In the field of computational anatomy, the Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework has proved to be highly efficient for addressing the problem of modeling and analyzing of the variability of populations of shapes, allowing for the direct comparison and quantization of diffeomorphic morphometric changes. However, with the progress achieved in medical imaging analysis, the interest for longitudinal data set has substantially increased in the last years and requires the processing of more complex changes, which especially appear during growth or aging phenomena. The observed organisms are subject to transformations over time that are no longer diffeomorphic, at least in a biological sense. One reason might be a gradual creation of new material. The evolution of the shape can then be described by the joint action of a deformation process and a creation process.In this paper, we extend the LDDMM framework to address the problem of non diffeomorphic structural variations in longitudinal data. We keep the geometric central concept of a group of deformations acting on embedded shapes. The need for partial mappings leads to a timevarying dynamic that modifies the action of the group of deformations. We develop a theoretical framework and two algorithms to estimate realistic individual growth scenarios from a set of observations sparsely distributed in time. We present few numerical experiments on animal horns where the shapes are modeled by oriented varifolds. Each computed scenario is parametrized by low-dimensional variables providing the support for statistical analysis.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.