A-expansion for multiple "hedgehog" shapes
This addresses segmentation problems with overlapping colors and weak edges, particularly in medical imaging, but is incremental as it extends star-convexity to multiple shapes.
The paper tackles multiobject segmentation with shape constraints by proposing a method where objects are restricted to separate 'hedgehog' shapes, showing that a-expansion moves are submodular for these constraints and enabling applications like separating non-star organs in medical data.
Overlapping colors and cluttered or weak edges are common segmentation problems requiring additional regularization. For example, star-convexity is popular for interactive single object segmentation due to simplicity and amenability to exact graph cut optimization. This paper proposes an approach to multiobject segmentation where objects could be restricted to separate "hedgehog" shapes. We show that a-expansion moves are submodular for our multi-shape constraints. Each "hedgehog" shape has its surface normals constrained by some vector field, e.g. gradients of a distance transform for user scribbles. Tight constraint give an extreme case of a shape prior enforcing skeleton consistency with the scribbles. Wider cones of allowed normals gives more relaxed hedgehog shapes. A single click and +/-90 degrees normal orientation constraints reduce our hedgehog prior to star-convexity. If all hedgehogs come from single clicks then our approach defines multi-star prior. Our general method has significantly more applications than standard one-star segmentation. For example, in medical data we can separate multiple non-star organs with similar appearances and weak or noisy edges.