Mathematical symbols and computing methods in high dimensional biomimetic informatics and their applications

High dimensional biomimetic informatics (HDBI) is a novel theory of informatics developed in recent years. Its primary object of research is points in high dimensional Euclidean space, and its exploratory and resolving procedures are based on simple geometric computations. However, the mathematical descriptions and computing of geometric objects are inconvenient because of the characters of geometry. With the increase of the dimension and the multiformity of geometric objects, these descriptions are more complicated and prolix especially in high dimensional space. In this paper, we give some definitions and mathematical symbols, and discuss some symbolic computing methods in high dimensional space systematically from the viewpoint of HDBI. With these methods, some multi-variables problems in high dimensional space can be solved easily. Three detailed algorithms are presented as examples to show the efficiency of our symbolic computing methods: the algorithm for judging the center of a circle given three points on this circle, the algorithm for judging whether two points are on the same side of a hyperplane, and the algorithm for judging whether a point is in a simplex constructed by points in high dimensional space. Two experiments in blurred image restoration and uneven lighting image correction are presented for all these algorithms to show their good behaviors.

The application of DBF neural networks for object recognition

On the basis of DBF nets proposed by Wang Shoujue, the model and properties of DBF neural network were discussed in this paper. When applied in pattern recognition, the algorithm and implement on hardware were presented respectively. We did experiments on recognition of omnidirectionally oriented rigid objects on the same level, using direction basis function neural networks, which acts by the method of covering the high dimensional geometrical distribution of the sample set in the feature space. Many animal and vehicle models (even with rather similar shapes) were recognized omnidirectionally thousands of times. For total 8800 tests, the correct recognition rate is 98.75%, the error rate and the rejection rate are 0.5% and 1.25% respectively. (C) 2003 Elsevier Inc. All rights reserved.

Double synaptic weight neuron theory and its application

In this paper, a novel mathematical model of neuron-Double Synaptic Weight Neuron (DSWN)(l) is presented. The DSWN can simulate many kinds of neuron architectures, including Radial-Basis-Function (RBF), Hyper Sausage and Hyper Ellipsoid models, etc. Moreover, this new model has been implemented in the new CASSANN-II neurocomputer that can be used to form various types of neural networks with multiple mathematical models of neurons. The flexibility of the DSWN has also been described in constructing neural networks. Based on the theory of Biomimetic Pattern Recognition (BPR) and high-dimensional space covering, a recognition system of omni directionally oriented rigid objects on the horizontal surface and a face recognition system had been implemented on CASSANN-II neurocomputer. In these two special cases, the result showed DSWN neural network had great potential in pattern recognition.

Cortical Learning of Recognition Categories: A Resolution of the Exemplar Vs. Prototype Debate

Do humans and animals learn exemplars or prototypes when they categorize objects and events in the world? How are different degrees of abstraction realized through learning by neurons in inferotemporal and prefrontal cortex? How do top-down expectations influence the course of learning? Thirty related human cognitive experiments (the 5-4 category structure) have been used to test competing views in the prototype-exemplar debate. In these experiments, during the test phase, subjects unlearn in a characteristic way items that they had learned to categorize perfectly in the training phase. Many cognitive models do not describe how an individual learns or forgets such categories through time. Adaptive Resonance Theory (ART) neural models provide such a description, and also clarify both psychological and neurobiological data. Matching of bottom-up signals with learned top-down expectations plays a key role in ART model learning. Here, an ART model is used to learn incrementally in response to 5-4 category structure stimuli. Simulation results agree with experimental data, achieving perfect categorization in training and a good match to the pattern of errors exhibited by human subjects in the testing phase. These results show how the model learns both prototypes and certain exemplars in the training phase. ART prototypes are, however, unlike the ones posited in the traditional prototype-exemplar debate. Rather, they are critical patterns of features to which a subject learns to pay attention based on past predictive success and the order in which exemplars are experienced. Perturbations of old memories by newly arriving test items generate a performance curve that closely matches the performance pattern of human subjects. The model also clarifies exemplar-based accounts of data concerning amnesia.

