Fitting model parameters to a set of noisy data points is a common problem in computer vision. In this work, we fit the 6D camera pose to a set of noisy correspondences between the 2D input image and a known 3D environment. We estimate these correspondences from the image using a neural network. Since the correspondences often contain outliers, we utilize a robust estimator such as Random Sample Consensus (RANSAC) or Differentiable RANSAC (DSAC) to fit the pose parameters. When the problem domain, e.g. the space of all 2D-3D correspondences, is large or ambiguous, a single network does not cover the domain well. Mixture of Experts (MoE) is a popular strategy to divide a problem domain among an ensemble of specialized networks, so called experts, where a gating network decides which expert is responsible for a given input. In this work, we introduce Expert Sample Consensus (ESAC), which integrates DSAC in a MoE. Our main technical contribution is an efficient method to train ESAC jointly and end-to-end. We demonstrate experimentally that ESAC handles two real-world problems better than competing methods, i.e. scalability and ambiguity. We apply ESAC to fitting simple geometric models to synthetic images, and to camera re-localization for difficult, real datasets.
The human brain can be described as containing a number of functional regions. These regions, as well as the connections between them, play a key role in information processing in the brain. However, most existing multi-voxel pattern analysis approaches either treat multiple regions as one large uniform region or several independent regions, ignoring the connections between them. In this paper we propose to model such connections in an Hidden Conditional Random Field (HCRF) framework, where the classifier of one region of interest (ROI) makes predictions based on not only its voxels but also the predictions from ROIs that it connects to. Furthermore, we propose a structural learning method in the HCRF framework to automatically uncover the connections between ROIs. We illustrate this approach with fMRI data acquired while human subjects viewed images of different natural scene categories and show that our model can improve the top-level (the classifier combining information from all ROIs) and ROI-level prediction accuracy, as well as uncover some meaningful connections between ROIs. We present a new supervised learning procedure for systems composed of many separate networks, each of which learns to handle a subset of the complete set of training cases. The new procedure can be viewed either as a modular version of a multilayer supervised network, or as an associative version of competitive learning. It therefore provides a new link between these two apparently different approaches. We demonstrate that the learning procedure divides up a vowel discrimination task into appropriate subtasks, each of which can be solved by a very simple expert network.