  Partial differential equations have recently garnered substantial attention
as an image processing framework due to their extensibility, the ability to
rigorously engineer and analyse the governing dynamics as well as the ease of
implementation using numerical methods. This paper explores a novel approach to
image trinarization with a concrete real-world application of classifying
regions of sperm images used in the automatic analysis of sperm morphology. The
proposed methodology engineers a diffusion equation with non-linear source
term, exhibiting three steady-states. The model is implemented as an image
processor using a standard finite difference method to illustrate the efficacy
of the proposed approach. The performance of the proposed approach is
benchmarked against standard image clustering/segmentation methods and shown to
be highly effective.
