[ABE-L] Fwd: title and abstract of my talk

[Alexandre Galvão Patriota]

Prezados,

Na próxima sexta-feira (23/11) às 14hr, haverá um seminário na sala A132 do
Dr.  Ali Al-Sharadqah, professor na Califorina State University at
Northridge, cujos titulo e resumo se encontram abaixo.

*Title*:  Statistical Optimization in Geometric Estimation

* Abstract*:  We will introduce Errors-in-Variables models (EIV) and its
applications in geometric estimation, a widely known problem in computer
vision and image processing. Two problems from geometric estimation will be
discussed: (1) fitting geometric curves, such as circles/or ellipses to a
set of noisy experimental observations, (2) other applications in computer
vision, such as, `Fundamental Matrix' estimation and `Homography'
computation that are essential in 3D-reconstruction.

Under our adopted statistical assumptions, the `Maximum Likelihood
Estimator' (MLE) coincides with the so-called `Orthogonal Distance
Regression' (ODR), which can be obtained iteratively by the Levenberg
Marquardt algorithm. Therefore, other non-iterative but less accurate
algebraic estimators were proposed. In spite of the superior performance of
the MLE and the adequate performance of some algebraic methods, they all
have an infinite first moment, while the least accurate algebraic estimator
has a finite first moment. These controversial results led to some
methodological questions that require further investigation. Therefore, we
developed our unconventional statistical analysis that allowed us to
effectively assess EIV parameter estimates in a general scheme. Then we
theoretically compared between the most popular fits for circle fitting
problem and we showed why and by how much each fit differs from others. The
problem of ellipse fitting is more involved, and as such, we present other
gradient-type iterative methods and we discuss the statistical properties
of ellipse-fitting methods. Our theoretical comparisons led to new
unbeatable fits with superior characteristics that surpass all existing
methods theoretically and experimentally. At the end of the talk, we will
discuss how these methods can be extended to the aforementioned computer
vision applications.

Saudações
Alexandre.
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