Traditionally in monocular SLAM, interest features are extracted and matched in successive images. Outliers are rejected a posteriori during a pose estimation process, and then the structure of the scene is reconstructed. In this paper, we propose a new approach for computing robustly and simultaneously the 3D camera displacement, the scene structure and the illumination changes directly from image intensity discrepancies. In this way, instead of depending on particular features, all possible image information is exploited. That problem is solved by using an efficient second-order optimization procedure and thus, high convergence rates and large domains of convergence are obtained. Furthermore, a new solution to the visual SLAM initialization problem is given whereby no assumptions are made either about the scene or the camera motion. The proposed approach is validated on experimental and simulated data. Comparisons with existing methods show significant performance improvements.