Untitled

Hartley, Richard

doi:10.1023/a:1007984508483

Cited by 79 publications

(55 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The search for the best plane at infinity can be narrowed by making a preliminary transformation to a quasi-affine transformation ( [5]). A quasi-affine reconstruction is computed by taking account of cheirality as described in [3].…”

Section: Obtaining a Quasi-affine Reconstructionmentioning

confidence: 99%

“…A quasi-affine reconstruction may be computed from a projective-reconstruction by solving a linear programming problem. In particular, for a projective reconstruction consisting of points X i and cameras P j , one finds a quasi-affine reconstruction in several steps as follows (for justification see [5,3]) :…”

Section: Obtaining a Quasi-affine Reconstructionmentioning

confidence: 99%

“…Multiply each P j and X i by ±1 as necessary so that P j X i = (x, y, w) with w > 0. This is always possible ( [5]). …”

Section: Obtaining a Quasi-affine Reconstructionmentioning

confidence: 99%

“…If solutions exist both for = 1 and = −1, then they have opposite orientation ( [5]). As explained in [3] one adds extra inequalities |v i | <= 1 for each component v i of V to constrain a solution.…”

Section: For Each = ±1 Form the Set Of Inequalitiesmentioning

confidence: 99%

See 3 more Smart Citations

Camera calibration and the search for infinity

Hartley

Hayman

Agapito

et al. 1999

Proceedings of the Seventh IEEE International Conference on Computer Vision

View full text Add to dashboard Cite

show abstract

Section: Obtaining a Quasi-affine Reconstructionmentioning

confidence: 99%

Section: Obtaining a Quasi-affine Reconstructionmentioning

confidence: 99%

“…Multiply each P j and X i by ±1 as necessary so that P j X i = (x, y, w) with w > 0. This is always possible ( [5]). …”

Section: Obtaining a Quasi-affine Reconstructionmentioning

confidence: 99%

Section: For Each = ±1 Form the Set Of Inequalitiesmentioning

confidence: 99%

See 2 more Smart Citations

Camera calibration and the search for infinity

Hartley

Hayman

Agapito

et al. 1999

Proceedings of the Seventh IEEE International Conference on Computer Vision

View full text Add to dashboard Cite

show abstract

“…On the other hand, in this paper, we use chirality constraints derived from the scene to compute a theoretically correct initial search space for the plane at infinity, within which we are guaranteed to find the global minimum (Hartley 1998;Hartley et al 1999). In practice, for a moderate number of cameras, the initial region determined by the chirality constraints are tight enough to allow rapid convergence of the search algorithm.…”

Section: Introductionmentioning

confidence: 99%

Globally Optimal Algorithms for Stratified Autocalibration

Chandraker,

Agarwal,

Kriegman

et al. 2009

Int J Comput Vis

View full text Add to dashboard Cite

We present practical algorithms for stratified autocalibration with theoretical guarantees of global optimality. Given a projective reconstruction, we first upgrade it to affine by estimating the position of the plane at infinity. The plane at infinity is computed by globally minimizing a least squares formulation of the modulus constraints. In the second stage, this affine reconstruction is upgraded to a metric one by globally minimizing the infinite homography relation to compute the dual image of the absolute conic (DIAC). The positive semidefiniteness of the DIAC is explicitly enforced as part of the optimization process, rather than as a post-processing step.For each stage, we construct and minimize tight convex relaxations of the highly non-convex objective functions in a branch and bound optimization framework. We exploit the inherent problem structure to restrict the search space for the DIAC and the plane at infinity to a small, fixed number of branching dimensions, independent of the number of views. Chirality constraints are incorporated into our convex relaxations to automatically select an initial region which is guaranteed to contain the global minimum. Experimental evidence of the accuracy, speed and scalability of our algorithm is presented on synthetic and real data.

show abstract

A web site for calculating the degree of chirality

et al. 2010

View full text Add to dashboard Cite

The web site, http://www.csm.huji.ac.il/, uses the Continuous Chirality Measure to evaluate quantitatively the degree of chirality of a molecule, a structure, a fragment. The value of this measure ranges from zero, the molecule is achiral, to higher values (the upper limit is 100); the higher the chirality value, the more chiral the molecule is. The measure is based on the distance between the chiral molecule and the nearest structure that is achiral. Questions such as the following can be addressed: by how much is one molecule more chiral than the other? how does chirality change along conformational motions? is there a correlation between chirality and enantioselectivity in a series of molecules? Both elementary and advanced features are offered. Related calculation options are the symmetry measures and shape measures.

show abstract

Untitled

Cited by 79 publications

References 0 publications

Camera calibration and the search for infinity

Camera calibration and the search for infinity

Globally Optimal Algorithms for Stratified Autocalibration

A web site for calculating the degree of chirality

Contact Info

Product

Resources

About