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Component analysis of spatial and spectral patterns in multispectral images. II. Entropy minimization.

In Part I [J. Opt. Soc. Am. A 4, 2101 (1987)] of this series, we developed a method for estimating both spatial patterns and spectral curves of components in a multispectral scene. This method does not need spatial and spectral information about the components but only multispread imagery data. The estimation is given as a feasible solution set satisfying the nonnegativity constraint for density and spectral response for all components at all pixels. In this paper, we estimate unique solutions for both the component patterns and the spectra from the feasible solution set. The solution is given by optimizing an entropy minimization criterion. This criterion enhances the spectral or spatial features of individual components. Two experimental results are shown to demonstrate the effectiveness of this method with biological and cytochemical specimens. The limitations of this method for unique pattern estimation are also discussed.

Algorithms

Spatial interactions in apparent contrast: inhibitory effects among grating patterns of different spatial frequencies, spatial positions and orientations.

Suppression of the apparent contrast of a small 4 cycle wide suprathreshold sine wave grating patch by a high contrast sine wave grating surround pattern was studied as a function of the spatial frequency, orientation and spatial extent of the surround. The data are consistent with the existence of a complex network of inhibitory interconnections among mechanisms that mediate contrast perception. These connections must extend over spatial distances equivalent to more than 12 cycles of the central grating patch.

Adaptation, Physiological

Electrosensory maps form a substrate for the distributed and parallel control of behavioral responses in weakly electric fish.

Electroreceptors, distributed over the body surface of weakly electric fish, code the local amplitude and phase, or timing of zerocrossing, of the animal's electric signals. These signals are generated by rhythmic discharges of the electric organ and form a dipole-like field around the animal. This field is perturbed by interference with electric fields of other fish as well as by the appearance of objects electrically different from water. The spatial and temporal structure of such perturbations can be interpreted as the electric image of interfering fields and moving objects. This strategy of assessing the environment is called 'electrolocation', a form of 'seeing' with the body surface. Electric images are analyzed in somatotopically ordered strata of neurons within the central nervous system. Primary electrosensory afferents project to somatotopically ordered layers of higher-order neurons in the electrosensory lateral line lobe (ELL) of the hindbrain. Phase and amplitude information are processed in separate layers of the ELL. The phase of the signal in a given region of the body surface is coded by the timing of spikes of spherical cells marking the zerocrossings of the electric signal. This phase information is relayed to lamina 6 of the torus semicircularis of the midbrain. Rises and falls in local amplitude are coded by the activity of different pyramidal cell types, E- and I-units, which project to various laminae of the torus above and below lamina 6. The somatotopic organization of the torus allows for computations of spatial patterns in electrosensory information. Within lamina 6, differences in the phase of signals from different parts of the body surface are computed. Differential-phase information is then relayed to deeper laminae of the torus and remains in topographic register with amplitude information. This organization allows for joint evaluation of spatially related patterns of amplitude and phase modulations on the animal's body surface within local neuronal circuits of the torus. A topographic projection of the torus relays amplitude and differential-phase information to the optic tectum where a further joint evaluation of amplitude and phase serves to control behavioral responses. The control of a particular behavioral performance, the 'jamming avoidance response', is of a distributed nature in that the representations of individual sites on the body surface contribute cumulatively to shift the electric organ pacemaker frequency.(ABSTRACT TRUNCATED AT 400 WORDS)

Action Potentials

Distribution of GABAergic neurons and axon terminals in the macaque striate cortex.

Antisera to glutamic acid decarboxylase (GAD) and gamma-aminobutyric acid (GABA) have been used to characterize the morphology and distribution of presumed GABAergic neurons and axon terminals within the macaque striate cortex. Despite some differences in the relative sensitivity of these antisera for detecting cell bodies and terminals, the overall patterns of labeling appear quite similar. GABAergic axon terminals are particularly prominent in zones known to receive the bulk of the projections from the lateral geniculate nucleus; laminae 4C, 4A, and the cytochrome-rich patches of lamina 3. In lamina 4A, GABAergic terminals are distributed in a honeycomb pattern which appears to match closely the spatial pattern of geniculate terminations in this region. Quantitative analysis of axon terminals that contain flat vesicles and form symmetric synaptic contacts (FS terminals) in lamina 4C beta and in lamina 5 suggest that the prominence of GAD and GABA axon terminal labeling in the geniculate recipient zones is due, at least in part, to the presence of larger GABAergic axon terminals in these regions. GABAergic cell bodies and their initial dendritic segments display morphological features characteristic of nonpyramidal neurons and are found in all layers of striate cortex. The density of GAD and GABA immunoreactive neurons is greatest in laminae 2-3A, 4A, and 4C beta. The distribution of GABAergic neurons within lamina 3 does not appear to be correlated with the patchy distribution of cytochrome oxidase in this region; i.e., there is no significant difference in the density of GAD and GABA immunoreactive neurons in cytochrome-rich and cytochrome-poor regions of lamina 3. Counts of labeled and unlabeled neurons indicate that GABA immunoreactive neurons make up at least 15% of the neurons in striate cortex. Layer 1 is distinct from the other cortical layers by virtue of its high percentage (77-81%) of GABAergic neurons. Among the other layers, the proportion of GABAergic neurons varies from roughly 20% in laminae 2-3A to 12% in laminae 5 and 6. Finally, there are conspicuous laminar differences in the size and dendritic arrangement of GAD and GABA immunoreactive neurons. Lamina 4C alpha and lamina 6 are distinguished from the other layers by the presence of populations of large GABAergic neurons, some of which have horizontally spreading dendritic processes. GABAergic neurons within the superficial layers are significantly smaller and the majority appear to have vertically oriented dendritic processes.(ABSTRACT TRUNCATED AT 400 WORDS)

