Sphere-packings, lattices, and groups
Sphere-packings, lattices, and groups
IEEE Transactions on Pattern Analysis and Machine Intelligence
Elements of information theory
Elements of information theory
Randomized Hough transform (RHT): basic mechanisms, algorithms, and computational complexities
CVGIP: Image Understanding
Assessing error of fit functions for ellipses
Graphical Models and Image Processing
Efficiently Locating Objects Using the Hausdorff Distance
International Journal of Computer Vision
Computable elastic distances between shapes
SIAM Journal on Applied Mathematics
Direct Least Square Fitting of Ellipses
IEEE Transactions on Pattern Analysis and Machine Intelligence
International Journal of Computer Vision - Special issue on statistical and computational theories of vision: modeling, learning, sampling and computing, Part I
Shape Detection in Computer Vision Using the Hough Transform
Shape Detection in Computer Vision Using the Hough Transform
Statistical Bias of Conic Fitting and Renormalization
IEEE Transactions on Pattern Analysis and Machine Intelligence
Identifying and Tracking Ellipses: A Technique Based on Elliptical Deformable Templates
ICIAP '99 Proceedings of the 10th International Conference on Image Analysis and Processing
Multiple View Geometry in Computer Vision
Multiple View Geometry in Computer Vision
The Mathematica Book
Estimation with Bilinear Constraints in Computer Vision
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Eye Gaze Estimation from a Single Image of One Eye
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Camera calibration using spheres: A semi-definite programming approach
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Invariant Fitting of Two View Geometry
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fast Robust GA-Based Ellipse Detection
ICPR '04 Proceedings of the Pattern Recognition, 17th International Conference on (ICPR'04) Volume 2 - Volume 02
Detection of Image Structures Using the Fisher Information and the Rao Metric
IEEE Transactions on Pattern Analysis and Machine Intelligence
The Fisher-Rao Metric for Projective Transformations of the Line
International Journal of Computer Vision
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Application of the Fisher-Rao Metric to Structure Detection
Journal of Mathematical Imaging and Vision
Near-optimal detection of geometric objects by fast multiscale methods
IEEE Transactions on Information Theory
On the Geometry of Multivariate Generalized Gaussian Models
Journal of Mathematical Imaging and Vision
A Fisher-Rao Metric for Paracatadioptric Images of Lines
International Journal of Computer Vision
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The parameter space for the ellipses in a two dimensional image is a five dimensional manifold, where each point of the manifold corresponds to an ellipse in the image. The parameter space becomes a Riemannian manifold under a Fisher-Rao metric, which is derived from a Gaussian model for the blurring of ellipses in the image. Two points in the parameter space are close together under the Fisher-Rao metric if the corresponding ellipses are close together in the image. The Fisher-Rao metric is accurately approximated by a simpler metric under the assumption that the blurring is small compared with the sizes of the ellipses under consideration. It is shown that the parameter space for the ellipses in the image has a finite volume under the approximation to the Fisher-Rao metric. As a consequence the parameter space can be replaced, for the purpose of ellipse detection, by a finite set of points sampled from it. An efficient algorithm for sampling the parameter space is described. The algorithm uses the fact that the approximating metric is flat, and therefore locally Euclidean, on each three dimensional family of ellipses with a fixed orientation and a fixed eccentricity. Once the sample points have been obtained, ellipses are detected in a given image by checking each sample point in turn to see if the corresponding ellipse is supported by the nearby image pixel values. The resulting algorithm for ellipse detection is implemented. A multiresolution version of the algorithm is also implemented. The experimental results suggest that ellipses can be reliably detected in a given low resolution image and that the number of false detections can be reduced using the multiresolution algorithm.