Multi-view triangulation is the gold standard for 3D reconstruction from 2D correspondences given known calibration and sufficient views. However in practice, expensive multi-view setups -- involving tens sometimes hundreds of cameras -- are required in order to obtain the high fidelity 3D reconstructions necessary for many modern applications. In this paper we present a novel approach that leverages recent advances in 2D-3D lifting using neural shape priors while also enforcing multi-view equivariance. We show how our method can achieve comparable fidelity to expensive calibrated multi-view rigs using a limited (2-3) number of uncalibrated camera views.

We propose a simple approach to visual alignment, focusing on the illustrative task of facial landmark estimation. While most prior work treats this as a regression problem, we instead formulate it as a discrete K-way classification task, where a classifier is trained to return one of K discrete alignments. One crucial benefit of a classifier is the ability to report back a (softmax) distribution over putative alignments. We demonstrate that this distribution is a rich representation that can be marginalized (to generate uncertainty estimates over groups of landmarks) and conditioned on (to incorporate top-down context, provided by temporal constraints in a video stream or an interactive human user). Such capabilities are difficult to integrate into classic regression-based approaches. We study performance as a function of the number of classes K, including the extreme "exemplar class" setting where K is equal to the number of training examples (140K in our setting). Perhaps surprisingly, we show that classifiers can still be learned in this setting. When compared to prior work in classification, our K is unprecedentedly large, including many "fine-grained" classes that are very similar. We address these issues by using a multi-label loss function that allows for training examples to be non-uniformly shared across discrete classes. We perform a comprehensive experimental analysis of our method on standard benchmarks, demonstrating state-of-the-art results for facial alignment in videos.

Estimation of facial expressions, as spatio-temporal processes, can take advantage of kernel methods if one considers facial landmark positions and their motion in 3D space. We applied support vector classification with kernels derived from dynamic time-warping similarity measures. We achieved over 99% accuracy - measured by area under ROC curve - using only the 'motion pattern' of the PCA compressed representation of the marker point vector, the so-called shape parameters. Beyond the classification of full motion patterns, several expressions were recognized with over 90% accuracy in as few as 5-6 frames from their onset, about 200 milliseconds.