On the Generalization of Subspace Detection in Unordered Multidimensional Data

• Leandro A. F. Fernandes UFRGS
• Manuel M. Oliveira UFRGS

Resumo

We present a generalized closed-form framework for detecting data alignments in large unordered noisy multidimensional datasets. In our ap proach, the intended type of data alignment may be a geometric shape (e.g., straight line, circle, conic section) or any other structure, with arbitrary di mensionality, that can be characterized by a linear subspace. We also present an extension of our detection scheme to data with Gaussian-distributed uncertainty. The proposed extension makes the framework more robust to the detection of spurious alignments. In contrast to existing solutions, the proposed approach is independent of the geometric properties of the alignments to be detected. Also, it is independent of the type of input data and automatically adapts to entries of arbitrary dimensionality. This allows application of the proposed framework (without changes) in a broad range of applications as a pattern detection tool.

Referências

Fernandes, L. A. F. (2010). On the generalization of subspace detection in unordered multidimensional data. PhD thesis, PPGC-UFRGS, Porto Alegre, Brazil.

Fernandes, L. A. F. and Oliveira, M. M. (2008). Real-time line detection through an improved Hough transform voting scheme. Pattern Recognit., 41(1):299–314.

Fernandes, L. A. F. and Oliveira, M. M. (2009). Geometric algebra: a powerful tool for solving geometric problems in visual computing. In Tutorials of Sibgrapi, pages 17–30.

Fernandes, L. A. F. and Oliveira, M. M. (2011). A general framework for subspace detection in unordered multidimensional data. IEEE Trans. PAMI. (submitted).

Fernandes, L. A. F. and Oliveira, M. M. (Jan. 11-22, 2010). Introduction to geometric algebra. Lecture Series of the VISGRAF Laboratory at IMPA, Summer School in CG.