Self-calibration is one of the most active issues concerning vision-based 3D measurements. However, in the case of the light sectioning method, there has been little research conducted on self-calibration techniques. In this paper, we study the problem of self-calibration for an active vision system which uses line lasers and a single camera. The problem can be defined as the estimation of multiple laser planes from the curves of laser reflections observed from a sequence of images captured by

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... single camera. The constraints of the problem can be obtained from observed intersection points between the curves. In this condition, the problem is formulated as simultaneous polynomial equations, in which the number of equations is larger than the number of variables. Approximated solutions of the equations can be computed by using Gröbner bases. By refining them using nonlinear optimization, the final result can be obtained. We developed an actual 3D measurement system using the proposed method, which consists of only a laser projector with two line lasers and a single camera. Users are just required to move the projector freely so that the projected lines sweep across the surface of the scene to get the 3D shape.