Related papers: Complex-Valued Hough Transforms for Circles
In this paper we show that a methodology based on a sampling with the Gaussian function of kind $h\,{e^{ - {{\left( {t/c} \right)}^2}}}/\left( {{c}\sqrt \pi } \right)$, where ${c}$ and $h$ are some constants, leads to the Fourier transform…
Convolutions or Hadamard products of analytic functions is a well explored area of research and many nice results are available in literature. On the other hand, very little is known in general about the convolutions of univalent harmonic…
This paper makes the case for using Shapley value to quantify the importance of random input variables to a function. Alternatives based on the ANOVA decomposition can run into conceptual and computational problems when the input variables…
Type systems usually characterize the shape of values but not their free variables. However, many desirable safety properties could be guaranteed if one knew the free variables captured by values. We describe CCsubBox, a calculus where such…
In standard quantum mechanics, complex numbers are used to describe the wavefunction. Although complex numbers have proven sufficient to predict the results of existing experiments, there is no apparent theoretical reason to choose them…
Clustering aims to group unlabelled samples based on their similarities. It has become a significant tool for the analysis of high-dimensional data. However, most of the clustering methods merely generate pseudo labels and thus are unable…
The Hausdorff fractal dimension has been a fast-to-calculate method to estimate complexity of fractal shapes. In this work, a modified version of this fractal dimension is presented in order to make it more robust when applied in estimating…
A complex-valued convolutional network (convnet) implements the repeated application of the following composition of three operations, recursively applying the composition to an input vector of nonnegative real numbers: (1) convolution with…
Voting theory has become increasingly integrated with computational social choice and multiagent systems. Computational complexity has been extensively used as a shield against manipulation of voting systems, however for several voting…
We investigate how robust approval-based multiwinner voting rules are to small perturbations in the votes. In particular, we consider the extent to which a committee can change after we add/remove/swap one approval, and we consider the…
Deep learning has become an area of interest in most scientific areas, including physical sciences. Modern networks apply real-valued transformations on the data. Particularly, convolutions in convolutional neural networks discard phase…
A wide variety of methods have been used to compute percolation thresholds. In lattice percolation, the most powerful of these methods consists of microcanonical simulations using the union-find algorithm to efficiently determine the…
Analysis of high-dimensional data is currently a popular field of research, thanks to many applications e.g. in genetics (DNA data in genomewide association studies), spectrometry or web analysis. At the same time, the type of problems that…
We introduce algorithms to visualize feature spaces used by object detectors. Our method works by inverting a visual feature back to multiple natural images. We found that these visualizations allow us to analyze object detection systems in…
Many inverse problems in nuclear fusion and high-energy astrophysics research, such as the optimization of tokamak reactor geometries or the inference of black hole parameters from interferometric images, necessitate high-dimensional…
The Shapley value is a conventional and well-studied function for determining the contribution of a player to the coalition in a cooperative game. Among its applications in a plethora of domains, it has recently been proposed to use the…
Detection of geometric features in digital images is an important exercise in image analysis and computer vision. The Hough Transform techniques for detection of circles require a huge memory space for data processing hence requiring a lot…
We introduce a new pattern recognition algorithm for track finding in High Energy Physics Experiments based on an extension of the Hough Transform to multiple dimensions. A remarkable property of this algorithm is that the execution time is…
It is proposed a complex valued channel encoding for multidimensional data. The basic approach contains overlapping of complex nonlinear mappings. Its development leads to sparse representation of multi-channel data, increasing their…
This study aims to analyze the benefits of improved multi-scale reasoning for object detection and localization with deep convolutional neural networks. To that end, an efficient and general object detection framework which operates on…