  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.
