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This paper proposes a biologically plausible matching method to recognize general shapes based on contour curvature information. The human visual system recognizes general shapes flexibly in real-world scenes through the ventral pathway. The pathway is typically modeled using artificial neural networks. These network models, however, do not construct a shape representation that satisfies the following required constraints: (1) The original shape should be represented by a group of partitioned contours in order to retrieve the whole shape (global information) from the partial contours (local information). (2) Coarse and fine structures of the original shapes should be individually represented in order for the visual system to respond to shapes as quickly as possible based on the least number of their features, and to discriminate between shapes based on detailed information. (3) The shape recognition realized with an artificial visual system should be invariant to geometric transformation such as expansion, rotation, or shear. In this paper, we propose a visual shape representation with geometrically characterized contour partitions described on multiple spatial scales.

The aim of this paper is to summarize and to compare some known mathematical models of orientation perception in random dot patterns and to propose new solutions of this question. The model adequacy is judged from the previously obtained experimental results. Apart from the models based on some simple function of the coordinates of dots forming a pattern, also models derived from the so-called image function of the pattern are analysed. The latter ones were found more flexible to render the different features of experimentally obtained data, mainly in the case of orientation ambiguity for some special patterns. The stochastic variants of the deterministic models are introduced.

In practice the relevant details of images exist only over a restricted range of scale. Hence it is important to study the dependence of image structure on the level of resolution. It seems clear enough that visual perception treats images on several levels of resolution simultaneously and that this fact must be important for the study of perception. However, no applicable mathematically formulated theory to deal with such problems appears to exist. In this paper it is shown that any image can be embedded in a one-parameter family of derived images (with resolution as the parameter) in essentially only one unique way if the constraint that no spurious detail should be generated when the resolution is diminished, is applied. The structure of this family is governed by the well known diffusion equation (a parabolic, linear, partial differential equation of the second order). As such the structure fits into existing theories that treat the front end of the visual system as a continuous stack of homogeneous layers, characterized by iterated local processing schemes. When resolution is decreased the images becomes less articulated because the extrem ("light and dark blobs") disappear one after the other. This erosion of structure is a simple process that is similar in every case. As a result any image can be described as a juxtaposed and nested set of light and dark blobs, wherein each blob has a limited range of resolution in which it manifests itself. The structure of the family of derived images permits a derivation of the sampling density required to sample the image at multiple scales of resolution.(ABSTRACT TRUNCATED AT 250 WORDS)

Various observations and conjectures have been made about how we perceive three dimensional objects under monocular viewing conditions; in particular, when such objects are rotating. In this paper these proposals are reviewed and reinterpreted in the light of geometric properties of objects and their projections. Some results are also presented which support the conclusion that the visual system, in reconstructing the object from its projections, requires a fixed time to establish the objects curvature and torsion parameters. In the perceptual reconstruction process these parameters assume positive or negative values, and this equivocation is related to a form of the adjacency principle involving central projections and "perceptual geodesics".

Discrete and continuous modes of visual pattern discrimination performance are analyzed using a model for the investigation of discrete internal pattern representations described in previous papers (Foster, 1980a, b). A simple quantitative criterion is derived to characterize the two kinds of visual discrimination performance. Values predicted by this criterion are then compared with values obtained from experimental data.

A mathematical model of the neuron, socalled D-neuron, is proposed on the basis of some new conceptions concerning the molecular mechanism of the synaptical memory. According to these conceptions, the receptors of the neuron reception surface are divided into functional independent fields of receptors. The receptors of any field belong to corresponding membrane protein complex which contains moreover Na+-channels, K+-channels and eventually other protein subunits. Three processes are supposed to take place in any complex by its interaction with chemical transmitters: i cooperative transitions of the subunits, ii time-controlled transport of ions and iii changes of concentrations of the protein complex subunits. These processes correspond to the following information processings: i recording in the memory, ii discrimination and iii accomodation. In this paper they all are described by an idealized system of algebraic and differential equations. The proposed neuron model can account for the short- and long-term memory mechanism on the level of a single neuron as well as for the control of the neuron networks by the hormones. finally, the neuron model is presented as a universal unit of self-learning networks.

The present paper considers the relation between the shape of a triangle and probability of its recognition. An effect of triangle size on perception of its shape is examined in the first experiment. In the second the loci of eye fixations during triangle recognition task are recorded and analysed. A simulation model of the recognition process is proposed. The model is based on two main assumptions: 1. an accuracy of shape processing is related to the cortical magnification factor, 2. a subject's response depends on actual position of eye fixation. The validity of the model is verified by comparing the theoretical and experimental response distributions. Some psycho-physiological implications are then discussed.

