RNDr. Martin Bujòák, PhD
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Research interests:
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My PhD thesis:
Algebraic solutions to absolute pose problemsAbstract
Estimating internal and external camera calibration is a very basic element in many computer vision applications. Camera localization, structure from motion, scene reconstruction, object localization, tracking and recognition are just a few examples of such applications. This thesis focuses on minimal algorithms for estimating camera calibration, i.e. algorithms which use all possible constraints and minimal number of inputs, for example point correspondences between 2D and 3D space, to calculate the camera pose and other camera parameters such as unknown focal length or coefficients modeling lens distortion.
In this work, we first study the absolute pose problem for a calibrated camera, which was an intensively studied problem in the past and many solutions were already developed. The problem itself can be formulated as a simple system of polynomial equations. Researches in the past focused on how to solve this problem, searched for different solutions, compared numerical stability, speed, or studied how to calculate the camera pose from more than three 2D-to-3D point correspondences. We review the state-of-the-art and present our own formulations to this problem based on the well known invariants and properties of the problem. We provide solutions to our formulations using different methods for solving system of polynomial equations. Next we provide solutions to the absolute pose for a camera without complete internal calibration or for a camera where some additional information about the scene is known. In particular, absolute pose of a camera calibrated up to an unknown focal length or a camera with unknown focal length and unknown radial distortion. Furthermore, we describe special cases when some of the scene or camera priors are known, for example, scene is planar, scene is non-planar or when vertical direction of a camera is known from a gyroscope or a vanishing point. The main contribution of this thesis is in finding minimal or finding optimal solutions to these problems. We formulate all studied problems, from very basic relations between 3D space and 2D measurements, show different formulations and how can different invariants be helpful in reducing the number of unknowns or to simplify the problem. All our formulations lead to systems of polynomial equations. We show how to solve these systems using methods for solving systems of polynomial equations, which we developed during our research. Solution the problems are evaluated with high level of detail and with focus on important properties such as numerical stability and resistance to noise in data. We compare our new solvers with the state-of-the-art on synthetic and real data. In this thesis we further present a general method which speeds up most of the presented solvers and can be also used to speed up other solvers based on eigenvalue computation. We have also found the connection between methods for converting basis of an ideal to a basis with respect to the lexicographic ordering and calculation of the characteristic polynomial of an action matrix. |
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Live & demo:
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Publications:
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Teaching:
But don't be disappointed when they are not; it helps them to keep trying. -- Merry Browne
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About me:
Education
Skills
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Other activities / projects:
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by Martin Bujnak © 2013. All rights reserved. |