombutbbz7bfubng6n433l4yga4

The Absolute Line Quadric and Camera Autocalibration

Antonio Valdés, José Ignacio Ronda, Guillermo Gallego
2006 International Journal of Computer Vision  
After the introduction of the necessary exterior algebra and Grassmannian geometry tools, we analyze the Grassmannian of lines of P 3 from both the projective and Euclidean points of view.  ...  The exterior algebra setting allows then to introduce the ALQ as a quadric arising very naturally from the dual absolute quadric.  ...  Sum and intersection of linear subspaces. The sum and intersection of linear subspaces are fundamental operations in Computer Vision.  ... 
doi:10.1007/s11263-005-3677-y fatcat:qxpop7mwrfcphh6bnnnb6axjny
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