3D Reconstruction of Planar Surface Patches: A Direct Solution

We propose a novel solution for reconstructing planar surface patches. The theoretical foundation relies on variational calculus, which yields a closed form solution for the normal and distance of a 3D planar surface patch, when an affine transformation is known between the corresponding image region pairs. Although we apply the proposed method to projective cameras, the theoretical derivation itself is not restricted to perspective projection. The method is quantitatively evaluated on a large set of synthetic data as well as on real images of urban scenes, where planar surface reconstruction is often needed. Experimental results confirm that the method provides good reconstructions in real-time.