For a given group with a generating set A a dipole with jAj parallel directed edges labeled by elements of A gives rise to a voltage graph whose covering graph denoted by H A is a bipartite regular graph called a bi Cayley graph In the case when is abelian we refer to H A as a Haar graph of with respect to the symbol A In particular for cyclic the above graph is referred to as a cyclic Haar gra...

Bent Boolean functions play a very significant role in the design of strong symmetric cryptosystems. In this paper, we present an analysis of Bent functions in the Haar domain. We first present a brief overview of Bent Boolean functions and then derive expressions for the Haar spectrum of Bent functions. The Haar spectral coefficients of Bent functions are given in two ways namely; in terms of ...

Image processing and analysis based on the continuous or discrete image transforms are classic techniques. The image transforms are widely used in image filtering, data description, etc. Nowadays the wavelet theorems make up very popular methods of image processing, denoising and compression. Considering that the Haar functions are the simplest wavelets, these forms are used in many methods of ...

This paper introduces an extended set of Haarlike features beyond the standard vertically and horizontally aligned Haar-like features [Viola and Jones, 2001a; 2001b] and the 45 twisted Haar-like features [Lienhart and Maydt, 2002; Lienhart et al., 2003a; 2003b]. The extended rotated Haar-like features are based on the standard Haar-like features that have been rotated based on whole integer pix...

If C ≃ 2 is the Cantor set realized as the infinite product of two-point groups, then a folklore result says the Cantor map from C into [0, 1] sends Haar measure to Lebesgue measure on the interval. In fact, C admits many distinct topological group structures. In this note, we show that the Haar measures induced by these distinct group structures all share this property. We prove this by showin...

We propose a superfast discrete Haar wavelet transform (SFHWT) as well as its inverse, using the QTT representation for the Haar transform matrices and input-output vectors. Though the Haar matrix itself does not have a low QTT-rank approximation, we show that factor matrices used at each step of the traditional multilevel Haar wavelet transform algorithm have explicit QTT representations of lo...

In this article, mutual relations between Haar and ReedMuller spectral and functional domains are presented. The new relations apply to any size of the transform matrices in the form of layered vertical and horizontal Kronecker matrices. They allow the direct conversions between Haar and Reed-Muller functions and their corresponding spectra.