d3web is a free, open-source platform for knowledge-based systems (expert systems). Its core is written in Java using XML and/or Office-based formats for the knowledge storage. All of its components are distributed under the terms of the Lesser General Public Licence (LGPL). The d3web diagnostic core implements reasoning and persistence components for problem-solving knowledge including decision trees, (heuristic) rules, set-covering models and diagnostic flowcharts. The software can be integrated into foreign applications (embedded or OEM), but a number of off-the-shelf components already exist. == Components == d3web is a component-based software platform providing applications for authoring and using/executing problem-solving knowledge. The following applications are primarily using d3web: KnowWE (Knowledge Wiki Environment): A semantic wiki building on JSPWiki. Problem-solving knowledge can be authored and executed through the wiki interface. Developed knowledge bases can be exported to be used in OEM or embedded reasoners. Additionally, knowledge exchange via OWL ontologies is provided. KnowME (Knowledge Modelling Environment): A rich-client application for the development of d3web knowledge bases. Problem-solving knowledge can be authored and executed within the desktop application. Developed knowledge bases can be used in OEM or embedded reasoners. The software KnowME is no longer under active development. It is replaced by the KnowWE component (see above). Dialog2: A web-based application for demonstrating the capabilities of the d3web core reasoner. The web servlet is based on Java Server Faces. It can be used out of box or as a starting point for own developments for building knowledge-based interview systems. == Application Domains == A number of industrial and academic projects already used or are currently using the d3web platform. The main application domains are: medical diagnosis, documentation, and therapy: technical fault diagnosis monitoring of technical devices. Some applications (both, commercial and free) created using the d3web diagnostic engine: SmartCare(c): a medical closed-loop system for weaning mechanically ventilated patients, created by Dräger SonoConsult Archived 2011-12-16 at the Wayback Machine: a medical support system for evaluating sonographic examinations (German only) eDOC: a web-based system for self-diagnosing various medical issues (German only) == History == The development of d3web originates from the research work of Prof. Dr. Frank Puppe (University Würzburg, Germany) going back to the 1980s, starting with the medical expert systems MED1 and MED2 . Whereas the original systems were focussed on medical diagnosis the applicability of the approach was generalized by the successor D3 . As the predecessors were implemented in the LISP programming language, d3web is a full Java re-implementation.
Connected-component labeling
Connected-component labeling (CCL), connected-component analysis (CCA), blob extraction, region labeling, blob discovery, or region extraction is an algorithmic application of graph theory, where subsets of connected components are uniquely labeled based on a given heuristic. Connected-component labeling is not to be confused with segmentation. Connected-component labeling is used in computer vision to detect connected regions in binary digital images, although color images and data with higher dimensionality can also be processed. When integrated into an image recognition system or human-computer interaction interface, connected component labeling can operate on a variety of information. Blob extraction is generally performed on the resulting binary image from a thresholding step, but it can be applicable to gray-scale and color images as well. Blobs may be counted, filtered, and tracked. Blob extraction is related to but distinct from blob detection. == Overview == A graph, containing vertices and connecting edges, is constructed from relevant input data. The vertices contain information required by the comparison heuristic, while the edges indicate connected 'neighbors'. An algorithm traverses the graph, labeling the vertices based on the connectivity and relative values of their neighbors. Connectivity is determined by the medium; image graphs, for example, can be 4-connected neighborhood or 8-connected neighborhood. Following the labeling stage, the graph may be partitioned into subsets, after which the original information can be recovered and processed . == Definition == The usage of the term connected-component labeling (CCL) and its definition is quite consistent in the academic literature, whereas connected-component analysis (CCA) varies both in terminology and in its definition of the problem. Rosenfeld et al. define connected components labeling as the “[c]reation of a labeled image in which the positions associated with the same connected component of the binary input image have a unique label.” Shapiro et al. define CCL as an operator whose “input is a binary image and [...] output is a symbolic image in which the label assigned to each pixel is an integer uniquely identifying the connected component to which that pixel belongs.” There is no consensus on the definition of CCA in the academic literature. It is often used interchangeably with CCL. A more extensive definition is given by Shapiro et