Enhancing images painted on manifolds

Abstract

The fields of image processing, computer vision and computer graphics have concentrated traditionally on regular 2D images. Recently, images painted on 2D manifolds are becoming more popular and are used in face recognition, volumetric medical image processing, 3D computer graphics, and many other applications. The need has risen to regularize this type of images. Various manifold representations are the input for these applications. Among the main representations are triangulated manifolds and parametric manifolds. We extend the short time image enhancing Beltrami kernel from 2D images to these manifold representations. This approach suits also other manifold representations that can be easily converted to triangulated manifolds, such as implicit manifolds and point clouds. The arbitrary time step enabled by the use of the kernel filtering approach offers a tradeoff between the accuracy of the flow and its execution time. The numerical scheme used to construct the kernel makes the method applicable to all types of manifolds, including open manifolds and self intersecting manifolds. The calculations are done on the 2D manifold itself and are not affected by the complexity of the manifold or the dimension of the space in which it is embedded. The method is demonstrated on images painted on synthetic manifolds and is used to selectively smooth face images. Incorporating the geometrical information of the face manifolds in the regularization process yields improved results. © Springer-Verlag Berlin Heidelberg 2005.