This research is a multidisciplinary effort combining computer science, physics and biology in order to advance a new microscopy technology, digital holographic microscopy (DHM). DHM is a technology that uses the properties of physical optics to image microscopic objects, e.g. transparent cells, digitally in three dimensions from a single capture. DHM, unlike other microscopy approaches, captures some volumetric information in a single capture and so no mechanical scanning of an object is required. Image processing is required to make sense of this data, but few applications of image processing in this domain appear in the literature. This research is a step towards enabling biological specimens to be analyzed at a cellular level in a completely unaltered environment in three dimensions, by using image processing. The techniques that were developed and tested as part of the research in this thesis encompass numerical reconstruction, segmentation and automatic segmentation, noise reduction and surface visualization of three-dimensional (3D) objects.