Training cellular automata for image processing

Elementary cellular automata realized by stateful three-memristor logic operations

Cellular automata (CA) are computational systems that exhibit complex global behavior arising from simple local rules, making them a fascinating candidate for various research areas. However, challenges such as limited flexibility and efficiency on conventional hardware platforms still exist. In this study, we propose a memristor-based circuit for implementing elementary cellular automata (ECA) by extending the stateful three-memristor logic operations derived from material implication (IMP) logic gates. By leveraging the inherent physical properties of memristors, this approach offers simplicity, minimal operational steps, and high flexibility in implementing ECA rules by adjusting the circuit parameters. The mathematical principles governing circuit parameters are analyzed, and the evolution of multiple ECA rules is successfully demonstrated, showcasing the robustness in handling the stochastic nature of memristors. This approach provides a hardware solution for ECA implementation and opens up new research opportunities in the hardware implementation of CA.

Cellular automata imbedded memristor-based recirculated logic in-memory computing

Memristor-based circuits offer low hardware costs and in-memory computing, but full-memristive circuit integration for different algorithm remains limited. Cellular automata (CA) has been noticed for its well-known parallel, bio-inspired, computational characteristics. Running CA on conventional chips suffers from low parallelism and high hardware costs. Establishing dedicated hardware for CA remains elusive. We propose a recirculated logic operation scheme (RLOS) using memristive hardware and 2D transistors for CA evolution, significantly reducing hardware complexity. RLOS's versatility supports multiple CA algorithms on a single circuit, including elementary CA rules and more complex majority classification and edge detection algorithms. Results demonstrate up to a 79-fold reduction in hardware costs compared to FPGA-based approaches. RLOS-based reservoir computing is proposed for edge computing development, boasting the lowest hardware cost (6 components/per cell) among existing implementations. This work advances efficient, low-cost CA hardware and encourages edge computing hardware exploration.

PSciLab: An Unified Distributed and Parallel Software Framework for Data Analysis, Simulation and Machine Learning—Design Practice, Software Architecture, and User Experience

In this paper, a hybrid distributed-parallel cluster software framework for heterogeneous computer networks is introduced that supports simulation, data analysis, and machine learning (ML), using widely available JavaScript virtual machines (VM) and web browsers to accommodate the working load. This work addresses parallelism, primarily on a control-path level and partially on a data-path level, targeting different classes of numerical problems that can be either data-partitioned or replicated. These are composed of a set of interacting worker processes that can be easily parallelized or distributed, e.g., for large-scale multi-element simulation or ML. Their suitability and scalability for static and dynamic problems are experimentally investigated regarding the proposed multi-process and communication architecture, as well as data management using customized SQL databases with network access. The framework consists of a set of tools and libraries, mainly the WorkBook (processed by a web browser) and the WorkShell (processed by node.js). It can be seen that the proposed distributed-parallel multi-process approach, with a dedicated set of inter-process communication methods (message- and shared-memory-based), scales up efficiently according to problem size and the number of processes. Finally, it is demonstrated that this JavaScript-based approach for exploiting parallelism can be used easily by any typical numerical programmer or data analyst and does not require any special knowledge about parallel and distributed systems and their interaction. The study is also focused on VM processing.

Chimera states in coupled map lattices: Spatiotemporally intermittent behavior and an equivalent cellular automaton

We construct an equivalent cellular automaton (CA) for a system of globally coupled sine circle maps with two populations and distinct values for intergroup and intragroup coupling. The phase diagram of the system shows that the coupled map lattice can exhibit chimera states with synchronized and spatiotemporally intermittent subgroups after evolution from random initial conditions in some parameter regimes, as well as to other kinds of solutions in other parameter regimes. The CA constructed by us reflects the global nature and the two population structure of the coupled map lattice and is able to reproduce the phase diagram accurately. The CA depends only on the total number of laminar and burst sites and shows a transition from co-existing deterministic and probabilistic behavior in the chimera region to fully probabilistic behavior at the phase boundaries. This identifies the characteristic signature of the transition of a cellular automaton to a chimera state. We also construct an evolution equation for the average number of laminar/burst sites from the CA, analyze its behavior and solutions, and correlate these with the behavior seen for the coupled map lattice. Our CA and methods of analysis can have relevance in wider contexts.

