Active stereo vision and direct surface parameter estimation: curve-to-curve image plane mappings

The projection of structured light is a technique frequently used in computer vision to infer information about the surface structure of scene objects. Many traditional techniques compute a set of points on the object surface via triangulation, and then fit an appropriate surface model to them. The authors explore a new approach which avoids computation of individual 3-D surface points and allows a direct estimation of the parameters of second-order object surface models. The projection of lines onto a quadratic surface (quadric) yields quadratic curves (conics) in the passive image whose parameters can be estimated using a least-squares procedure. If the parameters of at least two passive image curves are known, another least squares fit can be used to estimate the visible 3-D object surface parameters. Computer simulations reveal that the estimation accuracy is moderate, and that the selection of the projected lines is critical. Future efforts are indicated.