SrvfNet: A Generative Network for Unsupervised Multiple Diffeomorphic Functional Alignment

We present SrvfNet, a generative deep learning framework for the joint multiple alignment of large collections of functional data comprising square-root velocity functions (SRVF) to their templates. Our proposed framework is fully unsupervised and is capable of aligning to a predefined template as well as jointly predicting an optimal template from data while simultaneously achieving alignment. Our network is constructed as a generative encoder-decoder architecture comprising fully-connected layers capable of producing a distribution space of the warping functions. We demonstrate the strength of our framework by validating it on synthetic data as well as diffusion profiles from magnetic resonance imaging (MRI) data.