The second day of SSVM started with an invited lecture of Tony Lindeberg, who has written one very influential and very early book about scale space theory. His talk was both a tour through scale space and a recap of the recent developments in the field. Especially he show how the time aspect could be incorporated into scale space analysis by a close inspection of how receptive fiels are working. There were more talks but I only took notes from the talk of Jan Lellmann who talked about the problem of generating an elevation map from a few given level lines. One application of this could be to observe coastlines at different tides and then trying the reconstruct the full height map at the coast. One specific feature here is that the surface one looks for may have ridges which stem from kinks in the level lines and these ridges are important features of the surface. He argued that a pure convex regularization will not work and proposed to use more input namely a vector field which is derived from the contour lines such that the vector somehow “follows the ridges”, i.e. it connects to level lines in a correct way.

Finally another observation I had today: Well, this is not a trend, but a notion which I heard for the first time here but which sounds very natural is the informal classification of data terms in variational models as “weak” or “strong”. For example, a denoising data term {\|u-u^0\|^2_{L^2(\Omega)}} is a strong data term because it gives tight information on the whole set {\Omega}. On the other hand, an inpainting data term {u|_{\Omega\setminus\Omega'} = u^0|_{\Omega\setminus\Omega'}} is a weak data term because it basically tell nothing within the region {\Omega'}.

For afternoon the whole conference has been on tour to three amazing places:

  • the Riegersburg, which is not only an impressive castle but also features interesting exhibitions about old arm and witches,
  • the Zotter chocolate factory where they make amazing chocolate in mind-boggling varieties,
  • and to Schloss Kronberg for the conference dinner (although it was pretty tough to start eating the dinner after visiting Zotter…).