We present a novel variational approach to estimate dense depth maps from multiple images in real-time. By using robust penalizers for both data term and regularizer, our method preserves discontinuities in the depth map. We demonstrate that the integration of multiple images substantially increases the robustness of estimated depth maps to noise in the input images. The integration of our method into recently published algorithms for camera tracking allows dense geometry reconstruction in real-time using a single handheld camera. We demonstrate the performance of our algorithm with real-world data.