Section: New Results

Correlation and variational approaches for motion and diffusion estimation

Participants : Denis Fortun, Charles Kervrann.

Diffusion coefficient estimation in live cell fluorescence imaging is usually achieved with correlation-based methods related to Image Correlation Spectroscopy (ICS) [42] . This approach requires a high computational cost and the spatial resolution of the resulting diffusion map is limited by the inherent block-based principle of the method. To overcome these drawbacks, we propose a novel diffusion estimation method in a variational framework providing dense and discontinuity-preserving diffusion fields. The diffusion equation is integrated in a global energy via a neighborhood-wise data term, positivity constraint and temporal integration. The performances of the variational and ICS approaches were compared on simulated sequences. We have demonstrated the accuracy of ICS in stationarity conditions, and we pointed out the advantages of dense variational estimation to accurately recover spatial and temporal discontinuities (Fig. 10 ).

Reference: [17]

Partners: Perrine Paul-Gilloteaux, Francois Waharte and Chen Chen (UMR 144, PICT IBiSA, CNRS-Institut Curie)

Figure 10. Variational diffusion estimation on a simulated sequence with spatially variant diffusion. The curves of (f) are profiles of the dashed lines in (b),(c) and (e)

(a) Frame 1 (b) Ground-truth diffusion field (c) Estimated diffusion field $D$ (d) Histogram of $D$ (e) Segmented diffusion field (f) Profiles