SUMMARYWe address general filtering problems on the Euclidean groupSE(3). We first generalize, to stochastic nonlinear systems evolving onSE(3), the particle filter of Liu and West for simultaneous estimation of the state and covariance. The filter is constructed in a coordinate-invariant way, and explicitly takes into account the geometry ofSE(3) andP(n), the space of symmetric positive definite matrices. Some basic results for bilinear systems onSE(3) with linear and quadratic measurements are also derived. Three examples—GPS attitude estimation, needle tip location, and vision-based robot end-effector pose estimation—are presented to illustrate the framework.
Recently, convolutional neural networks (CNN) have been successfully applied to view synthesis problems. However, such CNN-based methods can suffer from lack of texture details, shape distortions, or high computational complexity. In this paper, we propose a novel CNN architecture for view synthesis called "Deep View Morphing" that does not suffer from these issues. To synthesize a middle view of two input images, a rectification network first rectifies the two input images. An encoder-decoder network then generates dense correspondences between the rectified images and blending masks to predict the visibility of pixels of the rectified images in the middle view. A view morphing network finally synthesizes the middle view using the dense correspondences and blending masks. We experimentally show the proposed method significantly outperforms the state-of-the-art CNN-based view synthesis method. *
We present a particle filtering algorithm for visual tracking, in which the state equations for the object motion evolve on the two-dimensional affine group. We first formulate, in a coordinateinvariant and geometrically meaningful way, particle filtering on the affine group that allows for combined state-covariance estimation. Measurement likelihoods are also calculated from the image covariance descriptors using incremental principal geodesic analysis, a generalization of principal component analysis to curved spaces. Comparative visual tracking studies demonstrate the increased robustness of our tracking algorithm.
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