In Defense of Gradient-Based Alignment on Densely Sampled Sparse Features

In this chapter, we explore the surprising result that gradient-based continuous optimization methods perform well for the alignment of image/object models when using densely sampled sparse features (HOG, dense SIFT, etc.). Gradient-based approaches for image/object alignment have many desirable properties—inference is typically fast and exact, and diverse constraints can be imposed on the motion of points. However, the presumption that gradients predicted on sparse features would be poor estimators of the true descent direction has meant that gradient-based optimization is often overlooked in favor of graph-based optimization. We show that this intuition is only partly true: sparse features are indeed poor predictors of the error surface, but this has no impact on the actual alignment performance. In fact, for general object categories that exhibit large geometric and appearance variation, sparse features are integral to achieving any convergence whatsoever. How the descent directions are predicted becomes an important consideration for these descriptors. We explore a number of strategies for estimating gradients, and show that estimating gradients via regression in a manner that explicitly handles outliers improves alignment performance substantially. To illustrate the general applicability of gradient-based methods to the alignment of challenging object categories, we perform unsupervised ensemble alignment on a series of nonrigid animal classes from ImageNet.