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We present an approach to jointly estimating camera motion and dense scene structure in terms of depth maps from monocular image sequences in driver-assistance scenarios. For two consecutive frames of a sequence taken with a single fast moving camera, the approach combines numerical estimation of egomotion on the Euclidean manifold of motion parameters with variational regularization of dense depth map estimation. Embedding this online joint estimator into a recursive framework achieves a pronounced spatio-temporal filtering effect and robustness. We report the evaluation of thousands of images taken from a car moving at speed up to 100 km/h. The results compare favorably with two alternative settings that require more input data: stereo based scene reconstruction and camera motion estimation in batch mode using multiple frames. The employed benchmark dataset is publicly available.