The scale and rotation invariance properties of a recently proposed algorithm, using the fuzzy evidence accumulation principle, for finding lines (ridges) of non-parametric shapes is analysed. The proposed modifications consist in scaling the accumulated value with the inverse of the line width and further fuzzifying the accumulation process – along the line width. Good invariance properties re...

We provide an explicit description of the convex hull of the set of matrices of bounded rank, restricted to balls for the spectral norm. As applications, we deduce two relaxed forms of the rank function restricted to balls for the spectral norm: one is the quasiconvex hull of this rank function, another one is the convex hull of the rank function, thus retrieving Fazel's theorem (2002). Key-wor...

Low-rank approximations are popular methods to reduce the high computational cost of algorithms involving large-scale kernel matrices. The success of low-rank methods hinges on the matrix rank, and in practice, these methods are effective even for high-dimensional datasets. The practical success has elicited the theoretical analysis of the function rank in this paper, which is an upper bound of...

An important problem to be solved in modeling head-related impulse responses (HRIRs) is how to individualize HRIRs so that they are suitable for a listener. We modeled the entire magnitude head-related transfer functions (HRTFs), in frequency domain, for sound sources on horizontal plane of 37 subjects using principal components analysis (PCA). The individual magnitude HRTFs could be modeled ad...

Most of the edge detection methods available in literature are gradient based, which further apply thresholding, to find the final edge map in an image. In this paper, we propose a novel method that is based on fuzzy logic for edge detection in gray images without using the gradient and thresholding. Fuzzy logic is a mathematical logic that attempts to solve problems by assigning values to an i...

  In this paper, we propose a nonparametric rank-based alternative to the least-squares independent component analysis algorithm developed. The basic idea is to estimate the squared-loss mutual information, which used as the objective function of the algorithm, based on its copula density version. Therefore, no marginal densities have to be estimated. We provide empirical evaluation of th...

We prove that the filling order is quadratic for a large class of solvable groups and asymptotically quadratic for all Q-rank one lattices in semisimple groups of R-rank at least 3. As a byproduct of auxiliary results we give a shorter proof of the theorem on the nondistorsion of horospheres providing also an estimate of a nondistorsion