In Part I Caelli and Julesz generated texture pairs of 4-disk micropatterns with identical dipole statistics. They found that this iso-dipole constraint could not prevent the quasi-collinearity of certain disk elements which, in turn, yielded effortless discrimination. They proposed two classes of perceptual analyzers to explain discrimination with these micropatern textures: Class A, corresponding to those which detect dipole differences; while Class B detectors, such as the quasi-collinear detector (QCD), acted when isodipole textures were presented. In this paper we show several new methods for generating iso-dipole textures with micropatterns consisting of 5 or more disks or non-disk shaped elements, and we report the discovery of two other Class B detectors, a corner detector (using a 6-disk method), and a closure detector (with 8---11 disk micropatterns). These QCD, corner, and closure detectors were verified by examining several hundred iso-dipole texture pairs. It appears that iso-dipole constraints make ineffective all other feature analyzers involved in effortless texture discrimination than the Class B types. These figural properties of collinearity, corners, and closure can be perceived without scrutiny and are precursors of form perception.

Corners, or discontinuities in orientation, are one of the most salient and useful properties of contours. But how sensitive are we in detecting them, and what does this sensitivity imply about the processes by which corners can be detected. In this paper we address both of these questions, starting with the observation that changing the samplign phase of a curve changes the geometry of its discrete trace, or the set of discrete (retinotopic) points onto which the curve projects. This motivates our stimuli -- dotted curves --and our experimental design: if curves are represented by dots, the placement of the dots effects whether or not corners are perceived. Specifically, we present quantitative data on sensitivity to discontinuities as a function of dot phase, and address its theoretical explanation within a two-stage model of orientation selection. Curvature plays a key role in this model, and, finally, the model and experimental data are brought together by showing that a very coarse approximation to change in curvature (or differences in local curvature estimates) is sufficent to account for the psychophysical data on sensitivity to discontinuities.

The objective of the paper is to determine in abstract terms the algorithms used by the cat detecting simple patterns and to quantify the contributions of the visual areas 17, 18, 19 for this task. The data incorporated in the algorithm are collected from behavioral experiments where the animals had to distinguish between two patterns. The patterns were superimposed with gaussian noise and the detection probability was measured. The resulting model describes pattern recognition in two steps: first extraction of features and second classification. The test of the validity of the model system was to predict the outcome of similar experiments but with different patterns. With the help of the model it is possible to describe the effect of a lesion in parametric form. This in turn gives some hints about the functions of the visual areas 17, 18, 19 for the specific fask, tested in the experiments.

Contemporary literature suggests that preattentive texture or pattern discrimination is induced by differences between local structure features or "textons." This paper presents a model for the description of such local structure features based on the computation of local autocorrelations within the image. By means of this structure model a measure of structure dissimilarity is introduced. Experiments have been carried out to test a hypothesized relation between the detectability of a target pattern in a field of background patterns and the value of the structure dissimilarity measure. The experimental results show that it seems justified to relate, in a quantitative way, the detectability of the target pattern to the value of the structure dissimilarity measure.

Performance of six subjects (Ss) in detecting randomly occurring visual signals of filtered sine bursts recorded on paper through four similar noisy channels is investigated and their decision behavior in that task is modelled. The noise channels were additive white Gaussian and independent from each other. This study confirms previous results that the detection outcome from a single channel may be predicted from the maximum signal-to-noise ratio at the output of a filter matched to signal and also that Ss make fewer errors than the optimum matched filter detector. The pattern of improvement in detection in the case of multiple channels was found to be similar to a combination of analog-digital aggregation scheme. Observations on Ss' decision behavior in these experiments were incorporated into a pattern recognition algorithm for single channel detection and into an information processing model for multiple channel aggregation.

A neural network model for a mechanism of visual pattern recognition is proposed in this paper. The network is self-organized by "learning without a teacher", and acquires an ability to recognize stimulus patterns based on the geometrical similarity (Gestalt) of their shapes without affected by their positions. This network is given a nickname "neocognitron". After completion of self-organization, the network has a structure similar to the hierarchy model of the visual nervous system proposed by Hubel and Wiesel. The network consists of an input layer (photoreceptor array) followed by a cascade connection of a number of modular structures, each of which is composed of two layers of cells connected in a cascade. The first layer of each module consists of "S-cells", which show characteristics similar to simple cells or lower order hypercomplex cells, and the second layer consists of "C-cells" similar to complex cells or higher order hypercomplex cells. The afferent synapses to each S-cell have plasticity and are modifiable. The network has an ability of unsupervised learning: We do not need any "teacher" during the process of self-organization, and it is only needed to present a set of stimulus patterns repeatedly to the input layer of the network. The network has been simulated on a digital computer. After repetitive presentation of a set of stimulus patterns, each stimulus pattern has become to elicit an output only from one of the C-cells of the last layer, and conversely, this C-cell has become selectively responsive only to that stimulus pattern. That is, none of the C-cells of the last layer responds to more than one stimulus pattern. The response of the C-cells of the last layer is not affected by the pattern's position at all. Neither is it affected by a small change in shape nor in size of the stimulus pattern.

