Efficient image segmentation using partial differential equations and morphology

The goal of this paper is to investigate segmentation methods that eombine fast preproeessing algorithms using partial differential equations (PD Es) with a watershed transformation with region merging. VVeeonsider two well-founded PDE methods: a nonlinear isotropie diffusion filter that permits edge enhaneement, and a eonvex nonquadratie variational image restoration method whieh gives good denoising. For the diffusion filter, an effieient algorithm is applied using an additive operator splitting (AOS) that leads to reeursive and separable filters. Für the variational restoration method, a novel algorithm is developed that uses AOS sehemes within a Gaussian pyramid deeomposition. Examples demonstrate that preproeessing by these PDE teehniques signifieantly improves the watershed segmentation, and that the resulting segmentation method gives better results than some traditional teehniques. The algorithm has linear eomplexity and it ean be used for arbitrary dimensional data sets. The typical CPU time for segmenting a 2562 image on a modern PC is far below one seeond.