1. A system for localizing landmarks on face images, the system comprising: an input for receiving a face image; an output for presenting landmarks identified by the system; and a plurality of neural network levels coupled in a cascade from the input to the output; wherein each neural network level produces an estimate of landmarks that is more refined than an estimate of landmarks of a previous neural network level, wherein the plurality of neural network levels comprise: at least three cascaded neural network levels for predicting inner points defining landmarks within a face of the face image, the at least three cascaded neural network levels including the following in order from input to output: a first bounding box estimator that receives the face image as input and produces a first cropped face image as output, the first cropped face image estimating a location of the face within the face image for purposes of estimating inner points, a first initial prediction module that receives the first cropped face image as input and produces a first landmarked face image as output, the first landmarked face image containing an initial prediction of inner points within the face image, and for each of the landmarks to be predicted, a component refinement module that receives the first landmarked face image as input and produces a landmarked component image as output, the landmarked component image containing a refined estimate of inner points defining the landmark, and two cascaded neural network levels for predicting outer points defining a contour of the face of the face image, the two cascaded neural network levels including the following in order from input to output: a second bounding box estimator that receives the face image as input and produces a second cropped face image as output, the second cropped face image estimating a location of the face within the face image for purposes of estimating outer points, and a second initial prediction module that receives the second cropped face image as input and produces a second landmarked face image as output, the second landmarked face image containing a prediction of outer points within the face image.