  Many computer vision problems are formulated as the optimization of a cost
function. This approach faces two main challenges: (i) designing a cost
function with a local optimum at an acceptable solution, and (ii) developing an
efficient numerical method to search for one (or multiple) of these local
optima. While designing such functions is feasible in the noiseless case, the
stability and location of local optima are mostly unknown under noise,
occlusion, or missing data. In practice, this can result in undesirable local
optima or not having a local optimum in the expected place. On the other hand,
numerical optimization algorithms in high-dimensional spaces are typically
local and often rely on expensive first or second order information to guide
the search. To overcome these limitations, this paper proposes Discriminative
Optimization (DO), a method that learns search directions from data without the
need of a cost function. Specifically, DO explicitly learns a sequence of
updates in the search space that leads to stationary points that correspond to
desired solutions. We provide a formal analysis of DO and illustrate its
benefits in the problem of 3D point cloud registration, camera pose estimation,
and image denoising. We show that DO performed comparably or outperformed
state-of-the-art algorithms in terms of accuracy, robustness to perturbations,
and computational efficiency.
