Morphology and Optics of Human Embryos from Light Microscopy

Evaluation of fertility of living embryos is of practical importance in the daily routinesat fertility clinics and an ongoing biological research topic. Living embryos may be stud-ied through a light microscope. By focusing the microscope at different optical sections,the three-dimensional structure of the embryo may be studied. The purpose of the Ferti-morph project is to develop methods for fertility evaluation via measurements of the three-dimensional embryo morphology.Reconstruction of the 3D structure of living embryos from optical sectional images, mustbe based on a model of the image formation. The image formation is a result of the opticalcharacteristics of the embryo and the microscope optics used. Human embryos are "large"refractive objects, so the usual model of rectilinear light propagation in a 3D Euclideangeometry does not hold. Since this model of light propagation is central in the linear trans-lational invariant models of light microscopy, these traditional models of image formationand corresponding techniques for 3D reconstruction cannot be used. Instead the morphologyhas to be inferred directly from the images.A major challenge in such inferences, in addition to modelling the image formation, ismodelling of the morphology and shape variability. Models of shape variability are neededas model structures for analyzing object shape and as tools for inferring and describing thetask specific prior knowledge of the imaged objects, often essential for successful inference.I present investigations of embryo optics, Hoffman Modulation Contrast image formation,and 3D reconstruction of human embryo morphology from HMC images all in the contextof the Fertimorph project. In addition to this, general Lie group models of point set variabil-ity inducing well-defined shape variability are discussed, as basic tools in models of shape;and the descriptive power of linear transformation groups for modelling shape variability isanalyzed.