Differential and numerical models of hysteretic systems with stochastic and deterministic inputs

Many deterministic models with hysteresis have been developed in the areas of economics, finance, terrestrial hydrology and biology. These models lack any stochastic element which can often have a strong effect in these areas. In this work stochastically driven closed loop systems with hysteresis type memory are studied. This type of system is presented as a possible stochastic counterpart to deterministic models in the areas of economics, finance, terrestrial hydrology and biology. Some price dynamics models are presented as a motivation for the development of this type of model. Numerical schemes for solving this class of stochastic differential equation are developed in order to examine the prototype models presented. As a means of further testing the developed numerical schemes, numerical examination is made of the behaviour near equilibrium of coupled ordinary differential equations where the time derivative of the Preisach operator is included in one of the equations. A model of two phenotype bacteria is also presented. This model is examined to explore memory effects and related hysteresis effects in the area of biology. The memory effects found in this model are similar to that found in the non-ideal relay. This non-ideal relay type behaviour is used to model a colony of bacteria with multiple switching thresholds. This model contains a Preisach type memory with a variable Preisach weight function. Shown numerically for this multi-threshold model is a pattern formation for the distribution of the phenotypes among the available thresholds.

Comparison of pattern detection methods in microarray time series of the segmentation clock.

While genome-wide gene expression data are generated at an increasing rate, the repertoire of approaches for pattern discovery in these data is still limited. Identifying subtle patterns of interest in large amounts of data (tens of thousands of profiles) associated with a certain level of noise remains a challenge. A microarray time series was recently generated to study the transcriptional program of the mouse segmentation clock, a biological oscillator associated with the periodic formation of the segments of the body axis. A method related to Fourier analysis, the Lomb-Scargle periodogram, was used to detect periodic profiles in the dataset, leading to the identification of a novel set of cyclic genes associated with the segmentation clock. Here, we applied to the same microarray time series dataset four distinct mathematical methods to identify significant patterns in gene expression profiles. These methods are called: Phase consistency, Address reduction, Cyclohedron test and Stable persistence, and are based on different conceptual frameworks that are either hypothesis- or data-driven. Some of the methods, unlike Fourier transforms, are not dependent on the assumption of periodicity of the pattern of interest. Remarkably, these methods identified blindly the expression profiles of known cyclic genes as the most significant patterns in the dataset. Many candidate genes predicted by more than one approach appeared to be true positive cyclic genes and will be of particular interest for future research. In addition, these methods predicted novel candidate cyclic genes that were consistent with previous biological knowledge and experimental validation in mouse embryos. Our results demonstrate the utility of these novel pattern detection strategies, notably for detection of periodic profiles, and suggest that combining several distinct mathematical approaches to analyze microarray datasets is a valuable strategy for identifying genes that exhibit novel, interesting transcriptional patterns.

A spatio-temporal 2D-models framework for human pose recovery in monocular sequences

This paper addresses the pose recovery problem of a particular articulated object: the human body. In this model-based approach, the 2D-shape is associated to the corresponding stick figure allowing the joint segmentation and pose recovery of the subject observed in the scene. The main disadvantage of 2D-models is their restriction to the viewpoint. To cope with this limitation, local spatio-temporal 2D-models corresponding to many views of the same sequences are trained, concatenated and sorted in a global framework. Temporal and spatial constraints are then considered to build the probabilistic transition matrix (PTM) that gives a frame to frame estimation of the most probable local models to use during the fitting procedure, thus limiting the feature space. This approach takes advantage of 3D information avoiding the use of a complex 3D human model. The experiments carried out on both indoor and outdoor sequences have demonstrated the ability of this approach to adequately segment pedestrians and estimate their poses independently of the direction of motion during the sequence. (c) 2008 Elsevier Ltd. All rights reserved.

2D silhouette and 3D skeletal models for human detection and tracking

In this paper we propose a statistical model for detection and tracking of human silhouette and the corresponding 3D skeletal structure in gait sequences. We follow a point distribution model (PDM) approach using a Principal Component Analysis (PCA). The problem of non-lineal PCA is partially resolved by applying a different PDM depending of pose estimation; frontal, lateral and diagonal, estimated by Fisher's linear discriminant. Additionally, the fitting is carried out by selecting the closest allowable shape from the training set by means of a nearest neighbor classifier. To improve the performance of the model we develop a human gait analysis to take into account temporal dynamic to track the human body. The incorporation of temporal constraints on the model increase reliability and robustness.

