Segmentation of Coarse and Fine Scale Features Using Multi-scale Diffusion and Mumford-Shah

Here we present a segmentation algorithm that uses multiscale diffusion with the Mumford-Shah model. The image data inside and outside a surface is smoothed by minimizing an energy functional using a partial differential equation that results in a trade-off between smoothing and data fidelity. We propose a scale-space approach that uses a good deal of diffusion as its coarse scale space and that gradually reduces the diffusion to get a fine scale space. So our algorithm continually moves to a particular diffusion level rather than just using a set diffusion coefficient with the Mumford-Shah model. Each time the smoothing is decreased, the data fidelity term increases and the surface is moved to a steady state. This method is useful in segmenting biomedical images acquired using high-resolution confocal fluorescence microscopy. Here we tested the method on images of individual dendrites of neurons in rat visual cortex. These dendrites are studded with dendritic spines, which have very small heads and faint necks. The coarse scale segments out the dendrite and the brighter spine heads, while avoiding noise. Backing off the diffusion to a medium scale fills in more of the structure, which gets some of the brighter spine necks. The finest scale fills in the small and detailed features of the spines that are missed in the initial segmentation. Because of the thin, faint structure of the spine necks, we incorporate into our level set framework a topology preservation method for the surface which aids in segmentation and keeps a simple topology.