We present a class-specific weighted Dominant Orientation Template (DOT) for class-specific object detection to exploit fast DOT, although the original DOT is intended for instance-specific object detection. We use automatic selection algorithm to select representative DOTs from training images of an object class and use three types of 2D Haar wavelets to construct weight templates of the objec...

In this work, we present a novel way of computing the continuous Haar, Fourier and cosine series coefficients of rectilinear polygons. We derive algorithms to compute the inner products with the continuous basis functions directly from the vertices of the polygons. We show that the overall computational complexity of those algorithms is lower than that of the traditional corresponding discrete ...

In modern sciences there are several method of image compression techniques are exist. Huge amount of data must be sent and stored efficiently and effectively, the aim of image compression is to scale back the size and form of image without degrading the quality retrieving the back the original image. the best Haar moving ridge transform, it's the foremost simplest among separate wavelet remode...

In this paper a novel algorithm for robust video watermarking in image using orthogonal wavelet transform (HAAR) and bi-orthogonal (Daubechies Lifting) based on an image texture is described. To embed the watermark, property of texture (rough area) is used as a measure to find actual target area. Watermark is embedded into LL sub-band as it is having highest texture. Image’s distortion is reduc...

This paper presents a novel face detection method by applying discriminating feature analysis (DFA) and support vector machine (SVM). The novelty of our DFA–SVM method comes from the integration of DFA, face class modeling, and SVM for face detection. First, DFA derives a discriminating feature vector by combining the input image, its 1-D Haar wavelet representation, and its amplitude projectio...

These are some brief notes on measure theory, concentrating on Lebesgue measure on Rn. Some missing topics I would have liked to have included had time permitted are: the change of variable formula for the Lebesgue integral on Rn; absolutely continuous functions and functions of bounded variation of a single variable and their connection with Lebesgue-Stieltjes measures on R; Radon measures on ...

Can we characterize the wavelets through linear transformation? the answer for this question is certainly YES. In this paper we have characterized the Haar wavelet matrix by their linear transformation and proved some theorems on properties of Haar wavelet matrix such as Trace, eigenvalue and eigenvector and diagonalization of a matrix.

We revisit the work of the first named author and using simpler algebraic arguments we calculate integrals of polynomial functions with respect to the Haar measure on the unitary group U(d). The previous result provided exact formulas only for 2d bigger than the degree of the integrated polynomial and we show that these formulas remain valid for all values of d. Also, we consider the integrals ...

In this note we shall prove that every locally compact group can be embedded as a closed subgroup in a unimodular group. If the original group is locally Euclidean, the enlarged group will be also, hence the fifth problem of Hilbert is reduced to the unimodular case. We shall use certain results concerning Haar measure whose proof may be found in A. Weil, U integration dans les groupes topologi...