IEEE Transactions on Pattern Analysis and Machine Intelligence
On the estimation of optical flow: relations between different approaches and some new results
Artificial Intelligence
Measurement of Visual Motion
From Images to Surfaces: A Computational Study of the Human Early Visual System
From Images to Surfaces: A Computational Study of the Human Early Visual System
On the Mathematical Foundations of Smoothness Constraints for the
On the Mathematical Foundations of Smoothness Constraints for the
A Fast Scalable Algorithm for Discontinuous Optical Flow Estimation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Reliable Estimation of Dense Optical Flow Fields with Large Displacements
International Journal of Computer Vision
A Theoretical Framework for Convex Regularizers in PDE-Based Computation of Image Motion
International Journal of Computer Vision
Variational Optic Flow Computation with a Spatio-Temporal Smoothness Constraint
Journal of Mathematical Imaging and Vision
Optic Flow Field Segmentation and Motion Estimation Using a Robust Genetic Partitioning Algorithm
IEEE Transactions on Pattern Analysis and Machine Intelligence
Symmetrical Dense Optical Flow Estimation with Occlusions Detection
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
Accurate optical flow computation under non-uniform brightness variations
Computer Vision and Image Understanding
Symmetrical Dense Optical Flow Estimation with Occlusions Detection
International Journal of Computer Vision
Accurate optical flow computation under non-uniform brightness variations
Computer Vision and Image Understanding
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Gradient-based approaches to the computation of optical flow often use a minimization technique incorporating a smoothness constraint on the optical flow field. The author derives the most general form of such a smoothness constraint that is quadratic in first derivatives of the grey-level image intensity function based on three simple assumptions about the smoothness constraint: (1) it must be expressed in a form that is independent of the choice of Cartesian coordinate system in the image: (2) it must be positive definite; and (3) it must not couple different component of the optical flow. It is shown that there are essentially only four such constraints; any smoothness constraint satisfying (1), (2), or (3) must be a linear combination of these four, possibly multiplied by certain quantities invariant under a change in the Cartesian coordinate system. Beginning with the three assumptions mentioned above, the author mathematically demonstrates that all best-known smoothness constraints appearing in the literature are special cases of this general form, and, in particular, that the 'weight matrix' introduced by H.H. Nagel is essentially (modulo invariant quantities) the only physically plausible such constraint.