Cue combination in the motion correspondence problem

Image motion is a primary source of visual information about the world. However, before this information can be used the visual system must determine the spatio-temporal displacements of the features in the dynamic retinal image, which originate from objects moving in space. This is known as the motion correspondence problem. We investigated whether cross-cue matching constraints contribute to the solution of this problem, which would be consistent with physiological reports that many directionally selective cells in the visual cortex also respond to additional visual cues. We measured the maximum displacement limit (Dmax) for two-frame apparent motion sequences. Dmax increases as the number of elements in such sequences decreases. However, in our displays the total number of elements was kept constant while the number of a subset of elements, defined by a difference in contrast polarity, binocular disparity or colour, was varied. Dmax increased as the number of elements distinguished by a particular cue was decreased. Dmax was affected by contrast polarity for all observers, but only some observers were influenced by binocular disparity and others by colour information. These results demonstrate that the human visual system exploits local, cross-cue matching constraints in the solution of the motion correspondence problem.     

A neural network model for stroboscopic alternative motion

A neural network which models multistable perception is presented. The network consists of sensor and inner neurons. The dynamics is established by a stochastic neuronal dynamics, a formal Hebb-type coupling dynamics and a resource mechanism that corresponds to saturation effects in perception. From this a system of coupled differential equations is derived and analyzed. Single stimuli are bound to exactly one percept, even in ambiguous situations where multistability occurs. The network exhibits discontinuous as well as continuous phase transitions and models various empirical findings, including the percepts of succession, alternative motion and simultaneity; the percept of oscillation is explained by oscillating percepts at a continuous phase transition. Received: 13 September 1995 / Accepted: 3 June 1996     

A neural network for the Steiner minimal tree problem

The problem of finding the shortest tree connecting a set of points is called the Steiner minimal tree problem and is nearly three centuries old. It has applications in transportation, computer networks, agriculture, telephony, building layout and very large scale integrated circuit (VLSI) design, among others, and is known to be NP-complete. We propose a neural network which self-organizes to find a minimal tree. Solutions found by the network compare favourably with the best known or optimal results on test problems from the literature. To the best of our knowledge, the proposed network is the first neural-based solution to the problem. We show that the neural network has a built-in mechanism to escape local minima.     

A neural network algorithm for the multiple traveling salesmen problem

We developed an efficient neural network algorithm for solving the Multiple Traveling Salesmen Problem (MTSP). A new transformation of the N-city M-salesmen MTSP to the standard Traveling Salesmen Problem (TSP) is introduced. The transformed problem is represented by an expanded version of Hopfield-Tank's neuromorphic city-position map with (N + M-1)-cities and a single fictitious salesmen. The dynamic model associated with the problem is based on the Basic Differential Multiplier Method (BDMM) [26] which evaluates Lagrange multipliers simultaneously with the problem's state variables. The algorithm was successfully tested on many problems with up to 30 cities and five salesmen. In all test cases, the algorithm always converged to valid solutions. The great advantage of this kind of algorithm is that it can provide solutions to complex decision making problems directly by solving a system of ordinary differential equations. No learning steps, logical if statements or adjusting of parameters are required during the computation. The algorithm can therefore be implemented in hardware to solve complex constraint satisfaction problems such as the MTSP at the speed of analog silicon VLSI devices or possibly future optical neural computers.     

An inference upon the neural network finding binocular correspondence

Previously, the authors proposed a model of neural network extracting binocular parallax (Hirai and Fukushima, 1975). It is a multilayered network whose final layers consist of neural elements corresponding to binocular depth neurons found in monkey's visual cortex. The binocular depth neuron is selectively sensitive to a binocular stimulus with a specific amount of binocular parallax and does not respond to a monocular one. As described in the last chapter of the previous article (Hirai and Fukushima, 1975), when a binocular pair of input patterns consist of, for example, many vertical bars placed very closely to each other, the binocular depth neurons might respond not only to correct binocular pairs, but also to incorrect ones. Our present study is concentrated upon how the visual system finds correct binocular pairs or binocular correspondence. It is assumed that some neural network is cascaded after the binocular depth neurons and finds out correct binocular correspondence by eliminating the incorrect binocular pairs. In this article a model of such neural network is proposed. The performance of the model has been simulated on a digital computer. The results of the computer simulation show that this model finds binocular correspondence satisfactorily. It has been demonstrated by the computer simulation that this model also explains the mechanism of the hysteresis in the binocular depth perception reported by Fender and Julesz (1967)This work has been done in the NHK Broadcasting Science Research Laboratories     

