Symmetry set

In geometry, the symmetry set is a method for representing the local symmetries of a curve, and can be used as a method for representing the shape of objects by finding the topological skeleton. The medial axis, a subset of the symmetry set is a set of curves which roughly run along the middle of an object.

Let ${\displaystyle I\subseteq \mathbb {R} }$ be an open interval, and ${\displaystyle \gamma :I\to \mathbb {R} ^{2}}$ be a parametrisation of a smooth plane curve.

The symmetry set of ${\displaystyle \gamma (I)\subset \mathbb {R} ^{2}}$ is defined to be the closure of the set of centres of circles tangent to the curve at at least two distinct points (bitangent circles).

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