The reconstruction of dense depth maps is of great value to resource-constrained Mirco Air Vehicles (MAVs), in the pursuit of achieving autonomous flight with a high situational awareness. Most MAVs implement sensing methods which provide a sparse depth map, limiting their capabilities significantly. This article introduces two novel methods to enhance existing depth reconstruction algorithms in terms of geometric reconstruction, depth approximation and computational time. The first contribution is the introduction of a novel method that includes edge information from the image-domain into the depth-regularization problem. This to enhance the retrieval of the complete scene geometry. The second contribution is a novel scheme which includes temporal information in the reconstruction approach, allowing extremely sparse depth scenes to be reconstructed. By estimating the geometric transformation with optical flow, previous depth reconstructions can be used as initial solutions for the current depth-regularization problem. Empirical results show a consistent reduction reconstruction error, while at the same time reducing the computational time. Qualitative estimation shows significant improvement in the retrieval of scene geometry.