Software implementations of 3D nonrigid image registration, an essential tool in medical applications like radiotherapies and image-guided surgeries, run excessively slow on traditional computers. These algorithms can be accelerated using hardware methods by exploiting parallelism at different levels in the algorithm. We present here, an implementation of a free-form deformation-based algorithm on a field programmable gate array (FPGA) with a customized, parallel and pipelined architecture. We overcome the performance bottlenecks and gain speedups of up to 40x over traditional computers while achieving accuracies comparable to software implementations. In this work, we also present a method to optimize the deformation field using a gradient descent-based optimization scheme and solve the problem of mesh folding, commonly encountered during registration using free-form deformations, using a set of linear constraints. Finally, we present the use of novel dataflow modeling tools to automatically map registration algorithms to hardware like FPGAs while allowing for dynamic reconfiguration.