2011/12/14 by Stefan Sommer, Mads Nielsen, Sommer, Stefan +5 · 1 citation
Computer Science · #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #FOS: Mathematics #Image and Object Detection Techniques #Medical Image Segmentation Techniques #Numerical Analysis (math.NA) #Target Tracking and Data Fusion in Sensor Networks
paper · pdf · doi:10.48550/arxiv.1112.3166
openalex publication_date 2011/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
To achieve sparse parametrizations that allows intuitive analysis, we aim to\nrepresent deformation with a basis containing interpretable elements, and we\nwish to use elements that have the description capacity to represent the\ndeformation compactly. To accomplish this, we introduce in this paper\nhigher-order momentum distributions in the LDDMM registration framework. While\nthe zeroth order moments previously used in LDDMM only describe local\ndisplacement, the first-order momenta that are proposed here represent a basis\nthat allows local description of affine transformations and subsequent compact\ndescription of non-translational movement in a globally non-rigid deformation.\nThe resulting representation contains directly interpretable information from\nboth mathematical and modeling perspectives. We develop the mathematical\nconstruction of the registration framework with higher-order momenta, we show\nthe implications for sparse image registration and deformation description, and\nwe provide examples of how the parametrization enables registration with a very\nlow number of parameters. The capacity and interpretability of the\nparametrization using higher-order momenta lead to natural modeling of\narticulated movement, and the method promises to be useful for quantifying\nventricle expansion and progressing atrophy during Alzheimer's disease.\n