Shift-symmetric configurations in two-dimensional cellular automata: Irreversibility, insolvability, and enumeration

The search for symmetry, as an unusual yet profoundly appealing phenomenon, and the origin of regular, repeating configuration patterns have long been a central focus of complexity science and physics. To better grasp and understand symmetry of configurations in decentralized toroidal architectures, we employ group-theoretic methods, which allow us to identify and enumerate these inputs, and argue about irreversible system behaviors with undesired effects on many computational problems. The concept of so-called "configuration shift-symmetry" is applied to two-dimensional cellular automata as an ideal model of computation. Regardless of the transition function, the results show the universal insolvability of crucial distributed tasks, such as leader election, pattern recognition, hashing, and encryption. By using compact enumeration formulas and bounding the number of shift-symmetric configurations for a given lattice size, we efficiently calculate the probability of a configuration being shift-symmetric for a uniform or density-uniform distribution. Further, we devise an algorithm detecting the presence of shift-symmetry in a configuration. Given the resource constraints, the enumeration and probability formulas can directly help to lower the minimal expected error and provide recommendations for system's size and initialization. Besides cellular automata, the shift-symmetry analysis can be used to study the nonlinear behavior in various synchronous rule-based systems that include inference engines, Boolean networks, neural networks, and systolic arrays.

Infrared Dim Target Detection Using Shearlet’s Kurtosis Maximization under Non-Uniform Background

A novel method based on multiscale and multidirectional feature fusion in the shearlet transform domain and kurtosis maximization for detecting the dim target in infrared images with a low signal-to-noise ratio (SNR) and serious interference caused by a cluttered and non-uniform background is presented in this paper. First, an original image is decomposed using the shearlet transform with translation invariance. Second, various directions of high-frequency subbands are fused and the corresponding kurtosis of fused image is computed. The targets can be enhanced by strengthening the column with maximum kurtosis. Then, processed high-frequency subbands on different scales of images are merged. Finally, the dim targets are detected by an adaptive threshold with a maximum contrast criterion (MCC). The experimental results show that the proposed method has good performance for infrared target detection in comparison with the nonsubsampled contourlet transform (NSCT) method.

Cellular Automata Modeling of Stem-Cell-Driven Development of Tissue in the Nervous System

Mathematical and computational modeling enables biologists to integrate data from observations and experiments into a theoretical framework. In this review, we describe how developmental processes associated with stem-cell-driven growth of tissue in both the embryonic and adult nervous system can be modeled using cellular automata (CA). A cellular automaton is defined by its discrete nature in time, space, and state. The discrete space is represented by a uniform grid or lattice containing agents that interact with other agents within their local neighborhood. This possibility of local interactions of agents makes the cellular automata approach particularly well suited for studying through modeling how complex patterns at the tissue level emerge from fundamental developmental processes (such as proliferation, migration, differentiation, and death) at the single-cell level. As part of this review, we provide a primer for how to define biologically inspired rules governing these processes so that they can be implemented into a CA model. We then demonstrate the power of the CA approach by presenting simulations (in the form of figures and movies) based on building models of three developmental systems: the formation of the enteric nervous system through invasion by neural crest cells; the growth of normal and tumorous neurospheres induced by proliferation of adult neural stem/progenitor cells; and the neural fate specification through lateral inhibition of embryonic stem cells in the neurogenic region of Drosophila.

Quantum Local Binary Pattern for Medical Edge Detection

Edge detection is one of the most important operations for extracting the different objects in medical images because it enables delimitation of the various structures present in the image. Most edge detection algorithms are based on the intensity variations in images. Edge detection is especially difficult when the images are textured, and it is essential to consider the texture in edge detection processes. In this article, the authors propose a new procedure to extract the texture from images, called the Quantum Local Binary Pattern (QuLBP). The authors introduce two applications that use QuLBP to detect edges in magnetic resonance images: a cellular automaton (CA) edge detector algorithm and a combination of the QuLBP and the Deriche-Canny algorithm for salt and pepper noise resistance. The proposed approach to extracting texture is designed for and applied to different gray scale image datasets with real and synthetic magnetic resonance imaging (MRI). The experiments demonstrate that the proposed approach produces good results in both applications, compared to classical algorithms.

