  Current algorithmic approaches for piecewise affine motion estimation are
based on alternating motion segmentation and estimation. We propose a new
method to estimate piecewise affine motion fields directly without intermediate
segmentation. To this end, we reformulate the problem by imposing piecewise
constancy of the parameter field, and derive a specific proximal splitting
optimization scheme. A key component of our framework is an efficient
one-dimensional piecewise-affine estimator for vector-valued signals. The first
advantage of our approach over segmentation-based methods is its absence of
initialization. The second advantage is its lower computational cost which is
independent of the complexity of the motion field. In addition to these
features, we demonstrate competitive accuracy with other piecewise-parametric
methods on standard evaluation benchmarks. Our new regularization scheme also
outperforms the more standard use of total variation and total generalized
variation.
