The Radon transform is a fundamental tool in many areas. For example, in reconstruction of an image from its projections (CT scanning). Recently A. Averbuch et al. [SIAM J. Sci. Comput., submitted for publication] developed a coherent discrete definition of the 2D discrete Radon transform for 2D discrete images. The definition in [SIAM J. Sci. Comput., submitted for publication] is shown to be ...

This paper presents a new fast discrete focal stack transform that can be used in the 3D depth recovery problem using a single image of a scene from a plenoptic camera. A plenoptic camera uses a microlens array between the lens of the camera and the image sensor to measure the radiance and direction of all the light rays in a scene. The microlens array creates many small images taken from sligh...

metal oxides play a very important role in many areas of chemistry, physics and materials science.the metal elements are able to form a large diversity of oxide compounds. in this investigation, wesynthesis sno2 and c,n,s-tridoped sno2 nanoparticles by precipitation method. the synthesizedsno2 and c,n,s-tridoped sno2 nanoparticles were characterized by instrumental analysis methods,such as x-ra...

The computation speed for distance transforms becomes important in a wide variety of image processing applications. Current ITK library filters do not see any benefit from a multithreading environment. We introduce an N-dimensional signed parallel implementation of the exact Euclidean distance transform algorithm developed by Maurer et al.[1] with a theoretical complexity of O(n/p) for n voxels...

The continuous wavelet transform (CWT) is a common signal-processing tool for the analysis of nonstationary signals. We propose here a new B-spline-based method that allows the CWT computation at any scale. A nice property of the algorithm is that the computational cost is independent of the scale value. Its complexity is of the same order as that of the fastest published methods, without being...

After the surface theory of Möbius geometry, this study concerns a pair of conformally immersed surfaces in n-sphere. Two new invariants θ and ρ associated with them are introduced as well as the notion of touch and co-touch. This approach is helpful in research about transforms of certain surface classes. As an application, we define adjoint transform for any given Willmore surface in n-sphere...

An efficient algorithm for computing the one-dimensional partial fast Fourier transform fj = ∑c(j) k=0 e Fk is presented. Naive computation of the partial fast Fourier transform requires O(N) arithmetic operations for input data of length N . Unlike the standard fast Fourier transform, the partial fast Fourier transform imposes on the frequency variable k a cutoff function c(j) that depends on ...

Given a sequence an, we denote by hn the general term of the sequence with hn = |ai+j|0≤i,j≤n. The sequence hn is called the Hankel transform of an [19, 20, 21]. This sequence of Hankel determinants has attracted much attention of late amongst those working in the area of integer and polynomial sequences in particular [7, 18, 24, 32]. In this note we shall introduce the notion of a related Hurw...

Due to the efficiency in implementation, the Walsh (Hadamard) transform plays an important role in signal analysis and communication. Recently, Lee generalized the Walsh transform into the Jacket transform. Since the entries of the Jacket transform can be ±2, it is more flexible than the Walsh transform. Both the Walsh transform and the Jacket transform are defined for the case where the length...

We study image compression by a separable wavelet basis { ψ(2k1x − i)ψ(2k2y − j), φ(x − i)ψ(2k2y − j), ψ(2k1(x − i)φ(y − j), φ(x − i)φ(y − i) } , where k1, k2 ∈ Z+; i, j ∈ Z; and φ, ψ are elements of a standard biorthogonal wavelet basis in L2(R). Because k1 6= k2, the supports of the basis elements are rectangles, and the corresponding transform is known as the rectangular wavelet transform. W...