Abstract: A computer model is trained to account for data samples in a high-dimensional space as lying on different manifolds, rather than a single manifold to represent the data set, accounting for the data set as a whole as a union of manifolds. Different data samples that may be expected to belong to the same underlying manifold are determined by grouping the data. For generative models, a generative model may be trained that includes a sub-model for each group trained on that group's data samples, such that each sub-model can account for the manifold of that group. The overall generative model includes information describing the frequency to sample from each sub-model to correctly represent the data set as a whole in sampling. Multi-class classification models may also use the grouping to improve classification accuracy by weighing group data samples according to the estimated latent dimensionality of the group.

Abstract: A method for estimating a pose of an object includes: receiving, by a processor, an observed image depicting the object from a viewpoint; computing, by the processor, an instance segmentation map identifying a class of the object depicted in the observed image; loading, by the processor, a 3-D model corresponding to the class of the object; computing, by the processor, a rendered image of the 3-D model in accordance with an initial pose estimate of the object and the viewpoint of the observed image; computing, by the processor, a plurality of dense image-to-object correspondences between the observed image of the object and the 3-D model based on the observed image and the rendered image; and computing, by the processor, the pose of the object based on the dense image-to-object correspondences.