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This paper proposes a new framework for real-time estimation of the onboard stereo head's position and orientation relative to the road surface, which is required for any advanced driver-assistance application. This framework can be used with all road types: highways, urban, etc. Unlike existing works that rely on feature extraction in either the image domain or 3-D space, we propose a framework that directly estimates the unknown parameters from the stream of stereo pairs' brightness. The proposed approach consists of two stages that are invoked for every stereo frame. The first stage segments the road region in one monocular view. The second stage estimates the camera pose using a featureless registration between the segmented monocular road region and the other view in the stereo pair. This paper has two main contributions. The first contribution combines a road segmentation algorithm with a registration technique to estimate the online stereo camera pose. The second contribution solves the registration using a featureless method, which is carried out using two different optimization techniques: 1) the differential evolution algorithm and 2) the Levenberg-Marquardt (LM) algorithm. We provide experiments and evaluations of performance. The results presented show the validity of our proposed framework.