A biologically plausible acoustic motion detection neural network

In this paper we present an acoustic motion detection system to be used in a small mobile robot. While the first purpose of the system has been to be a reliable computational implementation, cheap enough to be built in hardware, effort has also been taken to construct a biologically plausible solution. The motion detector consists of a neural network composed of motion-direction sensitive neurons with a preferred direction and a preferred region of the azimuth. The system was designed to produce a higher response when stimulated by motion in the preferred direction than in the null direction and that is in fact what the system does, which means that, as desired, the system can detect motion and distinguish its direction.     

A space-time delay neural network for motion recognition and its application to lipreading

Motion recognition has received increasing attention in recent years owing to heightened demand for computer vision in many domains, including the surveillance system, multimodal human computer interface, and traffic control system. Most conventional approaches classify the motion recognition task into partial feature extraction and time-domain recognition subtasks. However, the information of motion resides in the space-time domain instead of the time domain or space domain independently, implying that fusing the feature extraction and classification in the space and time domains into a single framework is preferred. Based on this notion, this work presents a novel Space-Time Delay Neural Network (STDNN) capable of handling the space-time dynamic information for motion recognition. The STDNN is unified structure, in which the low-level spatiotemporal feature extraction and high-level space-time-domain recognition are fused. The proposed network possesses the spatiotemporal shift-invariant recognition ability that is inherited from the time delay neural network (TDNN) and space displacement neural network (SDNN), where TDNN and SDNN are good at temporal and spatial shift-invariant recognition, respectively. In contrast to multilayer perceptron (MLP), TDNN, and SDNN, STDNN is constructed by vector-type nodes and matrix-type links such that the spatiotemporal information can be accurately represented in a neural network. Also evaluated herein is the performance of the proposed STDNN via two experiments. The moving Arabic numerals (MAN) experiment simulates the object's free movement in the space-time domain on image sequences. According to these results, STDNN possesses a good generalization ability with respect to the spatiotemporal shift-invariant recognition. In the lipreading experiment, STDNN recognizes the lip motions based on the inputs of real image sequences. This observation confirms that STDNN yields a better performance than the existing TDNN-based system, particularly in terms of the generalization ability. In addition to the lipreading application, the STDNN can be applied to other problems since no domain-dependent knowledge is used in the experiment.     

A neural network learns trajectory of motion from the least action principle

This paper considers the problem of training layered neural networks to generate sequences of states. Aiming at application for situations when an integral characteristic of the process is known rather than the specific sequence of states we put forward a method in which underlying general principle is used as a foundation for the learning procedure. To illustrate the ability of a network to learn a task and to generalize algorithm we consider an example where a network generates sequences of states referred to as trajectories of motion of a particle under an external field. Training is grounded on the employment of the least action principle. In the course of training at restricted sections of the path the network elaborates a recurrent rule for the trajectory generation. The rule proves to be equivalent to the correct equation of motion for the whole trajectory.     

A flexible annealing chaotic neural network to maximum clique problem

Based on the analysis and comparison of several annealing strategies, we present a flexible annealing chaotic neural network which has flexible controlling ability and quick convergence rate to optimization problem. The proposed network has rich and adjustable chaotic dynamics at the beginning, and then can converge quickly to stable states. We test the network on the maximum clique problem by some graphs of the DIMACS clique instances, p-random and k random graphs. The simulations show that the flexible annealing chaotic neural network can get satisfactory solutions at very little time and few steps. The comparison between our proposed network and other chaotic neural networks denotes that the proposed network has superior executive efficiency and better ability to get optimal or near-optimal solution.     

