Robust face recognition using convolutional neural networks combined with Krawtchouk moments

Face recognition is a challenging task due to the complexity of pose variations, occlusion and the variety of face expressions performed by distinct subjects. Thus, many features have been proposed, however each feature has its own drawbacks. Therefore, in this paper, we propose a robust model called Krawtchouk moments convolutional neural networks (KMCNN) for face recognition. Our model is divided into two main steps. Firstly, we use 2D discrete orthogonal Krawtchouk moments to represent features. Then, we fed it into convolutional neural networks (CNN) for classification. The main goal of the proposed approach is to improve the classification accuracy of noisy grayscale face images. In fact, Krawtchouk moments are less sensitive to noisy effects. Moreover, they can extract pertinent features from an image using only low orders. To investigate the robustness of the proposed approach, two types of noise (salt and pepper and speckle) are added to three datasets (YaleB extended, our database of faces (ORL), and a subset of labeled faces in the wild (LFW)). Experimental results show that KMCNN is flexible and performs significantly better than using just CNN or when we combine it with other discrete moments such as Tchebichef, Hahn, Racah moments in most densities of noises

On The Potential of Image Moments for Medical Diagnosis

Medical imaging is widely used for diagnosis and postoperative or post-therapy monitoring. The ever-increasing number of images produced has encouraged the introduction of automated methods to assist doctors or pathologists. In recent years, especially after the advent of convolutional neural networks, many researchers have focused on this approach, considering it to be the only method for diagnosis since it can perform a direct classification of images. However, many diagnostic systems still rely on handcrafted features to improve interpretability and limit resource consumption. In this work, we focused our efforts on orthogonal moments, first by providing an overview and taxonomy of their macrocategories and then by analysing their classification performance on very different medical tasks represented by four public benchmark data sets. The results confirmed that convolutional neural networks achieved excellent performance on all tasks. Despite being composed of much fewer features than those extracted by the networks, orthogonal moments proved to be competitive with them, showing comparable and, in some cases, better performance. In addition, Cartesian and harmonic categories provided a very low standard deviation, proving their robustness in medical diagnostic tasks. We strongly believe that the integration of the studied orthogonal moments can lead to more robust and reliable diagnostic systems, considering the performance obtained and the low variation of the results. Finally, since they have been shown to be effective on both magnetic resonance and computed tomography images, they can be easily extended to other imaging techniques

Classifying Reported and "Missing" Resonances According to Their P and C Properties

The Hilbert space H^3q of the three quarks with one excited quark is decomposed into Lorentz group representations. It is shown that the quantum numbers of the reported and ``missing'' resonances fall apart and populate distinct representations that differ by their parity or/and charge conjugation properties. In this way, reported and ``missing'' resonances become distinguishable. For example, resonances from the full listing reported by the Particle Data Group are accommodated by Rarita-Schwinger (RS) type representations (k/2,k/2)*[(1/2,0)+(0,1/2)] with k=1,3, and 5, the highest spin states being J=3/2^-, 7/2^+, and 11/2^+, respectively. In contrast to this, most of the ``missing'' resonances fall into the opposite parity RS fields of highest-spins 5/2^-, 5/2^+, and 9/2^+, respectively. Rarita-Schwinger fields with physical resonances as lower-spin components can be treated as a whole without imposing auxiliary conditions on them. Such fields do not suffer the Velo-Zwanziger problem but propagate causally in the presence of electromagnetic fields. The pathologies associated with RS fields arise basically because of the attempt to use them to describe isolated spin-J=k+1/ 2 states, rather than multispin-parity clusters. The positions of the observed RS clusters and their spacing are well explained trough the interplay between the rotational-like (k/2)(k/2 +1)-rule and a Balmer-like -(k+1)^{-2}-behavior

Accelerated and Improved Stabilization for High Order Moments of Racah Polynomials

Discrete Racah polynomials (DRPs) are highly efficient orthogonal polynomials and used in various scientific fields for signal representation. They find applications in disciplines like image processing and computer vision. Racah polynomials were originally introduced by Wilson and later modified by Zhu to be orthogonal on a discrete set of samples. However, when the degree of the polynomial is high, it encounters numerical instability issues. In this paper, we propose a novel algorithm called Improved Stabilization (ImSt) for computing DRP coefficients. The algorithm partitions the DRP plane into asymmetric parts based on the polynomial size and DRP parameters. We have optimized the use of stabilizing conditions in these partitions. To compute the initial values, we employ the logarithmic gamma function along with a new formula. This combination enables us to compute the initial values efficiently for a wide range of DRP parameter values and large polynomial sizes. Additionally, we have derived a symmetry relation for the case when the Racah polynomial parameters are zero ( a=0 , =0 ). This symmetry makes the Racah polynomials symmetric about the main diagonal, and we present a different algorithm for this specific scenario. We have demonstrated that the ImSt algorithm works for a broader range of parameters and higher degrees compared to existing algorithms. A comprehensive comparison between ImSt and the existing algorithms has been conducted, considering the maximum polynomial degree, computation time, restriction error analysis, and reconstruction error. The results of the comparison indicate that ImSt outperforms the existing algorithms for various values of Racah polynomial parameters

Efficient Computation of NN-point Correlation Functions in DD Dimensions

We present efficient algorithms for computing the $N$-point correlation functions (NPCFs) of random fields in arbitrary $D$-dimensional homogeneous and isotropic spaces. Such statistics appear throughout the physical sciences, and provide a natural tool to describe a range of stochastic processes. Typically, NPCF estimators have $\mathcal{O}(n^N)$ complexity (for a data set containing $n$ particles); their application is thus computationally infeasible unless $N$ is small. By projecting onto a suitably-defined angular basis, we show that the estimators can be written in separable form, with complexity $\mathcal{O}(n^2)$, or $\mathcal{O}(n_{\rm g}\log n_{\rm g})$ if evaluated using a Fast Fourier Transform on a grid of size $n_{\rm g}$. Our decomposition is built upon the $D$-dimensional hyperspherical harmonics; these form a complete basis on the $(D-1)$-sphere and are intrinsically related to angular momentum operators. Concatenation of $(N-1)$ such harmonics gives states of definite combined angular momentum, forming a natural separable basis for the NPCF. In particular, isotropic correlation functions require only states with zero combined angular momentum. We provide explicit expressions for the NPCF estimators as applied to both discrete and gridded data, and discuss a number of applications within cosmology and fluid dynamics. The efficiency of such estimators will allow higher-order correlators to become a standard tool in the analysis of random fields.Comment: 12 pages, 2 figures, submitted to PNAS. Comments welcome

Self-Assembled Nanometer-Scale Magnetic Networks on Surfaces: Fundamental Interactions and Functional Properties

Nanomagnets of controlled size, organized into regular patterns open new perspectives in the fields of nanoelectronics, spintronics, and quantum computation. Self-assembling processes on various types of substrates allow designing fine-structured architectures and tuning of their magnetic properties. Here, starting from a description of fundamental magnetic interactions at the nanoscale, we review recent experimental approaches to fabricate zero-, one-, and two-dimensional magnetic particle arrays with dimensions reduced to the atomic limit and unprecedented areal density. We describe systems composed of individual magnetic atoms, metal-organic networks, metal wires, and bimetallic particles, as well as strategies to control their magnetic moment, anisotropy, and temperature-dependent magnetic behavior. The investigation of self-assembled subnanometer magnetic particles leads to significant progress in the design of fundamental and functional aspects, mutual interactions among the magnetic units, and their coupling with the environment