al.: “Connected component analysis consists of connected component labeling of the black pixels followed by property measurement of the component regions and decision making.” The definition for connected-component analysis presented here is more general, taking the thoughts expressed in into account. == Algorithms == The algorithms discussed can be generalised to arbitrary dimensions, albeit with increased time and space complexity. === One component at a time === This is a fast and very simple method to implement and understand. It is based on graph traversal methods in graph theory. In short, once the first pixel of a connected component is found, all the connected pixels of that connected component are labelled before going onto the next pixel in the image. This algorithm is part of Vincent and Soille's watershed segmentation algorithm, other implementations also exist. In order to do that a linked list is formed that will keep the indexes of the pixels that are connected to each other, steps (2) and (3) below. The method of defining the linked list specifies the use of a depth or a breadth first search. For this particular application, there is no difference which strategy to use. The simplest kind of a last in first out queue implemented as a singly linked list will result in a depth first search strategy. It is assumed that the input image is a binary image, with pixels being either background or foreground and that the connected components in the foreground pixels are desired. The algorithm steps can be written as: Start from the first pixel in the image. Set current label to 1. Go to (2). If this pixel is a foreground pixel and it is not already labelled, give it the current label and add it as the first element in a queue, then go to (3). If it is a background pixel or it was already labelled, then repeat (2) for the next pixel in the image. Pop out an element from the queue, and look at its neighbours (based on any type of connectivity). If a neighbour is a foreground pixel and is not already labelled, give it the current label and add it to the queue. Repeat (3) until there are no more elements in the queue. Go to (2) for the next pixel in the image and increment current label by 1. Note that the pixels are labelled before being put into the queue. The queue will only keep a pixel to check its neighbours and add them to the queue if necessary. This algorithm only needs to check the neighbours of each foreground pixel once and doesn't check the neighbours of background pixels. The pseudocode is: algorithm OneComponentAtATime(data) input : imageData[xDim][yDim] initialization : label = 0, labelArray[xDim][yDim] = 0, statusArray[xDim][yDim] = false, queue1, queue2; for i = 0 to xDim do for j = 0 to yDim do if imageData[i][j] has not been processed do if imageData[i][j] is a foreground pixel do check its four neighbors(north, south, east, west) : if neighbor is not processed do if neighbor is a foreground pixel do add it to queue1 else update its status to processed end if labelArray[i][j] = label (give label) statusArray[i][j] = true (update status) while queue1 is not empty do For each pixel in the queue do : check its four neighbors if neighbor is not processed do if neighbor is a foreground pixel do add it to queue2 else update its status to processed end if give it the current label update its status to processed remove the current element from queue1 copy queue2 into queue1 end While increase the label end if else update its status to processed end if end if end if end for end for === Two-pass === Relatively simple to implement and understand, the two-pass algorithm, (also known as the Hoshen–Kopelman algorithm) iterates through 2-dimensional binary data. The algorithm makes two passes over the image: the first pass to assign temporary labels and record equivalences, and the second pass to replace each temporary label by the smallest label of its equivalence class. The input data can be modified in situ (which carries the risk of data corruption), or labeling information can be maintained in an additional data structure. Connectivity checks are carried out by checking neighbor pixels' labels (neighbor elements whose labels are not assigned yet are ignored), or say, the north-east, the north, the north-west and the west of the current pixel (assuming 8-connectivity). 4-connectivity uses only north and west neighbors of the current pixel. The following conditions are checked to determine the value of the label to be assigned to the current pixel (4-connectivity is assumed) Conditions to check: Does the pixel to the left (west) have the same value as the current pixel? Yes – We are in the same region. Assign the same label to the current pixel No – Check next condition Do both pixels to the north and west of the current pixel have the same value as the current pixel but not the same label? Yes – We know that the north and west pixels belong to the same region and must be merged. Assign the current pixel the minimum of the north and west labels, and record their equivalence relationship No – Check next condition Does the pixel to the left (west) have a different value and the one to the north the same value as the current pixel? Yes – Assign the label of the north pixel to the current pixel No – Check next condition Do the pixel's north and west neighbors have