Reconstruction of missing cells by a Killing energy minimizing nonrigid image registration

Fluorescent microscopy has been a popular and important tool for studying live cells. One challenge of analyzing cell images obtained from fluorescent microscopy is that cells in fluorescent images frequently disappear and reappear, making cell tracking difficult. In this paper, we present an image registration approach which can reconstruct both the cell appearance and location of the missing cells from the image frames where the cells become invisible. The idea is to perform an image registration on the images before and after a cell disappears. The missing image frames between these two images are given by the intermediate registration results. The formulation is based on the nonrigid particle registration model, which captures soft deformation of the cells. In addition, to obtain natural and more rigid cell movements such as translation and rotation, we propose a new registration technique which is Killing energy minimizing, motivated by the fact that a Killing vector field with zero Killing energy will generate an isometric deformation. We will present reconstruction results of C2C12 cells in fluorescent images to illustrate the effectiveness of our model by different numerical examples.