Computer Vision, IEEE International Conference on (2007)
Rio de Janeiro, Brazil
Oct. 14, 2007 to Oct. 21, 2007
Ramunas Girdziusas , Laboratory of Computer and Information Science, Helsinki University of Technology, P.O.Box 5400, FI-02015 TKK, FINLAND. Ramunas.Girdziusas@tkk.fi
Jorma Laaksonen , Laboratory of Computer and Information Science, Helsinki University of Technology, P.O.Box 5400, FI-02015 TKK, FINLAND. Jorma.Laaksonen@tkk.fi
Necessary and sufficient conditions are discussed which state when the Euler-inspired forward diffusion in a discrete space-time is a scale-space in the sense of both the total and sign variation diminishing. We emphasize that the problem is algebraic and reduces to characterization of the elements of the generalized Laplacian so that the diffusion propagators are positive definite. As a key-product, explicit analytical expressions are found for the principal minors of the frequently-applied class of tridiagonal (Jacobi) matrices. Further generalizations are outlined by introducing novel techniques of evaluating matrix determinants.
R. Girdziusas and J. Laaksonen, "When is a Discrete Diffusion a Scale-Space?," 2007 11th IEEE International Conference on Computer Vision(ICCV), Rio de Janeiro, 2007, pp. 1-6.