# Perceptual Grouping from Motion Cues Using Tensor Voting in 4-D

## Abstract

We present a novel approach for motion grouping from two frames, that recovers the dense velocity field, motion boundaries and regions, based on a 4-D Tensor Voting computational framework. Given two sparse sets of point tokens, we encode the image position and potential velocity for each token into a 4-D tensor. The voting process then enforces the motion smoothness while preserving motion discontinuities, thus selecting the correct velocity for each input point, as the most salient token. By performing an additional dense voting step we infer velocities at every pixel location, motion boundaries and regions. Using a 4-D space for this Tensor Voting approach is essential, since it allows for a spatial separation of the points according to both their velocities and image coordinates. Unlike other methods that optimize a specific objective function, our approach does not involve initialization or search in a parametric space, and therefore does not suffer from local optima or poor convergence problems. We demonstrate our method with synthetic and real images, by analyzing several difficult cases — opaque and transparent motion, rigid and non-rigid motion, curves and surfaces in motion.

## Keywords

Optical Flow Motion Capture Motion Boundary Perceptual Group Candidate Match## References

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