Feature-Centered First Order Structure Tensor Scale-Space in 2D and 3D

The structure tensor method is often used for 2D and 3D analysis of imaged structures, but its results are in many cases very dependent on the user’s choice of method parameters. We simplify this parameter choice in first order structure tensor scale-space by directly connecting the width of the derivative filter to the size of image features. By introducing a ring-filter step, we substitute the Gaussian integration/smoothing with a method that more accurately shifts the derivative filter response from feature edges to their center. We further demonstrate how extracted structural measures can be used to correct known inaccuracies in the scale map, resulting in a reliable representation of the feature sizes both in 2D and 3D. Compared to the traditional first order structure tensor, or previous structure tensor scale-space approaches, our solution is much more accurate and can serve as an out-of-the-box method for extracting a wide range of structural parameters with minimal user input.

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A New Strategy for Combining Nonlinear Kalman Filters With Smooth Variable Structure Filters

Bayesian filters exemplified by the celebrated Kalman Filter (KF), and its non-linear variants rely on a fairly accurate state-space model of the system under study. To address the issue of modelling uncertainty in state estimation, the Smooth Variable Structure Filter (SVSF) was proposed in 2007. Since then, several SVSF variants have been proposed to extend its domain of applicability. In some of these algorithms, SVSF has been viewed as a complementary approach alongside the well-established nonlinear Kalman Filters. This paper seeks a general framework for SVSF formulation to unify some of the recent developments in SVSF literature under one umbrella. In this way, the SVSF variants are revisited as special cases of the proposed framework. This paper proposes a new strategy to combine SVSF filters with other nonlinear filters and puts existing SVSF filters under one umbrella. Six filters are formulated based on the proposed method of combining filters. The proposed filters relax limitations of existing SVSF variants, making the proposed filters more universal. In simulations, the new filters outperform state-of-the-art nonlinear KFs and some existing SVSF filters. To demonstrate the merits of the proposed framework, the new filters are applied to target tracking and are comparatively evaluated.

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