A heat method to interpolate z-stacked cell images that preserves interfaces without explicit identification of object boundaries

A multitude of methods have been developed to morph one image into another. In scientific and medical imaging, it is common to have lower resolution in one imaging direction. To improve the quality of surface meshes generated from these images, morphing is used to produce intermediate images to achieve equal resolution in all directions. The most common method is based on interpolating signed distance functions that describe the shapes of objects in the images. Most methods rely on identification and recording of object boundaries. The situation becomes more complex in the case of interpolating images containing multiple objects of interest wherein the morphing method must not introduce gaps or overlaps of objects in the intermediate images. The goal of the present work was to develop an interpolation method for biological cells in transmission electron microscopy images meeting the constraints listed above. A heat diffusion method was developed that produces steady state isotherms in a 3D model of the intervening space between two images. The isotherms are then used to produce paths from pixels that are unique to a biological cell in one frame towards the overlap region. Instead of identifying boundaries, only membership in the overlap region is tested. For each pixel that terminates paths, the path lengths of all members are normalized to the maximum path length. The path lengths are then used to produce intermediate frames. The method succeeds in avoiding the introduction of gaps or overlap between neighboring biological cells without the need for boundary identification.