Primary visual coding can be characterized by the receptive field (RF) properties of single neurons. Subject of this paper is our search for a global, second coding step beyond the RF-concept that links related features in a visual scene. In recent models of visual coding, oscillatory activities have been proposed to constitute such linking signals. We tested the neurophysiological relevance of this hypothesis for the visual system. Single and multiple spikes as well as local field potentials were recorded simultaneously from several locations in the primary visual cortex (A17 and A18) using 7 or 19 individually advanceable fiber-microelectrodes (250 or 330 microns apart). Stimulus-evoked (SE)-resonances of 35-85 Hz were found in these three types of signals throughout the visual cortex when the primary coding channels were activated by their specific stimuli. Stimulus position, orientation, movement direction and velocity, ocularity and stationary flicker caused specific SE-resonances. Coherent SE-resonances were found at distant cortical positions when at least one of the primary coding properties was similar. Coherence was found 1) within a vertical cortex column, 2) between neighbouring hypercolumns, and 3) between two different cortical areas. We assume that the coherence of SE-resonances is mediated by recurrent excitatory intra- and inter-areal connections via phase locking between assemblies that represent the linking features of the actual visual scene. Visually related activities are, thus, transiently labelled by a temporal code that signalizes their momentary association.

In order to characterize temporal pattern sensitivity in the cat ganglion cells, a new analysis technique by semi-Markov models which was developed in the previous papers (Tsukada et al., 1975---1977) was applied to input-output relations of the receptive-field. Three types of statistical spot stimuli positioned in the center region of receptive fields were used. Each type of stimulus has an identical histogram in the inter-stimulus intervals and therefore the same mean and variance, but different correlations between adjacent inter-stimulus intervals (Type 1, positive; Type 2, negative; and Type 3, independent processes). From the output spike trains of cat retinal ganglion cells to each stimulus, mean, variance, and histogram were computed. As the result of investigating these data, we could draw the following conclusion from the resultant output interval histograms. The receptive-field-center responses of cat ganglion cells can be classified into two groups (Types L and N) according to the difference of responsiveness to the three types of statistical spot stimuli. A Type L response has the same histogram in interspike intervals for all three stimuli, and is not sensitive to the temporal pattern, while a Type N response has three different forms depending on each type of stimulus showing high sensitivity to the temporal pattern. These results were also simulated by the Markov chain model and discussed with relation to neural coding and classification of ganglion cell types.

A brief outline of the texton theory was given in several review papers (Julesz and Bergen 1983; Julesz 1984a, b, 1985) without going into details. Here a more complete version of the texton theory is presented, with emphasis on the critical distances within which the density of textons is determined by the preattentive system. Particularly some recent findings by Sagi and Julesz (1985a, b) influenced the current version of the texton theory. The stimuli are restricted to drawings composed of line segments that permit a precise definition of neighborhoods and distances to which the line segments and texture elements have to be confined in order to quality for preattentive texture discrimination. These critical distances and the aperture of focal attention are scaled by the average size of the texture elements. Furthermore, it is stressed that even when the stimuli are restricted to line segments, the blobs outlined by line segments behave like textons. The preattentive system ignores the exact shape of these blobs, but is sensitive to their average width, length, and orientation.

Illumination allows solid object perception to be obtained and depicted by a shading pattern produced by lighting. The shading cue, as one of solid perception cues (Gibson 1979), was investigated in regard to a white corrugated wave shape, using computer graphic device: Tospix-2. The reason the corrugated wave was chosen, is that an alternately bright and dark pattern, produced by shading, can be conveniently analyzed into contained spatial frequencies. This paper reports spatial frequency properties contained in the shading pattern. The shading patterns, input into the computer graphic device, are analyzed by Fourier Transformation by the same device. After the filtration by various spatial frequency low and high pass filters, Inverse Fourier Transformation is carried out for the residual components. The result of the analysis indicates that the third through higher harmonics components are important in regard to presenting a solid reality feeling in solid perception. Sakata (1983) also reported that an edged pattern, superimposed onto a lower sinusoidal pattern, was important in solid perception. The third through higher harmonics components express the changing position of luminance on the pattern, and a slanted plane relating to the light direction. Detection of a solid shape, constructed with flat planes, is assumed to be on the bottom of the perfect curved solid perception mechanism. Apparent evidence for this assumption, in difficult visual conditions, is that a flat paneled solid is seen before the curved solid. This mechanism is explained by two spatial frequency neural network systems, assumed as having correspondence with higher spatial frequency detection and lower spatial frequency detection.

A model of the visual pathways it has been developed consisting of two neural systems working together: a feed-forward mechanism given by convolutions through different layers and a feed-back one consiting of the comparison of the results of the first one. The first mechanism would be predominant at lower centers, and it would be able, for example, to explain the increase in contrast sensitivity at different stations of visual pathways. The second mechanism seems apter to explain the behaviour of complex and hypercomplex cells whose activity is to a great extent independent of the position of the stimulus in the receptive field. The ideas developed in this paper could have some implications for building a machine able to recognize patterns independently of their position.