Bilateral symmetry of object silhouettes under perspective projection

Symmetry is an important property of objects and is exhibited in different forms e.g., bilateral, rotational, etc. This paper presents an algorithm for computing the bilateral symmetry of silhouettes of shallow objects under perspective distortion, exploiting the invariance of the cross ratio to projective transformations. The basic idea is to use the cross ratio to compute a number of midpoints of cross sections and then fit a straight line through them. The goodness-of-fit determines the likelihood of the line to be the axis of symmetry. We analytically estimate the midpointpsilas location as a function of the vanishing point for a given object silhouette. Hence finding the symmetry axis amounts to a 2D search in the space of vanishing points. We present experiments on two datasets as well as Internet images of symmetric objects that validate our approach.