Segmentation of visual motion by minimizing convex non-quadratic functionals

A minimization problem is proposed to combine smoothing of locally computed motion data (e.g. normal flow) with the detection of motion boundaries. The continuous formulation of the cost functional allows one to incorporate arbitrary continuity-equations which locally determine apparent motion, and a nonlinear smoothing term adapts to the magnitude of the flow-gradient or to its components divergence, rotation, and shear. The approach has been designed such that gradient descent converges to a unique solution.