Principal Warps: Thin-Plate Splines and the Decomposition of Deformations
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Method for Registration of 3-D Shapes
IEEE Transactions on Pattern Analysis and Machine Intelligence - Special issue on interpretation of 3-D scenes—part II
Alignment by maximization of mutual information
Alignment by maximization of mutual information
Unsupervised Learning of Image Manifolds by Semidefinite Programming
International Journal of Computer Vision
Segmentation informed by manifold learning
EMMCVPR'05 Proceedings of the 5th international conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Segmenting cardiopulmonary images using manifold learning with level sets
CVBIA'05 Proceedings of the First international conference on Computer Vision for Biomedical Image Applications
Learning basic patterns from repetitive texture surfaces under non-rigid deformations
ICIAR'07 Proceedings of the 4th international conference on Image Analysis and Recognition
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Isomap is an exemplar of a set of data driven non-linear dimensionality reduction techniques that have shown promise for the analysis of images and video. These methods parameterize each image as coordinates on a low-dimensional manifold, but, unlike PCA, the low dimensional parameters do not have an explicit meaning, and are not natural projection operators between the high and low-dimensional spaces. For the important special case of image sets of an unknown object undergoing an unknown deformation, we show that Isomap gives a valuable pre-processing step to find an ordering of the images in terms of their deformation. Using the continuity of deformation implied in the Isomap ordering allows more accurate solutions for a thin-plate spline deformation from a specific image to all others. This defines a mapping between the Isomap coordinates and a specific deformation, which is extensible to give projection functions between the image space and the Isomap space. Applications of this technique are shown for cardiac MRI images undergoing chest cavity deformation due to patient breathing.