Some geometric insight in self-calibration and critical motion sequences

Self-calibration and critical motion sequences are problems which have received a lot of attention lately. The key concept for these problems is the absolute conic which appears as a natural calibration object always present in space. To observe it, however, self-calibration constraints are needed. In this paper a method to represent the rather abstract concept of the absolute conic through real geometric entities is proposed. The main beneet of this approach is that it allows to apply geometric intuition to understand problems related to self-calibration and critical motion sequences. The image of the absolute conic can be represented as an ellipse in the image. In this case self-calibration constraints are translated to simple geometric constraints on this ellipse. Several researchers have recently worked on critical motion sequences for self-calibration. The problem is however that the obtained results are hard to understand. Some cases are very hard to grasp intuitively and in an eeort to do so the proposed method was developed. By mapping the problem to real geometric entities, even the most intricate cases obtained by the previous analyses (often through the help of automated solving tools) can be understood and visualized. Several of these cases are discussed explicitly in this paper. Several new insights are also presented.

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