Deep Directional Statistics: Pose Estimation with Uncertainty Quantification

Modern deep learning systems successfully solve many perception tasks such as object pose estimation when the input image is of high quality. However, in challenging imaging conditions such as on low-resolution images or when the image is corrupted by imaging artifacts, current systems degrade considerably in accuracy. While a loss in performance is unavoidable, we would like our models to quantify their uncertainty in order to achieve robustness against images of varying quality. Probabilistic deep learning models combine the expressive power of deep learning with uncertainty quantification. In this paper, we propose a novel probabilistic deep learning model for the task of angular regression. Our model uses von Mises distributions to predict a distribution over object pose angle. Whereas a single von Mises distribution is making strong assumptions about the shape of the distribution, we extend the basic model to predict a mixture of von Mises distributions. We show how to learn a mixture model using a finite and infinite number of mixture components. Our model allows for likelihood-based training and efficient inference at test time. We demonstrate on a number of challenging pose estimation datasets that our model produces calibrated probability predictions and competitive or superior point estimates compared to the current state-of-the-art

Fast Optimal Transport Averaging of Neuroimaging Data

Knowing how the Human brain is anatomically and functionally organized at the level of a group of healthy individuals or patients is the primary goal of neuroimaging research. Yet computing an average of brain imaging data defined over a voxel grid or a triangulation remains a challenge. Data are large, the geometry of the brain is complex and the between subjects variability leads to spatially or temporally non-overlapping effects of interest. To address the problem of variability, data are commonly smoothed before group linear averaging. In this work we build on ideas originally introduced by Kantorovich to propose a new algorithm that can average efficiently non-normalized data defined over arbitrary discrete domains using transportation metrics. We show how Kantorovich means can be linked to Wasserstein barycenters in order to take advantage of an entropic smoothing approach. It leads to a smooth convex optimization problem and an algorithm with strong convergence guarantees. We illustrate the versatility of this tool and its empirical behavior on functional neuroimaging data, functional MRI and magnetoencephalography (MEG) source estimates, defined on voxel grids and triangulations of the folded cortical surface.Comment: Information Processing in Medical Imaging (IPMI), Jun 2015, Isle of Skye, United Kingdom. Springer, 201

An Unsupervised Learning Model for Deformable Medical Image Registration

We present a fast learning-based algorithm for deformable, pairwise 3D medical image registration. Current registration methods optimize an objective function independently for each pair of images, which can be time-consuming for large data. We define registration as a parametric function, and optimize its parameters given a set of images from a collection of interest. Given a new pair of scans, we can quickly compute a registration field by directly evaluating the function using the learned parameters. We model this function using a convolutional neural network (CNN), and use a spatial transform layer to reconstruct one image from another while imposing smoothness constraints on the registration field. The proposed method does not require supervised information such as ground truth registration fields or anatomical landmarks. We demonstrate registration accuracy comparable to state-of-the-art 3D image registration, while operating orders of magnitude faster in practice. Our method promises to significantly speed up medical image analysis and processing pipelines, while facilitating novel directions in learning-based registration and its applications. Our code is available at https://github.com/balakg/voxelmorph .Comment: 9 pages, in CVPR 201