Let λ denote Carmichael’s function, so λ(n) is the universal exponent for the multiplicative group modulo n. It is closely related to Euler’s φ-function, but we show here that the image of λ is much denser than the image of φ. In particular the number of λ-values to x exceeds x/(log x).36 for all large x, while for φ it is equal to x/(log x)1+o(1), an old result of Erdős. We also improve on an ...

In a recent paper by Chen et al., the authors present a clever means of decomposing the Laplacian-of-Gaussian (LOG) kernel into the product of a Gaussian and a (smaller) LOG mask. They then proceed to develop a fast algorithm for convolution which exploits thespatial frequency properties of these operators to allow the image tobe decimated (subsampled). Although this approach is both no...

The shortest circular-path problem is similar to the ordinary shortest path problem, but instead of specifying a distinguished starting and end node, the path has to form a closed loop. This problem has several applications in optimization problems as they occur in image segmentation or shape matching. We propose a new algorithm to compute shortest circular paths on planar graphs that has a typ...

We propose a fast pairwise nearest neighbor (PNN)based O(N log N) time algorithm for multilevel nonparametric thresholding, where N denotes the size of the image histogram. The proposed PNN-based multilevel thresholding algorithm is considerably faster than optimal thresholding. On a set of 8 to 16 bits-per-pixel real images, experimental results also reveal that the proposed method provides be...

fractures are considered as one of the important structures in fractured reservoirs due to their effect on fluid currents and reservoirparameters such as porosity and permeability. fracture parameters can only be directly calculated with core and image logs. cores haveserious limitations, so image logs are the best method. the aim of this study is the systematic fractures analysis of the asmari...

This paper presents an unsupervised distribution free change detection for Synthetic Aperture Radar (SAR) images based on an image fusion strategy and novel fuzzy clustering algorithm with a Markov Random Field (MRF). By finding the mean ratio and log ratio on the two original images the SWT based fusion rules is applied for performing image fusion. This image fusion technique is introduced to ...

This paper investigates, how two fundamental measurement operations in Euclidean space, namely the construction of a straight line of given orientation angle and the measurement of distances along this line, are mapped to the non-Euclidean log-polar image plane. It is shown, how these two operations can be efficiently implemented for discrete log-polar images. The measurement operations are use...

We present a new algorithm for penalized-likelihood emission image reconstruction. The algorithm monotonically increases the objective function, converges globally to the unique maximizer, and easily accommodates the nonnegativity constraint and nonquadratic but convex penalty functions. The algorithm is based on finding paraboloidal surrogate functions for the log-likelihood at each iteration:...

This paper presents a novel framework for visual object recognition using infinite-dimensional covariance operators of input features in the paradigm of kernel methods on infinite-dimensional Riemannian manifolds. Our formulation provides in particular a rich representation of image features by exploiting their non-linear correlations. Theoretically, we provide a finite-dimensional approximatio...