Localised manifold learning for cardiac image analysis

Manifold learning is increasingly being used to discover the underlying structure of medical image data. Traditional approaches operate on whole images with a single measure of similarity used to compare entire images. In this way, information on the locality of differences is lost and smaller trends may be masked by dominant global differences. In this paper, we propose the use of multiple local manifolds to analyse regions of images without any prior knowledge of which regions are important. Localised manifolds are created by partitioning images into regular subsections with a manifold constructed for each patch. We propose a framework for incorporating information from the neighbours of each patch to calculate a coherent embedding. This generates a simultaneous dimensionality reduction of all patches and results in the creation of embeddings which are spatially-varying. Additionally, a hierarchical method is presented to enable a multi-scale embedding solution. We use this to extract spatially-varying respiratory and cardiac motions from cardiac MRI. Although there is a complex interplay between these motions, we show how they can be separated on a regional basis. We demonstrate the utility of the localised joint embedding over a global embedding of whole images and over embedding individual patches independently.