Feature guided Gaussian mixture model with semi-supervised EM and local geometric constraint for retinal image registration

Retinal image registration, which can be formulated by matching two sets of sparse features extracted from two observed retinal images, is a crucial step in the diagnosis and treatment of various eye diseases. Existing methods suffer from missing true correspondences or do not fully consider local appearance information, which causes difficulty in matching low-quality retinal images due to insufficient reliable features. In addition, the relationships between retinal image pairs are usually modeled by linear transformation, such as affine transformation, which cannot generate accurate alignments in large viewpoint changes due to the nonplanar eyeball surface. To address these issues, a feature guided Gaussian mixture model (GMM) is proposed for the non-rigid registration of retinal images. We formulate the problem as an estimation of a feature guided mixture of densities: a GMM is fitted to one point set in which the centers of the Gaussian densities characterized by spatial positions associated with local appearance descriptors are constrained to coincide with the other point set. The problem is solved under a maximum-likelihood framework, and semi-supervised expectation-maximization is used to iteratively estimate the feature correspondence and spatial transformation, which is initialized by a set of confidential feature matches obtained previously. Non-rigid transformation is specified in a reproducing kernel Hilbert space, and a local geometric constraint is imposed to establish the transformation estimation for obtaining a meaningful solution. A fast implementation based on sparse approximation is also provided and reduces the time complexity from cubic to quadratic. Moreover, we use the edge map, which can extract more reliable features, as a uniform representation of retinal images. Experimental results on publicly available retinal images show that our approach is robust in different registration tasks and outperforms several competing approaches, especially when data is severely degraded.