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To date, the successful application of\nPointNet to point cloud registration has remained elusive. In this paper we\nargue that PointNet itself can be thought of as a learnable \"imaging\" function.\nAs a consequence, classical vision algorithms for image alignment can be\napplied on the problem - namely the Lucas & Kanade (LK) algorithm. Our central\ninnovations stem from: (i) how to modify the LK algorithm to accommodate the\nPointNet imaging function, and (ii) unrolling PointNet and the LK algorithm\ninto a single trainable recurrent deep neural network. We describe the\narchitecture, and compare its performance against state-of-the-art in common\nregistration scenarios. The architecture offers some remarkable properties\nincluding: generalization across shape categories and computational efficiency\n- opening up new paths of exploration for the application of deep learning to\npoint cloud registration. 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