Multiple Luminaire Identification in Airborne Images of Airport’s Approach Lighting Using Mathematical Morphology With Variable Length Structuring Element

The increasing demand for fast air transportation around the clock
has increased the number of night flights in civil aviation over
the past few decades. In night aviation, to land an aircraft, a
pilot needs to be able to identify an airport. The approach
lighting system (ALS) at an airport is used to provide
identification and guidance to pilots from a distance. ALS
consists of more than $100$ luminaires which are installed in a
defined pattern following strict guidelines by the International
Civil Aviation Organization (ICAO). ICAO also has strict
regulations for maintaining the performance level of the
luminaires. However, once installed, to date there is no automated
technique by which to monitor the performance of the lighting. We
suggest using images of the lighting pattern captured using a camera
placed inside an aircraft. Based on the information contained
within these images, the performance of the luminaires has to be
evaluated which requires identification of over $100$ luminaires
within the pattern of ALS image. This research proposes analysis
of the pattern using morphology filters which use a variable
length structuring element (VLSE). The dimension of the VLSE changes
continuously within an image and varies for different images.
A novel
technique for automatic determination of the VLSE is proposed and
it allows successful identification of the luminaires from the
image data as verified through the use of simulated and real data.

3D Morphable Model Construction for Robust Ear and Face Recognition

Recent work suggests that the human ear varies significantly between different subjects and can be used for identification. In principle, therefore, using ears in addition to the face within a recognition system could improve accuracy and robustness, particularly for non-frontal views. The paper describes work that investigates this hypothesis using an approach based on the construction of a 3D morphable model of the head and ear. One issue with creating a model that includes the ear is that existing training datasets contain noise and partial occlusion. Rather than exclude these regions manually, a classifier has been developed which automates this process. When combined with a robust registration algorithm the resulting system enables full head morphable models to be constructed efficiently using less constrained datasets. The algorithm has been evaluated using registration consistency, model coverage and minimalism metrics, which together demonstrate the accuracy of the approach. To make it easier to build on this work, the source code has been made available online.

Face Recognition in the Scrambled Domain via Salience-Aware Ensembles of Many Kernels

With the rapid development of internet-of-things (IoT), face scrambling has been proposed for privacy protection during IoT-targeted image/video distribution. Consequently in these IoT applications, biometric verification needs to be carried out in the scrambled domain, presenting significant challenges in face recognition. Since face models become chaotic signals after scrambling/encryption, a typical solution is to utilize traditional data-driven face recognition algorithms. While chaotic pattern recognition is still a challenging task, in this paper we propose a new ensemble approach – Many-Kernel Random Discriminant Analysis (MK-RDA) to discover discriminative patterns from chaotic signals. We also incorporate a salience-aware strategy into the proposed ensemble method to handle chaotic facial patterns in the scrambled domain, where random selections of features are made on semantic components via salience modelling. In our experiments, the proposed MK-RDA was tested rigorously on three human face datasets: the ORL face dataset, the PIE face dataset and the PUBFIG wild face dataset. The experimental results successfully demonstrate that the proposed scheme can effectively handle chaotic signals and significantly improve the recognition accuracy, making our method a promising candidate for secure biometric verification in emerging IoT applications.

Face segregation and recognition by cortical multi-scale line and edge coding

Models of visual perception are based on image representations in cortical area V1 and higher areas which contain many cell layers for feature extraction. Basic simple, complex and end-stopped cells provide input for line, edge and keypoint detection. In this paper we present an improved method for multi-scale line/edge detection based on simple and complex cells. We illustrate the line/edge representation for object reconstruction, and we present models for multi-scale face (object) segregation and recognition that can be embedded into feedforward dorsal and ventral data streams (the “what” and “where” subsystems) with feedback streams from higher areas for obtaining translation, rotation and scale invariance.

Modeling sequencing errors by combining Hidden Markov models.

Among the largest resources for biological sequence data is the large amount of expressed sequence tags (ESTs) available in public and proprietary databases. ESTs provide information on transcripts but for technical reasons they often contain sequencing errors. Therefore, when analyzing EST sequences computationally, such errors must be taken into account. Earlier attempts to model error prone coding regions have shown good performance in detecting and predicting these while correcting sequencing errors using codon usage frequencies. In the research presented here, we improve the detection of translation start and stop sites by integrating a more complex mRNA model with codon usage bias based error correction into one hidden Markov model (HMM), thus generalizing this error correction approach to more complex HMMs. We show that our method maintains the performance in detecting coding sequences.