different pixel values than current pixel? Yes – Create a new label id and assign it to the current pixel The algorithm continues this way, and creates new region labels whenever necessary. The key to a fast algorithm, however, is how this merging is done. This algorithm uses the union-find data structure which provides excellent performance for keeping track of equivalence relationships. Union-find essentially stores labels which correspond to the same blob in a disjoint-set data structure, making it easy to remember the equivalence of two labels by the use of an interface method E.g.: findSet(l). findSet(l) returns the minimum label value that is equivalent to the function argument 'l'. Once the initial labeling and equivalence recording is completed, the second pass merely replaces each pixel label with its equivalent disjoint-set representative element. A faster-scanning algorithm for connected-region extraction is presented below. On the first pass: Iterate through each element of the data by column, then by row (Raster Scanning) If the element is not the background Get the neighboring elements of the current element If there are no neighbors, uniquely
Quantum neural network
Quantum neural networks are computational neural network models which are based on the principles of quantum mechanics. The first ideas on quantum neural computation were published independently in 1995 by Subhash Kak and Ron Chrisley, engaging with the theory of quantum mind, which posits that quantum effects play a role in cognitive function. However, typical research in quantum neural networks involves combining classical artificial neural network models (which are widely used in machine learning for the important task of pattern recognition) with the advantages of quantum information in order to develop more efficient algorithms. One important motivation for these investigations is the difficulty to train classical neural networks, especially in big data applications. The hope is that features of quantum computing such as quantum parallelism or the effects of interference and entanglement can be used as resources. Since the technological implementation of a quantum computer is still in a premature stage, such quantum neural network models are mostly theoretical proposals that await their full implementation in physical experiments. Most Quantum neural networks are developed as feed-forward networks. Similar to their classical counterparts, this structure intakes input from one layer of qubits, and passes that input onto another layer of qubits. This layer of qubits evaluates this information and passes on the output to the next layer. Eventually the path leads to the final layer of qubits. The layers do not have to be of the same width, meaning they don't have to have the same number of qubits as the layer before or after it. This structure is trained on which path to take similar to classical artificial neural networks. This is discussed in a lower section. Quantum neural networks refer to three different categories: Quantum computer with classical data, classical computer with quantum data, and quantum computer with quantum data. == Examples == Quantum neural network research is still in its infancy, and a conglomeration of proposals and ideas of varying scope and mathematical rigor have been put forward. Most of them are based on the idea of replacing classical binary or McCulloch-Pitts neurons with a qubit (which can be called a "quron"), resulting in neural units that can be in a superposition of the state 'firing' and 'resting'. === Quantum perceptrons === A lot of proposals attempt to find a quantum equivalent for the perceptron unit from which neural nets are constructed. A problem is that nonlinear activation functions do not immediately correspond to the mathematical structure of quantum theory, since a quantum evolution is described by linear operations and leads to probabilistic observation. Ideas to imitate the perceptron activation function with a quantum mechanical formalism reach from special measurements to postulating non-linear quantum operators (a mathematical framework that is disputed). A direct implementation of the activation function using the circuit-based model of quantum computation has recently been proposed by Schuld, Sinayskiy and Petruccione based on the quantum phase estimation algorithm. === Quantum networks === At a larger scale, researchers have attempted to generalize neural networks to the quantum setting. One way of constructing a quantum neuron is to first generalise classical neurons and then generalising them further to make unitary gates. Interactions between neurons can be controlled quantumly, with unitary gates, or classically, via measurement of the network states. This high-level theoretical technique can be applied broadly, by taking different types of networks and different implementations of quantum neurons, such as photonically implemented neurons and quantum reservoir processor (quantum version of reservoir computing). Most learning algorithms follow the classical model of training an artificial neural network to learn the input-output function of a given training set and use classical feedback loops to update parameters of the quantum system until they converge to an optimal configuration. Learning as a parameter optimisation problem has