Shape Estimation from Defocus Cue for Microscopy Images via Belief Propagation

In recent years, the usefulness of 3D shape estimation is being realized in microscopic or close-range imaging, as the 3D information can further be used in various applications. Due to limited depth of field at such small distances, the defocus blur induced in images can provide information about the 3D shape of the object. The task of `shape from defocus' (SFD), involves the problem of estimating good quality 3D shape estimates from images with depth-dependent defocus blur. While the research area of SFD is quite well-established, the approaches have largely demonstrated results on objects with bulk/coarse shape variation. However, in many cases, objects studied under microscopes often involve fine/detailed structures, which have not been explicitly considered in most methods. In addition, given that, in recent years, large data volumes are typically associated with microscopy related applications, it is also important for such SFD methods to be efficient. In this work, we provide an indication of the usefulness of the Belief Propagation (BP) approach in addressing these concerns for SFD. BP has been known to be an efficient combinatorial optimization approach, and has been empirically demonstrated to yield good quality solutions in low-level vision problems such as image restoration, stereo disparity estimation etc. For exploiting the efficiency of BP in SFD, we assume local space-invariance of the defocus blur, which enables the application of BP in a straightforward manner. Even with such an assumption, the ability of BP to provide good quality solutions while using non-convex priors, reflects in yielding plausible shape estimates in presence of fine structures on the objects under microscopy imaging.