A survey of the Hough transform
Computer Vision, Graphics, and Image Processing
A probabilistic Hough transform
Pattern Recognition
CVGIP: Image Understanding
Mixtures of probabilistic principal component analyzers
Neural Computation
A Method to Detect and Characterize Ellipses Using the Hough Transform
IEEE Transactions on Pattern Analysis and Machine Intelligence
Finding circles by an array of accumulators
Communications of the ACM
Use of the Hough transformation to detect lines and curves in pictures
Communications of the ACM
Computational Framework for Segmentation and Grouping
Computational Framework for Segmentation and Grouping
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1 - Volume 01
Generalized Principal Component Analysis (GPCA)
IEEE Transactions on Pattern Analysis and Machine Intelligence
Gaigen 2:: a geometric algebra implementation generator
Proceedings of the 5th international conference on Generative programming and component engineering
Real-time line detection through an improved Hough transform voting scheme
Pattern Recognition
Geometric Algebra with Applications in Engineering
Geometric Algebra with Applications in Engineering
IEEE Transactions on Pattern Analysis and Machine Intelligence
Geometric Algebra for Computer Science: An Object-Oriented Approach to Geometry
Geometric Algebra for Computer Science: An Object-Oriented Approach to Geometry
Finding picture edges through collinearity of feature points
IJCAI'73 Proceedings of the 3rd international joint conference on Artificial intelligence
Geometric Algebra: A Powerful Tool for Solving Geometric Problems in Visual Computing
SIBGRAPI-TUTORIALS '09 Proceedings of the 2009 Tutorials of the XXII Brazilian Symposium on Computer Graphics and Image Processing
A robust framework for aligning lecture slides with video
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
A Robust Iris Localization Method Using an Active Contour Model and Hough Transform
ICPR '10 Proceedings of the 2010 20th International Conference on Pattern Recognition
A closed form solution to robust subspace estimation and clustering
CVPR '11 Proceedings of the 2011 IEEE Conference on Computer Vision and Pattern Recognition
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The analysis of large volumes of unordered multidimensional data is a problem confronted by scientists and data analysts every day. Often, it involves searching for data alignments that emerge as well-defined structures or geometric patterns in datasets. For example, straight lines, circles, and ellipses represent meaningful structures in data collected from electron backscatter diffraction, particle accelerators, and clonogenic assays. Also, customers with similar behavior describe linear correlations in e-commerce databases. We describe a general approach for detecting data alignments in large unordered noisy multidimensional datasets. In contrast to classical techniques such as the Hough transforms, which are designed for detecting a specific type of alignment on a given type of input, our approach is independent of the geometric properties of the alignments to be detected, as well as independent of the type of input data. Thus, it allows concurrent detection of multiple kinds of data alignments, in datasets containing multiple types of data. Given its general nature, optimizations developed for our technique immediately benefit all its applications, regardless the type of input data.