35 research outputs found
L1TV computes the flat norm for boundaries
We show that the recently introduced L1TV functional can be used to
explicitly compute the flat norm for co-dimension one boundaries. While this
observation alone is very useful, other important implications for image
analysis and shape statistics include a method for denoising sets which are not
boundaries or which have higher co-dimension and the fact that using the flat
norm to compute distances not only gives a distance, but also an informative
decomposition of the distance. This decomposition is made to depend on scale
using the "flat norm with scale" which we define in direct analogy to the L1TV
functional. We illustrate the results and implications with examples and
figures
A Matlab Implementation of a Flat Norm Motivated Polygonal Edge Matching Method using a Decomposition of Boundary into Four 1-Dimensional Currents
We describe and provide code and examples for a polygonal edge matching
method.Comment: Contains Matlab code and 4 figure
Cone Monotonicity: Structure Theorem, Properties, and Comparisons to Other Notions of Monotonicity
In search of a meaningful 2-dimensional analog to mono- tonicity, we
introduce two new definitions and give examples of and dis- cuss the
relationship between these definitions and others that we found in the
literature. Note: After we published the article in Abstract and Applied
Analysis and after we searched multiple times for previous work, we discovered
that Clarke at al. had introduced the definition of cone monotonicity and given
a characterization. See the addendum at the end of this paper for full
reference information