also been approached by adiabatic models of quantum computing. Quantum neural networks can be applied to algorithmic design: given qubits with tunable mutual interactions, one can attempt to learn interactions following the classical backpropagation rule from a training set of desired input-output relations, taken to be the desired output algorithm's behavior. The quantum network thus 'learns' an algorithm. === Quantum associative memory === The first quantum associative memory algorithm was introduced by Dan Ventura and Tony Martinez in 1999. The authors do not attempt to translate the structure of artificial neural network models into quantum theory, but propose an algorithm for a circuit-based quantum computer that simulates associative memory. The memory states (in Hopfield neural networks saved in the weights of the neural connections) are written into a superposition, and a Grover-like quantum search algorithm retrieves the memory state closest to a given input. As such, this is not a fully content-addressable memory, since only incomplete patterns can be retrieved. The first truly content-addressable quantum memory, which can retrieve patterns also from corrupted inputs, was proposed by Carlo A. Trugenberger. Both memories can store an exponential (in terms of n qubits) number of patterns but can be used only once due to the no-cloning theorem and their destruction upon measurement. Trugenberger, however, has shown that his probabilistic model of quantum associative memory can be efficiently implemented and re-used multiples times for any polynomial number of stored patterns, a large advantage with respect to classical associative memories. === Classical neural networks inspired by quantum theory === A substantial amount of interest has been given to a "quantum-inspired" model that uses ideas from quantum theory to implement a neural network based on fuzzy logic. == Training == Quantum Neural Networks can be theoretically trained similarly to training classical/artificial neural networks. A key difference lies in communication between the layers of a neural networks. For classical neural networks, at the end of a given operation, the current perceptron copies its output to the next layer of perceptron(s) in the network. However, in a quantum neural network, where each perceptron is a qubit, this would violate the no-cloning theorem. A proposed generalized solution to this is to replace the classical fan-out method with an arbitrary unitary that spreads out, but does not copy, the output of one qubit to the next layer of qubits. Using this fan-out Unitary ( U f {\displaystyle U_{f}} ) with a dummy state qubit in a known state (Ex. | 0 ⟩ {\displaystyle |0\rangle } in the computational basis), also known as an Ancilla bit, the information from the qubit can be transferred to the next layer of qubits. This process adheres to the quantum operation requirement of reversibility. Using this quantum feed-forward network, deep neural networks can be executed and trained efficiently. A deep neural network is essentially a network with many hidden-layers, as seen in the sample model neural network above. Since the Quantum neural network being discussed uses fan-out Unitary operators, and each operator only acts on its respective input, only two layers are used at any given time. In other words, no Unitary operator is acting on the entire network at any given time, meaning the number of qubits required for a given step depends on the number of inputs in a given layer. Since Quantum Computers are notorious for their ability to run multiple iterations in a short period of time, the efficiency of a quantum neural network is solely dependent on the number of qubits in any given layer, and not on the depth of the network. === Cost functions === To determine the effectiveness of a neural network, a cost function is used, which essentially measures the proximity of the network's output to the expected or desired output. In a Classical Neural Network, the weights ( w {\displaystyle w} ) and biases ( b {\displaystyle b} ) at each step determine the outcome of the cost function C ( w , b ) {\displaystyle C(w,b)} . When training a Classical Neural network, the weights and biases are adjusted after each iteration, and given equation 1 below, where y ( x ) {\displaystyle y(x)} is the desired output and a out ( x ) {\displaystyle a^{\text{out}}(x)} is the actual output, the cost function is optimized when C ( w , b ) {\displaystyle C(w,b)} = 0. For a quantum neural network, the cost function is determined by measuring the fidelity of the outcome state ( ρ out {\displaystyle \rho ^{\text{out}}} ) with the desired outcome state ( ϕ out {\displaystyle \phi ^{\text{out}}} ), seen in Equation 2 below. In this case, the Unitary operators are adjusted after each it
Spiking neural network
