  Gradient-descent methods have exhibited fast and reliable performance for
image alignment in the facial domain, but have largely been ignored by the
broader vision community. They require the image function be smooth and
(numerically) differentiable -- properties that hold for pixel-based
representations obeying natural image statistics, but not for more general
classes of non-linear feature transforms. We show that transforms such as Dense
SIFT can be incorporated into a Lucas Kanade alignment framework by predicting
descent directions via regression. This enables robust matching of instances
from general object categories whilst maintaining desirable properties of Lucas
Kanade such as the capacity to handle high-dimensional warp parametrizations
and a fast rate of convergence. We present alignment results on a number of
objects from ImageNet, and an extension of the method to unsupervised joint
alignment of objects from a corpus of images.
