We propose machine learning methods for the estimation of deformation fields that transform two given objects into each other, thereby establishing a dense point to point correspondence. The fields are computed using a modified support vector machine containing a penalty enforcing that points of one object will be mapped to "similar" points on the other one. Our system, which contains little engineering or domain knowledge, delivers state of the art performance. We present application results including close to photorealistic morphs of 3D head models.