Spiking neural networks (SNNs) are artificial neural networks (ANN) that mimic natural neural networks. These models leverage timing of discrete spikes as the main information carrier. In addition to neuronal and synaptic state, SNNs incorporate the concept of time into their operating model. The idea is that neurons in the SNN do not transmit information at each propagation cycle (as it happens with typical multi-layer perceptron networks), but rather transmit information only when a membrane potential—an intrinsic quality of the neuron related to its membrane electrical charge—reaches a specific value, called the threshold. When the membrane potential reaches the threshold, the neuron fires, and generates a signal that travels to other neurons which, in turn, increase or decrease their potentials in response to this signal. A neuron model that fires at the moment of threshold crossing is also called a spiking neuron model. While spike rates can be considered the analogue of the variable output of a traditional ANN, neurobiology research indicated that high speed processing cannot be performed solely through a rate-based scheme. For example humans can perform an image recognition task requiring no more than 10ms of processing time per neuron through the successive layers (going from the retina to the temporal lobe). This time window is too short for rate-based encoding. The precise spike timings in a small set of spiking neurons also has a higher information coding capacity compared with a rate-based approach. The most prominent spiking neuron model is the leaky integrate-and-fire model. In that model, the momentary activation level (modeled as a differential equation) is normally considered to be the neuron's state, with incoming spikes pushing this value higher or lower, until the state eventually either decays or—if the firing threshold is reached—the neuron fires. After firing, the state variable is reset to a lower value. Various decoding methods exist for interpreting the outgoing spike train as a real-value number, relying on either the frequency of spikes (rate-code), the time-to-first-spike after stimulation, or the interval between spikes. == History == Many multi-layer artificial neural networks are fully connected, receiving input from every neuron in the previous layer and signalling every neuron in the subsequent layer. Although these networks have achieved breakthroughs, they do not match biological networks and do not mimic neurons. The biology-inspired Hodgkin–Huxley model of a spiking neuron was proposed in 1952. This model described how action potentials are initiated and propagated. Communication between neurons, which requires the exchange of chemical neurotransmitters in the synaptic gap, is described in models such as the integrate-and-fire model, FitzHugh–Nagumo model (1961–1962), and Hindmarsh–Rose model (1984). The leaky integrate-and-fire model (or a derivative) is commonly used as it is easier to compute than Hodgkin–Huxley. While the notion of an artificial spiking neural network became popular only in the twenty-first century, studies between 1980 and 1995 supported the concept. The first models of this type of ANN appeared to simulate non-algorithmic intelligent information processing systems. However, the notion of the spiking neural network as a mathematical model was first worked on in the early 1970s. As of 2019 SNNs lagged behind ANNs in accuracy, but the gap is decreasing, and has vanished on some tasks. == Underpinnings == Information in the brain is represented as action potentials (neuron spikes), which may group into spike trains or coordinated waves. A fundamental question of neuroscience is to determine whether neurons communicate by a rate or temporal code. Temporal coding implies that a single spiking neuron can replace hundreds of hidden units on a conventional neural net. SNNs define a neuron's current state as its potential (possibly modeled as a differential equation). An input pulse causes the potential to rise and then gradually decline. Encoding schemes can interpret these pulse sequences as a number, considering pulse frequency and pulse interval. Using the precise time of pulse occurrence, a neural network can consider more information and offer better computing properties. SNNs compute in the continuous domain. Such neurons test for activation only when their potentials reach a certain value. When a neuron is activated, it produces a signal that is passed to connected neurons, accordingly raising or lowering their potentials. The SNN approach produces a continuous output instead of the binary output of traditional ANNs. Pulse trains are not easily interpretable, hence the need for encoding schemes. However, a pulse train representation may be more suited for processing spatiotemporal data (or real-world sensory data classification). SNNs connect neurons only to nearby neurons so that they process input blocks separately (similar to CNN using filters). They consider time by encoding information as pulse trains so as not to lose information. This avoids the complexity of a recurrent neural network (RNN). Impulse neurons are more powerful computational units than traditional artificial neurons. SNNs are theoretically more powerful than so called "second-generation networks" defined as ANNs "based on computational units that apply activation function with a continuous set of possible output values to a weighted sum (or polynomial) of the inputs"; however, SNN training issues and hardware requirements limit their use. Although unsupervised biologically inspired learning methods are available such as Hebbian learning and STDP, no effective supervised training method is suitable for SNNs that can provide better performance than second-generation networks. Spike-based activation of SNNs is not differentiable, thus gradient descent-based