  Regularization functionals that lower level set boundary length when used
with L^1 fidelity functionals on signal de-noising on images create artifacts.
These are (i) rounding of corners, (ii) shrinking of radii, (iii) shrinking of
cusps, and (iv) non-smoothing of staircasing. Regularity functionals based upon
total curvature of level set boundaries do not create artifacts (i) and (ii).
An adjusted fidelity term based on the flat norm on the current (a
distributional graph) representing the density of curvature of level sets
boundaries can minimize (iii) by weighting the position of a cusp. A regularity
term to eliminate staircasing can be based upon the mass of the current
representing the graph of an image function or its second derivatives.
Densities on the Grassmann bundle of the Grassmann bundle of the ambient space
of the graph can be used to identify patterns, textures, occlusion and lines.
