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Robust Analysis





Research: Estimation under Heteroscedasticity

In the errors-in-variables model all the components of a measurement vector are corrupted by noise. When the structure of the model is polynomial, linearization of the estimation problem introduces data-dependent (heteroscedastic) noise. The estimator developed by us provides an iterative solution which has superior numerical behavior, and compares favorably with the Levenberg-Marquardt based direct solution of the original, nonlinear problem. A general, multivariate version is available and was applied to several vision problems: ellipse fitting, estimation of the fundamental matrix, 3D rigid motion from stereo data, calibration etc.


Heteroscedastic regression
C++ code implementing the estimation of errors-in-variables models under point dependent noise. It includes examples for linear, ellipse, fundamental matrix and trifocal tensor estimation. The theory is described in Estimation of nonlinear errors-in-variables models for computer vision applications.
For comments, please contact Bogdan Georgescu.

Please use the link "Abstract" to see the publishing history of a paper.
The links "Paper" also contain the abstract.

B. Matei, P. Meer: Estimation of nonlinear errors-in-variables models for computer vision applications.
Abstract    Paper (pdf)

R. Subbarao, P. Meer, Y. Genc: A balanced approach to 3D tracking from image streams.
Abstract   Paper (pdf)

B. Georgescu, P. Meer: Balanced recovery of 3D structure and camera motion from uncalibrated image sequences.
Abstract   Paper (pdf)   Paper (ps.gz)

J. Bride, P. Meer: Registration via direct methods: A statistical approach.
Abstract    Paper (pdf)    Paper (ps.gz)

B. Matei, B. Georgescu, P. Meer: A versatile method for trifocal tensor estimation.
Abstract   Paper (pdf)   Paper (ps.gz)

B. Matei, P. Meer: Reduction of bias in maximum likelihood ellipse fitting.
Abstract   Paper (pdf)   Paper (ps.gz)

B. Matei, P. Meer: A general method for errors-in-variables problems in computer vision.
Abstract   Paper (pdf)   Paper (ps.gz)

B. Matei, P. Meer: Bootstrapping errors-in-variables models.
Abstract   Paper (pdf)   Paper (ps.gz)

B. Matei, P. Meer: Optimal rigid motion estimation and performance evaluation with bootstrap.
BEST STUDENT PAPER AWARD     1999 IEEE Computer Vision and Pattern Recognition Conference.
Abstract   Paper (pdf)   Paper (ps.gz)

Y. Leedan, P. Meer: Heteroscedastic regression in computer vision: Problems with bilinear constraint.
Abstract   Paper (pdf)   Paper (ps.gz)

Related Ph.D Theses

Bogdan Matei: Heteroscedastic errors-in-variables models in computer vision.

Yoram Leedan: Statistical analysis of quadratic problems in computer vision.