Chaotic neural network applied to two-dimensional motion control

Chaotic dynamics generated in a chaotic neural network model are applied to 2-dimensional (2-D) motion control. The change of position of a moving object in each control time step is determined by a motion function which is calculated from the firing activity of the chaotic neural network. Prototype attractors which correspond to simple motions of the object toward four directions in 2-D space are embedded in the neural network model by designing synaptic connection strengths. Chaotic dynamics introduced by changing system parameters sample intermediate points in the high-dimensional state space between the embedded attractors, resulting in motion in various directions. By means of adaptive switching of the system parameters between a chaotic regime and an attractor regime, the object is able to reach a target in a 2-D maze. In computer experiments, the success rate of this method over many trials not only shows better performance than that of stochastic random pattern generators but also shows that chaotic dynamics can be useful for realizing robust, adaptive and complex control function with simple rules.     

An annealed chaotic maximum neural network for bipartite subgraph problem

In this paper, based on maximum neural network, we propose a new parallel algorithm that can help the maximum neural network escape from local minima by including a transient chaotic neurodynamics for bipartite subgraph problem. The goal of the bipartite subgraph problem, which is an NP- complete problem, is to remove the minimum number of edges in a given graph such that the remaining graph is a bipartite graph. Lee et al. presented a parallel algorithm using the maximum neural model (winner-take-all neuron model) for this NP- complete problem. The maximum neural model always guarantees a valid solution and greatly reduces the search space without a burden on the parameter-tuning. However, the model has a tendency to converge to a local minimum easily because it is based on the steepest descent method. By adding a negative self-feedback to the maximum neural network, we proposed a new parallel algorithm that introduces richer and more flexible chaotic dynamics and can prevent the network from getting stuck at local minima. After the chaotic dynamics vanishes, the proposed algorithm is then fundamentally reined by the gradient descent dynamics and usually converges to a stable equilibrium point. The proposed algorithm has the advantages of both the maximum neural network and the chaotic neurodynamics. A large number of instances have been simulated to verify the proposed algorithm. The simulation results show that our algorithm finds the optimum or near-optimum solution for the bipartite subgraph problem superior to that of the best existing parallel algorithms.     

An improved transiently chaotic neural network for the maximum independent set problem

By analyzing the dynamic behaviors of the transiently chaotic neural network and greedy heuristic for the maximum independent set (MIS) problem, we present an improved transiently chaotic neural network for the MIS problem in this paper. Extensive simulations are performed and the results show that this proposed transiently chaotic neural network can yield better solutions to p-random graphs than other existing algorithms. The efficiency of the new model is also confirmed by the results on the complement graphs of some DIMACS clique instances in the second DIMACS challenge. Moreover, the improved model uses fewer steps to converge to stable state in comparison with the original transiently chaotic neural network.     

Perceived motion in complementary afterimages: verification of a neural network theory

Steady fixation of a regular pattern like a bar grating or concentric circles leads to a complementary afterimage at pattern offset. The afterimage has the appearance of shimmering lines that are locally orthogonal to the orientations of the inducing image. Additionally, the afterimage includes motion running parallel to the orientation of the afterimage lines. We argue that this afterimage motion supports the existence of a cue to motion that is based on the spatial organization of oriented responses. This cue was previously proposed after analysis of a neural network model of visual perception. We test predictions of the model on various types of complementary afterimage inducing stimuli. When a contrast or size gradient is included in the inducing image, the afterimage motion moves toward the higher part of the gradient, in agreement with the model. Implications of this cue for computational and neurophysiological theories of motion perception are discussed.     

