Effective and real-time face detection has been made possible by using the method of rectangle Haar-like features with AdaBoost learning since Viola and Jones’ work [12]. In this paper, we present the use of a new set of distinctive rectangle features, called Multi-block Local Binary Patterns (MB-LBP), for face detection. The MB-LBP encodes rectangular regions’ intensities by local binary patte...

For each irreducible module of the symmetric group SN there is a set of parametrized nonsymmetric Jack polynomials in N variables taking values in the module. These polynomials are simultaneous eigenfunctions of a commutative set of operators, self-adjoint with respect to two Hermitian forms, one called the contravariant form and the other is with respect to a matrix-valued measure on the N -to...

Let (AZ, F ) be a bipermutative algebraic cellular automaton. We present conditions which force a probability measure which is invariant for the N×Z-action of F and the shift map σ to be the Haar measure on Σ, a closed shift-invariant subgroup of the Abelian compact group AZ. This generalizes simultaneously results of B. Host, A. Maass and S. Mart́ınez [7] and M. Pivato [14]. This result is appl...

In this note we show that the general theory of vector valued singular integral operators Calderon-Zygmund defined on metric measure spaces, can be applied to obtain Sobolev type regularity properties for solutions dyadic fractional Laplacian. doing so, define partial derivatives in terms Haar multipliers and homogeneous operators.

Each homeomorphism from the n-dimensional Sierpiński gasket into itself is a similarity map with respect to the usual metrization. Moreover, the topology of this space determines a kind of Haar measure and a canonical metric. We study spaces with similar properties. It turns out that in many cases, “fractal structure” is not a metric but a topological phenomenon.

We consider several orthogonal quantum groups satisfying the “easiness” assumption axiomatized in our previous paper. For each of them we discuss the computation of the asymptotic law of Tr(u) with respect to the Haar measure, u being the fundamental representation. For the classical groups On, Sn we recover in this way some well-known results of Diaconis and Shahshahani.

this paper presents a proof of stirling's formula using haar wavelets and some properties of hilbert space, such as parseval's identity. the present paper shows a connection between haar wavelets and certain sequences.

Given any fixed N×N positive semi-definite diagonal matrix G ≥ 0 we derive the explicit formula for the density of complex eigenvalues for random matrices A of the form A = U √ G where the random unitary matrices U are distributed on the group U(N) according to the Haar measure.

Combinatorial formulas for the moments of the Brownian motion on classical compact Lie groups are obtained. These expressions are deformations of formulas of B. Collins and P. Śniady for moments of the Haar measure and yield a proof of the First Fundamental Theorem of Invariant and of classical Schur-Weyl dualities based on stochastic calculus.