Fast algorithms for Segmentation & Subjective Surfaces

Segmenting the contour of the brain in a 2D CT slice

In many instances, numerical integration of space-scale PDEs is the most time consuming operation of image processing. This is because the scale step is limited by conditional stability of explicit schemes. In this work, we introduce the unconditionally stable semi-implicit linearized difference scheme that is fashioned after additive operator split (AOS) (Weickert et al 1998, Goldenberg et al, 2001) for the Beltrami and the subjective surface flow.

We show with numerical simulations that the AOS method results in an unconditionally stable semi-implicit linearized difference scheme in 2D and 3D. We then apply this approach to fast subjective surface computation (Sarti et al 2002), both in 2D and 3D, and show that the compute time can be reduced by a factor of 20 or more.

Segmentation of the heart left ventricle with the Subjective-Surfaces

Links

• Fast Evolution of Image Manifolds and Application to Filtering and Segmentation in 3D Medical Images(article)
• One movie of a subjective surface extracting the contour of the brain in a 2D slice
• One movie of a subjective surface extracting the contour of the brain in a 2D slice, using the Fast-Marching method as initialization
• One movie of the segmentation of the heart left-ventricule with the Fast-Marching algorithm, before applying the Subjective Surface algorithm.
• Another movie of the segmentation of the same object with the Subjective Surfaces

math.lbl.gov/~deschamp