On symmetry, perspectivity, and level-set-based segmentation.

We introduce a novel variational method for the extraction of objects with either bilateral or rotational symmetry in the presence of perspective distortion. Information on the symmetry axis of the object and the distorting transformation is obtained as a by--product of the segmentation process. The key idea is the use of a flip or a rotation of the image to segment as if it were another view of the object. We call this generated image the symmetrical counterpart image. We show that the symmetrical counterpart image and the source image are related by planar projective homography. This homography is determined by the unknown planar projective transformation that distorts the object symmetry. The proposed segmentation method uses a level-set-based curve evolution technique. The extraction of the object boundaries is based on the symmetry constraint and the image data. The symmetrical counterpart of the evolving level-set function provides a dynamic shape prior. It supports the segmentation by resolving possible ambiguities due to noise, clutter, occlusions, and assimilation with the background. The homography that aligns the symmetrical counterpart to the source level-set is recovered via a registration process carried out concurrently with the segmentation. Promising segmentation results of various images of approximately symmetrical objects are shown.