Robust line detection using a weighted MSE estimator

In this paper we introduce a novel line detection algorithm based on a weighted minimum mean square error (MSE) formulation. This algorithm has been developed to enable an autonomous robot to follow a white line drawn on the floor, but is general in nature and widely applicable to line detection problems. Traditional approaches to line detections consist of two stages, an edge detection stage and a line detection stage using the edge detection result. There are several problems with this approach. First, the initial edge detection stage is sensitive to noise. Second, the second stage does not use all the information available in the image and therefore incorrect decisions made by the first stage cannot be corrected in the second stage. The proposed algorithm achieves its robustness by operating in one step, using all pixels of the image (correctly weighted) and not using any thresholds. The detected line is the solution of a weighted MSE problem. The following three questions are answered in the paper: (I) what mathematical model should be used for the line? (II) how should the weighted MSE problem be set up so that the optimal solution results in the parameters of the line model? And (III), how should the pixels in the image be weighted such that a weighted MSE optimal solution results in a robust line detection? Experimental results demonstrate the performance of the algorithm in noiseless and noisy conditions.