Maximum likelihood estimation in calibrating a stereo camera setup

Motion and deformation of the cardiac wall may be measured by following the positions of implanted radiopaque markers in three dimensions, using two x -ray cameras simultaneously. Regularly, calibration of the position measure ment system is obtained by registration of the images of a calibration obje ct, containing 10-20 radiopaque markers at known positions. Unfortunately, an accidental change of the position of a camera after calibration requires complete recalibration. Alternatively, redundant information in the measur ed image positions of stereo pairs can be used for calibration. Thus, a sep arate calibration procedure can be avoided. In the current study a model is developed that describes the geometry of the camera setup by five dimensio nless parameters. Maximum Likelihood (ML) estimates of these parameters wer e obtained in an error analysis. It is shown that the ML estimates can be f ound by application of a nonlinear least squares procedure. Compared to the standard unweighted least squares procedure, the ML method resulted in mor e accurate estimates without noticeable bias. The accuracy of the ML method was investigated in relation to the object aperture. The reconstruction pr oblem appeared well conditioned as long as the object aperture is larger th an 0.1 rad. The angle between the two viewing directions appeared to be the parameter that was most likely to cause major inaccuracies in the reconstr uction of the 3-D positions of the markers. Hence, attempts to improve the robustness of the method should primarily focus on reduction of the error i n this parameter. (C) 1999 American Association of Physicists in Medicine. [S0094-2405(99)02502-X].