We propose a geometric method for visual tracking, in which the 2-D affine motion of a given object template is estimated in a video sequence by means of coordinateinvariant particle filtering on the 2-D affine group Aff(2). Tracking performance is further enhanced through a geometrically defined optimal importance function, obtained explicitly via Taylor expansion of a principal component analysis based measurement function on Aff (2). The efficiency of our approach to tracking is demonstrated via comparative experiments. 991 978-1-4244-3991-1/09/$25.00 ©2009 IEEE

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.

Existing approaches to template-based visual tracking, in which the objective is to continuously estimate the spatial transformation parameters of an object template over video frames, have primarily been based on deterministic optimization, which as is well-known can result in convergence to local optima. To overcome this limitation of the deterministic optimization approach, in this paper we present a novel particle filtering approach to template-based visual tracking. We formulate the problem as a particle filtering problem on matrix Lie groups, specifically the three-dimensional Special Linear group SL(3) and the two-dimensional affine group Aff(2). Computational performance and robustness are enhanced through a number of features: (i) Gaussian importance functions on the groups are iteratively constructed via local linearization; (ii) the inverse formulation of the Jacobian calculation is used; (iii) template resizing is performed; and (iv) parent-child particles are developed and used. Extensive experimental results using challenging video sequences demonstrate the enhanced performance and robustness of our particle filtering-based approach to template-based visual tracking. We also show that our approach outperforms several state-of-the-art template-based visual tracking methods via experiments using the publicly available benchmark data set.

Handling motion blur is one of important issues in vi-

We propose a novel geometric Rao-Blackwellized particle

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