Fast Hough transform: A hierarchical approach
Computer Vision, Graphics, and Image Processing
Digital image processing (2nd ed.)
Digital image processing (2nd ed.)
A survey of the Hough transform
Computer Vision, Graphics, and Image Processing
Elements of information theory
Elements of information theory
Efficiently Locating Objects Using the Hausdorff Distance
International Journal of Computer Vision
Constrained Hough transforms for curve detection
Computer Vision and Image Understanding
A Bayesian Method for Fitting Parametric and Nonparametric Models to Noisy Data
IEEE Transactions on Pattern Analysis and Machine Intelligence
Asymptotic approximations of integrals
Asymptotic approximations of integrals
Statistical Optimization for Geometric Computation: Theory and Practice
Statistical Optimization for Geometric Computation: Theory and Practice
Shape Detection in Computer Vision Using the Hough Transform
Shape Detection in Computer Vision Using the Hough Transform
Multiple View Geometry in Computer Vision
Multiple View Geometry in Computer Vision
The Mathematica Book
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
Fisher information and stochastic complexity
IEEE Transactions on Information Theory
Application of the Fisher-Rao Metric to Ellipse Detection
International Journal of Computer Vision
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Certain structure detection problems can be solved by sampling a parameter space for the different structures at a finite number of points and checking each point to see if the corresponding structure has a sufficient number of inlying measurements. The measurement space is a Riemannian manifold and the measurements relevant to a given structure are near to or on a submanifold which constitutes the structure. The probability density function for the errors in the measurements is described using a generalisation of the Gaussian density to Riemannian manifolds. The conditional probability density function for the measurements yields the Fisher information which defines a metric, known as the Fisher-Rao metric, on the parameter space. The main result is a derivation of an asymptotic approximation to the Fisher-Rao metric, under the assumption that the measurement noise is small. Using this approximation to the Fisher-Rao metric, the parameter space is sampled, such that each point of the parameter space is near to at least one sample point, to within the level of accuracy allowed by the measurement errors. The probability of a false detection of a structure is estimated. The feasibility of this approach to structure detection is tested experimentally using the example of line detection in digital images.