A neural network for computing eigenvectors and eigenvalues

A dynamic method which produces estimates of real eigenvectors and eigenvalues is presented. More generally, the technique can be applied to estimate eigenspectra of real n-dimensional k-forms. The proposed approach is based on a spectral splicing property of the line manifolds often found in solutions of polynomial differential equations. As such, it defines an artificial continuous time neural network with stored memories determined by the eigenspectra locations. This paradigm provides a good insight into an analog behavior of large scale neural structures which provide auto- or hetero-associative memories. Consequently, it has applications not only in computational sciences but also as an information processor.     

The computational measurement of apparent motion: A recurrent pattern recognition strategy as an approach to solve the correspondence problem

In short, the model consists of a two-dimensional set of edge detecting units, modelled according to the zero-crossing detectors introduced first by Marr and Ullman (1981). These detectors are located peripherally in our synthetic vision system and are the input elements for an intelligent recurrent network. The purpose of that network is to recognize and categorize the previously detected contrast changes in a multi-resolution representation of the original image in such a manner that the original information will be decomposed into a relatively small numberN of well-defined edge primitives. The advantage of such a construction is that time-consuming pattern recognition has no longer to be done on the originally complex motion-blurred images of moving objects, but on a limited number of categorized forms. Based on a numberM of elementary feature attributes for each individual edge primitive, the model is then able to decompose each edge pattern into certain features. In this way anM-dimensional vector can be constructed for each edge. For each sequence of two successive frames a tensor can be calculated containing the distances (measured inM-dimensional feature space) between all features in both images. This procedure yields a set ofK—1 tensors for a sequence ofK images. After cross-correlation of allN ×M feature attributes from image (i) with those from image (i+1), wherei = 1, ...,K - 1, probability distributions can be computed. The final step is to search for maxima in these probability functions and then to construct from these extremes an optimal motion field. A number of simulation examples will be presented.     

A neural network for processing olfactory-like stimuli

Several critical issues associated with the processing of olfactory stimuli in animals (but focusing on insects) are discussed with a view to designing a neural network which can process olfactory stimuli. This leads to the construction of a neural network that can learn and identify the quality (direction cosines) of an input vector or extract information from a sequence of correlated input vectors, where the latter corresponds to sampling a time varying olfactory stimulus (or other generically similar pattern recognition problems). The network is constructed around a discrete time content-addressable memory (CAM) module which basically satisfies the Hopfield equations with the addition of a unit time delay feedback. This modification improves the convergence properties of the network and is used to control a switch which activates the learning or template formation process when the input is “unknown”. The network dynamics are embedded within a sniff cycle which includes a larger time delay (i.e. an integert _s <1) that is also used to control the template formation switch. In addition, this time delay is used to modify the input into the CAM module so that the more dominant of two mingling odors or an odor increasing against a background of odors is more readily identified. The performance of the network is evaluated using Monte Carlo simulations and numerical results are presented.     

A neural network model for trace conditioning

We studied the dynamics of a neural network that has both recurrent excitatory and random inhibitory connections. Neurons started to become active when a relatively weak transient excitatory signal was presented and the activity was sustained due to the recurrent excitatory connections. The sustained activity stopped when a strong transient signal was presented or when neurons were disinhibited. The random inhibitory connections modulated the activity patterns of neurons so that the patterns evolved without recurrence with time. Hence, a time passage between the onsets of the two transient signals was represented by the sequence of activity patterns. We then applied this model to represent the trace eye blink conditioning, which is mediated by the hippocampus. We assumed this model as CA3 of the hippocampus and considered an output neuron corresponding to a neuron in CA1. The activity pattern of the output neuron was similar to that of CA1 neurons during trace eye blink conditioning, which was experimentally observed.     

A neural network architecture for data classification

This article aims at showing an architecture of neural networks designed for the classification of data distributed among a high number of classes. A significant gain in the global classification rate can be obtained by using our architecture. This latter is based on a set of several little neural networks, each one discriminating only two classes. The specialization of each neural network simplifies their structure and improves the classification. Moreover, the learning step automatically determines the number of hidden neurons. The discussion is illustrated by tests on databases from the UCI machine learning database repository. The experimental results show that this architecture can achieve a faster learning, simpler neural networks and an improved performance in classification.