Mammogram segmentation using maximal cell strength updation in cellular automata

Breast cancer is the most frequently diagnosed type of cancer among women. Mammogram is one of the most effective tools for early detection of the breast cancer. Various computer-aided systems have been introduced to detect the breast cancer from mammogram images. In a computer-aided diagnosis system, detection and segmentation of breast masses from the background tissues is an important issue. In this paper, an automatic segmentation method is proposed to identify and segment the suspicious mass regions of mammogram using a modified transition rule named maximal cell strength updation in cellular automata (CA). In coarse-level segmentation, the proposed method performs an adaptive global thresholding based on the histogram peak analysis to obtain the rough region of interest. An automatic seed point selection is proposed using gray-level co-occurrence matrix-based sum average feature in the coarse segmented image. Finally, the method utilizes CA with the identified initial seed point and the modified transition rule to segment the mass region. The proposed approach is evaluated over the dataset of 70 mammograms with mass from mini-MIAS database. Experimental results show that the proposed approach yields promising results to segment the mass region in the mammograms with the sensitivity of 92.25% and accuracy of 93.48%.

Anomalous diffusion process applied to magnetic resonance image enhancement

Diffusion process is widely applied to digital image enhancement both directly introducing diffusion equation as in anisotropic diffusion (AD) filter, and indirectly by convolution as in Gaussian filter. Anomalous diffusion process (ADP), given by a nonlinear relationship in diffusion equation and characterized by an anomalous parameters q, is supposed to be consistent with inhomogeneous media. Although classic diffusion process is widely studied and effective in various image settings, the effectiveness of ADP as an image enhancement is still unknown. In this paper we proposed the anomalous diffusion filters in both isotropic (IAD) and anisotropic (AAD) forms for magnetic resonance imaging (MRI) enhancement. Filters based on discrete implementation of anomalous diffusion were applied to noisy MRI T2w images (brain, chest and abdominal) in order to quantify SNR gains estimating the performance for the proposed anomalous filter when realistic noise is added to those images. Results show that for images containing complex structures, e.g. brain structures, anomalous diffusion presents the highest enhancements when compared to classical diffusion approach. Furthermore, ADP presented a more effective enhancement for images containing Rayleigh and Gaussian noise. Anomalous filters showed an ability to preserve anatomic edges and a SNR improvement of 26% for brain images, compared to classical filter. In addition, AAD and IAD filters showed optimum results for noise distributions that appear on extreme situations on MRI, i.e. in low SNR images with approximate Rayleigh noise distribution, and for high SNR images with Gaussian or non central χ noise distributions. AAD and IAD filter showed the best results for the parametric range 1.2 < q < 1.6, suggesting that the anomalous diffusion regime is more suitable for MRI. This study indicates the proposed anomalous filters as promising approaches in qualitative and quantitative MRI enhancement.

Fast rule identification and neighborhood selection for cellular automata

Cellular automata (CA) with given evolution rules have been widely investigated, but the inverse problem of extracting CA rules from observed data is less studied. Current CA rule extraction approaches are both time consuming and inefficient when selecting neighborhoods. We give a novel approach to identifying CA rules from observed data and selecting CA neighborhoods based on the identified CA model. Our identification algorithm uses a model linear in its parameters and gives a unified framework for representing the identification problem for both deterministic and probabilistic CA. Parameters are estimated based on a minimum variance criterion. An incremental procedure is applied during CA identification to select an initial coarse neighborhood. Redundant cells in the neighborhood are then removed based on parameter estimates, and the neighborhood size is determined using the Bayesian information criterion. Experimental results show the effectiveness of our algorithm and that it outperforms other leading CA identification algorithms.