We propose an Active Learning approach to training a segmentation classifier that exploits geometric priors to streamline the annotation process in 3D image volumes. To this end, we use these priors not only to select voxels most in need of annotation but to guarantee that they lie on 2D planar patch, which makes it much easier to annotate than if they were randomly distributed in the volume. A simplified version of this approach is effective in natural 2D images. We evaluated our approach on Electron Microscopy and Magnetic Resonance image volumes, as well as on natural images. Comparing our approach against several accepted baselines demonstrates a marked performance increase.