Untangling fibers by quotient appearance manifold mapping for grayscale shape classification

Appearance manifolds have been one of the most powerful methods for object recognition. However, they could not be used for grayscale shape classification, particularly in three dimensions, such as classifying medical lesion volumes or galaxy images. The main cause of the difficulty is that the appearance manifolds of shape classes have entangled fibers in their embedded Euclidean space. This paper proposes a novel appearance-based method called the quotient appearance manifold mapping to untangle the fibers of the appearance manifolds. First, the quotient manifold is constructed to untangle the fiber bundles of appearance manifolds. The mapping from each point of the manifold to the quotient submanifold is then proposed to classify grayscale shapes. We show the effectiveness in grayscale 3D shape recognition using medical images.