—We study tight wavelet frames associated with given refinable functions which are obtained with the unitary extension principles. All possible solutions of the corresponding matrix equations are found. It is proved that the problem of the extension may be always solved with two framelets. In particular, if symbols of the refinable functions are polynomials… (More)
This paper proposes a directional image force (DIF) for active contouring. DIF is the inner product of the zero crossing strength (ZCS) of wavelet frame coefficients, and the normal of a snake, by representing strength and orientation of edges at multiple resolution levels. DIF markedly improves the immunity of snakes to noise and convexity.
We construct integrable lattice realizations of conformal twisted boundary conditions for sℓ(2) unitary minimal models on a torus. These conformal field theories are realized as the continuum scaling limit of critical AD -E lattice models with positive spectral parameter. The integrable seam boundary conditions are labelled by (r, s, ζ) ∈ (A g−2 , A g−1 ,… (More)
New non-asymptotic uniform error bounds for approximating functions in reproducing kernel Hilbert spaces are given using F. Girosi's approach to derive approximation theoretic results from statistical learning theory. The authors congratulate Professor Charles Chui on the occasion of his sixty fifth birthday.
We study integrable realizations of conformal twisted boundary conditions for sℓ(2) unitary minimal models on a torus. These conformal field theories are realized as the continuum scaling limit of critical G = A, D, E lattice models with positive spectral parameter u > 0 and Coxeter number g. Integrable seams are constructed by fusing blocks of elementary… (More)
We study the conformal spectra of the critical square lattice Ising model on the Klein bottle and Möbius strip using Yang-Baxter techniques and the solution of functional equations. In particular, we obtain expressions for the finitized conformal partition functions in terms of finitized Virasoro characters. This demonstrates that Yang-Baxter techniques and… (More)
We derive the fusion hierarchy of functional equations for critical AD -E lattice models related to the sℓ(2) unitary minimal models, the parafermionic models and the supersymmetric models of conformal field theory and deduce the related TBA functional equations. The derivation uses fusion projectors and applies in the presence of all known integrable… (More)
— We introduce a local image statistic for identifying noise pixels in images corrupted with impulse noise of random values. The statistical values quantify how different in intensity the particular pixels are from their most similar neighbors. We continue to demonstrate how this statistic may be incorporated into a filter designed to remove additive… (More)
Manipulation of control points is a standard procedure in B-spline surface patch design. Unfortunately, this tool alone is not suucient to achieve certain goals such as removing gaps among patches. In this paper, we introduce another approach for removing gaps but maintaining the geometrical smoothness condition. The only requirement is to sacriice the true… (More)