backpropagation (BP) is not available. SNNs have much larger computational costs for simulating realistic neural models than traditional ANNs. Pulse-coupled neural networks (PCNN) are often confused with SNNs. A PCNN can be seen as a kind of SNN. Researchers are actively working on various topics. The first concerns differentiability. The expressions for both the forward- and backward-learning methods contain the derivative of the neural activation function which is not differentiable because a neuron's output is either 1 when it spikes, and 0 otherwise. This all-or-nothing behavior disrupts gradients and makes these neurons unsuitable for gradient-based optimization. Approaches to resolving it include: resorting to entirely biologically inspired local learning rules for the hidden units translating conventionally trained "rate-based" NNs to SNNs smoothing the network model to be continuously differentiable defining an SG (Surrogate Gradient) as a continuous relaxation of the real gradients The second concerns the optimization algorithm. Standard BP can be expensive in terms of computation, memory, and communication and may be poorly suited to the hardware that implements it (e.g., a computer, brain, or neuromorphic device). Incorporating additional neuron dynamics such as Spike Frequency Adaptation (SFA) is a notable advance, enhancing efficiency and computational power. These neurons sit between biological complexity and computational complexity. Originating from biological insights, SFA offers significant computational benefits by reducing power usage, especially in cases of repetitive or intense stimuli. This adaptation improves signal/noise clarity and introduces an elementary short-term memory at the neuron level, which in turn, improves accuracy and efficiency. This was mostly achieved using compartmental neuron models. The simpler versions are of neuron models with adaptive thresholds, are an indirect way of achieving SFA. It equips SNNs with improved learning capabilities, even with constrained synaptic plasticity, and elevates computational efficiency. This feature lessens the demand on network layers by decreasing the need for spike processing, thus lowering computational load and memory access time—essential aspects of neural computation. Moreover, SNNs utilizing neurons capable of SFA achieve levels of accuracy that rival those of conventional ANNs, while also requiring fewer neurons for comparable tasks. This efficiency streamlines the computational workflow and conserves space and energy, while maintaining technical integrity. High-performance deep spiking neural networks can operate with 0.3 spikes per neuron. == Applications == SNNs can in principle be applied to the same applications as traditional ANNs. In addition, SNNs can model the central nervous system of biological organisms, such as an insect seeking food without prior knowledge of the environment. Due to their relative realism, they can be used to study biological neural circuits. Starting with a hypothesis about the topology of a biological neuronal circuit and its functi
Independent component analysis
In signal processing, independent component analysis (ICA) is a computational method for separating a multivariate signal into additive subcomponents. This is done by assuming that at most one subcomponent is Gaussian and that the subcomponents are statistically independent from each other. ICA was invented by Jeanny Hérault and Christian Jutten in 1985. ICA is a special case of blind source separation. A common example application of ICA is the "cocktail party problem" of listening in on one person's speech in a noisy room. == Introduction == Independent component analysis attempts to decompose a multivariate signal into independent non-Gaussian signals. As an example, sound is usually a signal that is composed of the numerical addition, at each time t, of signals from several sources. The question then is whether it is possible to separate these contributing sources from the observed total signal. When the statistical independence assumption is correct, blind ICA separation of a mixed signal gives very good results. It is also used for signals that are not supposed to be generated by mixing for analysis purposes. A simple application of ICA is the "cocktail party problem", where the underlying speech signals are separated from a sample data consisting of people talking simultaneously in a room. Usually the problem is simplified by assuming no time delays or echoes. Note that a filtered and delayed signal is a copy of a dependent component, and thus the statistical independence assumption is not violated. Mixing weights for constructing the M {\textstyle M} observed signals from the N {\textstyle N} components can be placed in an M × N {\textstyle M\times N} matrix. An important thing to consider is that if N {\textstyle N} sources are present, at least N {\textstyle N} observations (e.g. microphones if the observed signal is audio) are needed to recover the original signals. When there are an equal number of observations and source signals, the mixing matrix is square ( M = N {\textstyle M=N} ). Other cases of underdetermined ( M < N {\textstyle M
ViBe
