Semisupervised Manifold Alignment of Multimodal Remote Sensing Images

We introduce a method for manifold alignment of different modalities (or domains) of remote sensing images. The problem is recurrent when a set of multitemporal, multisource, multisensor, and multiangular images is available. In these situations, images should ideally be spatially coregistered, corrected, and compensated for differences in the image domains. Such procedures require massive interaction of the user, involve tuning of many parameters and heuristics, and are usually applied separately. Changes of sensors and acquisition conditions translate into shifts, twists, warps, and foldings of the (typically nonlinear) manifolds where images lie. The proposed semisupervised manifold alignment (SS-MA) method aligns the images working directly on their manifolds and is thus not restricted to images of the same resolutions, either spectral or spatial. SS-MA pulls close together samples of the same class while pushing those of different classes apart. At the same time, it preserves the geometry of each manifold along the transformation. The method builds a linear invertible transformation to a latent space where all images are alike and reduces to solving a generalized eigenproblem of moderate size. We study the performance of SS-MA in toy examples and in real multiangular, multitemporal, and multisource image classification problems. The method performs well for strong deformations and leads to accurate classification for all domains. A MATLAB implementation of the proposed method is provided at http://isp. uv.es/code/ssma.htm.