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- W1994328650 abstract "This paper presents a new group-theoretic perspective for signal and image analysis. It addresses the problem of motion analysis and trajectory determination. The construction exploits the properties of motion parameters to be structured in Lie algebras and Lie groups. The motion models are provided by the group structure which carries an entire theoretical build-up. This theoretical construction is based on a natural association of Lie group representations, minimum-mean-squared-error estimations, and variational principles of optimality. These concepts naturally provide a corresponding association of tools based on continuous wavelet transforms, Kalman filters, and Lagrangians. These tools result in highly parallelizable algorithms based on FFTs, gradients, and dynamic programming. The core of the construction is made of spatiotemporal continuous wavelets that are tuned to the motion parameters to perform motion estimation. The motion parameters consist of scale, orientation, location, velocity, acceleration, rotation, and deformation. The approach allows one to detect moving objects, estimate motion parameters, extract trajectories, suppress decoys and background clutter, and resolve objects with crossing trajectories. It also allows one to select particular motion to be tracked while rejecting others. The paper presents simulations on synthetic scenes including noise and motion jitter." @default.
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- W1994328650 date "2000-01-01" @default.
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- W1994328650 title "SpatioTemporal Wavelets: A Group-Theoretic Construction for Motion Estimation and Tracking" @default.
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- W1994328650 doi "https://doi.org/10.1137/s0036139999351864" @default.
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