ViBe is a background subtraction algorithm which has been presented at the IEEE ICASSP 2009 conference and was refined in later publications. More precisely, it is a software module for extracting background information from moving images. It has been developed by Oliver Barnich and Marc Van Droogenbroeck of the Montefiore Institute, University of Liège, Belgium. ViBe is patented: the patent covers various aspects such as stochastic replacement, spatial diffusion, and non-chronological handling. ViBe is written in the programming language C, and has been implemented on CPU, GPU and FPGA. == Technical description == Source: === Pixel model and classification process === Many advanced techniques are used to provide an estimate of the temporal probability density function (pdf) of a pixel x. ViBe's approach is different, as it imposes the influence of a value in the polychromatic space to be limited to the local neighborhood. In practice, ViBe does not estimate the pdf, but uses a set of previously observed sample values as a pixel model. To classify a value pt(x), it is compared to its closest values among the set of samples. === Model update: Sample values lifespan policy === ViBe ensures a smooth exponentially decaying lifespan for the sample values that constitute the pixel models. This makes ViBe able to successfully deal with concomitant events with a single model of a reasonable size for each pixel. This is achieved by choosing, randomly, which sample to replace when updating a pixel model. Once the sample to be discarded has been chosen, the new value replaces the discarded sample. The pixel model that would result from the update of a given pixel model with a given pixel sample cannot be predicted since the value to be discarded is chosen at random. === Model update: Spatial Consistency === To ensure the spatial consistency of the whole image model and handle practical situations such as small camera movements or slowly evolving background objects, ViBe uses a technique similar to that developed for the updating process in which it chooses at random and update a pixel model in the neighborhood of the current pixel. By denoting NG(x) and p(x) respectively the spatial neighborhood of a pixel x and its value, and assuming that it was decided to update the set of samples of x by inserting p(x), then ViBe also use this value p(x) to update the set of samples of one of the pixels in the neighborhood NG(x), chosen at random. As a result, ViBe is able to produce spatially coherent results directly without the use of any post-processing method. === Model initialization === Although the model could easily recover from any type of initialization, for example by choosing a set of random values, it is convenient to get an accurate background estimate as soon as possible. Ideally a segmentation algorithm would like to be able to segment the video sequences starting from the second frame, the first frame being used to initialize the model. Since no temporal information is available prior to the second frame, ViBe populates the pixel models with values found in the spatial neighborhood of each pixel; more precisely, it initializes the background model with values taken randomly in each pixel neighborhood of the first frame. The background estimate is therefore valid starting from the second frame of a video sequence.
Promoter based genetic algorithm
The promoter based genetic algorithm (PBGA) is a genetic algorithm for neuroevolution developed by F. Bellas and R.J. Duro in the Integrated Group for Engineering Research (GII) at the University of Coruña, in Spain. It evolves variable size feedforward artificial neural networks (ANN) that are encoded into sequences of genes for constructing a basic ANN unit. Each of these blocks is preceded by a gene promoter acting as an on/off switch that determines if that particular unit will be expressed or not. == PBGA basics == The basic unit in the PBGA is a neuron with all of its inbound connections as represented in the following figure: The genotype of a basic unit is a set of real valued weights followed by the parameters of the neuron and proceeded by an integer valued field that determines the promoter gene value and, consequently, the expression of the unit. By concatenating units of this type we can construct the whole network. With this encoding it is imposed that the information that is not expressed is still carried by the genotype in evolution but it is shielded from direct selective pressure, maintaining this way the diversity in the population, which has been a design premise for this algorithm. Therefore, a clear difference is established between the search space and the solution space, permitting information learned and encoded into the genotypic representation to be preserved by disabling promoter genes. == Results == The PBGA was originally presented within the field of autonomous robotics, in particular in the real time learning of environment models of the robot. It has been used inside the Multilevel Darwinist Brain (MDB) cognitive mechanism developed in the GII for real robots on-line learning. In another paper it is shown how the application of the PBGA together with an external memory that stores the successful obtained world models, is an optimal strategy for adaptation in dynamic environments. Recently, the PBGA has provided results that outperform other neuroevolutionary algorithms in non-stationary problems, where the fitness function varies in time.