Auto guiding a mobile projector

Abstract

This paper presents a mathematical model, simulation and analysis of auto guided (robot) mobile projector using a feedback camera. The camera-projector system is consisting of a mobile projector, a stationary camera, and a planar screen. The camera is calibrated and can capture the full planar screen site with some accuracy error. For an ideal system, the geometrically compensating image projected from the projector need to fit onto the screen so that the displayed image will always be aligned and centered with the screen accurately. The system needs to automatically perform calculation on-line on the captured frame, find the coordinates of the corresponding quadrilateral and recovers the correct position and orientation for auto guidance of the mobile projector. The proposed approach adopts a mathematical model to measure the actual coordinates of the projector from which we calculate the transformation matrix for (robot) mobile projector. The matrix is used by the robot to auto guide itself back to the intended correct position. Practically, we apply the mathematical model on an approximated quadrilateral of a captured frame, estimate coordinates of the projector and send the matrix transformation for the (robot) mobile projector to auto adjust its position and orientation. Our simulation showed that the error estimation of the estimated position and orientation is proportional to applied error due to the error accuracy of the camera. When the mathematical model is applied repetitively, the auto fitting of the frame in the screen reaches the best estimation with an error of 27% less than the applied one and only within the second iteration.