Pose estimation from reflections for specular surface recovery

Abstract

This thesis introduces novel methods for estimating the poses of a reference plane from its reflections for specular surface recovery. Traditional methods for specular surface recovery usually introduce a second camera and an auxiliary calibration pattern to calibrate the poses of the reference plane with respect to the camera. The calibration procedures are comparatively tedious. Auto-estimating the poses of the reference plane is therefore an appealing problem. In the first part of this thesis, two novel and practical methods are proposed to recover the poses of a moving reference plane from its reflections produced on the specular surface given its initial position. As for the first approach, the reference plane is constrained to undergo an unknown pure translation. By observing the reflections of the moving reference plane produced on the specular surface, a closed form solution is derived for recovering the unknown translation. Degenerate cases in which the proposed method fails are studied. As for the second approach, the constraint on the motion of the reference plane is removed, and the reference plane can move freely. Again, a closed form solution is derived for the unknown motion defined by a rotation matrix and a translation vector, and the degenerate cases are also presented. The thesis finally considers the problem for auto-calibrating the reference plane against the camera for specular surface recovery without prior knowledge of the reference plane’s initial position. By only observing its reflections produced on the specular surface, the poses of the reference planes can be recovered in two steps. First, by applying a collinearity constraint to the specular correspondences, a simple closed form solution is derived for recovering the poses of the reference plane relative to its initial pose. Second, by applying a ray incidence constraint to the incident rays formed by the specular correspondences and the visual rays cast from the image, a closed form solution is derived for recovering the poses of the reference plane relative to the camera. The shape of the specular surface then follows.