Image Manifold Interpolation using Free-Form Deformations

An important class of image data sets depict an object undergoing deformation. When there are only a few underlying causes of the deformation, these images have a natural low-dimensional structure which can be parameterized using manifold learning. This paper presents a method to solve for the deformation field as a function of the manifold coordinates-implicitly optimizing the deformation between all pairs of images simultaneously. Additionally, we provide a mechanism to create images for arbitrary coordinates of the manifold, addressing an important limitation of manifold learning algorithms for the case of images related through deformations. We give quantitative results in an artificial image morphing example and illustrate the method by finding the deformations relating all images of a cardiopulmonary MR image sequence.