Animals

Spatial and temporal patterns of deoxyribonucleic acid synthesis and mitosis in the endometrial stroma during decidualization in the pseudopregnant rat.

A quantitative study was made of the spatial patterns of stromal cell mitosis and DNA synthesis in the endometrium of the pseudopregnant rat before and during decidualization. A colchicine block was used for mitotic counts, and DNA synthesis was studied by [3H] thymidine autoradiography. Observations were also made on the subsequent fates of [3H] thymidine-labeled stromal cells. Before the onset of decidualization, on Days 3 and 4 (vaginal cornification = Day 0), mitosis was largely confined to the subepithelial stroma along the sides and around the antimesometrial pole of the lumen. [3H] thymidine labeling and stromal mitosis following a decidualizing stimulus at noon on Day 4 of pseudopregnancy were first seen close to the uterine lumen, with subsequent spread to deeper layers of the endometrium. At noon on Day 5, mitotic figures were numerous on all sides of the lumen and at all depths in the endometrium. At later stages, mitosis and the development of polyploidy continued in the decidual tissue, but little DNA synthesis or mitosis occurred in the basal zone of the stroma adjacent to the myometrium. In this zone, many cells in animals given [3H] thymidine 18 to 24 h after induction of decidualization remained heavily labeled throughout the growth and regression of deciduomata. Labeled cells derived from the basal zone and outer edge of the decidual capsule were present in the stroma of the regenerated endometrium following the regression of deciduomata. It was concluded that although cells at all depths in the endometrial stroma undergo DNA synthesis and mitosis in the early stages of response to a decidualizing stimulus, their subsequent behavior and fate depend upon their position in the endometrium.

Animals

The dynamics of the cat retinal X cell centre.

1. The dynamics of the centre mechanism of individual cat X retinal ganglion cells is investigated. The visual stimuli consist of temporal contrast modulation of stationary patterns. In order to study the response of the centre mechanism, patterns were either sine gratings of high spatial frequency or small circular spots positioned over the receptive-field centre. 2. Responses to contrast reversal are approximately linear. However, as the modulation depth of the stimulus increases, responses become more transient. Ganglion cell responses show this phenomenon at moderate contrasts (e.g. 0.1), which do not elicit discharges that approach the maximum firing rate of the ganglion cell. 3. A sequence of dynamical models are constructed from responses elicited by sum-of-sinusoids modulation of the spatial pattern. The first model is strictly linear. It consists of a series of low-pass filters and a single high-pass filter. The linear model predicts the approximate shape of the step response, but does not account for the change in shape of the response as a function of modulation depth. 4. The second model, a quasi-linear model, allows the 'linear' dynamics to vary slowly with a neural measure of contrast. The main effect of high contrast is a shorter time constant in the high-pass filter. This model accounts qualitatively for the increased transience of the response, but fails to predict the magnitude of the effect at higher modulation depths. 5. In the third model, the transfer characteristics of the centre response adjust rapidly as contrast changes. This intrinsically non-linear model provides excellent agreement with observed response to steps and more complex modulation patterns. 6. The non-linearity necessitated by a voltage-to-spikes transduction is analysed quantitatively. In most ganglion cells, a simple truncation at 0 impulses/s (and no saturation) explains the changes in apparent gain and mean firing rate that occur as modulation depth is increased. A non-linear voltage-to-spike transduction per se cannot account for the observed effect of contrast on dynamics. 7. The parameters of the dynamical model are measured for a population of twenty-seven X ganglion cells (nineteen on-centre and eight off-centre). The low-pass stage and the strength of the high-pass stage are relatively uniform across the population. The over-all gain and the dynamics of the high-pass stage vary substantially across the population, but show no consistent dependence on the on-off distinction or on retinal location. Some implications of this variability for retinal function are discussed.

Action Potentials

Pattern Formation in a Spatial Public Goods Dilemma due to Diffusive or Directed Motion.

The costly provision of public goods serves as a model problem for the evolution of cooperative behavior, presenting a social dilemma between the collective benefits of shared resources and the individual incentive to free-ride in resource production. The spatial structure of populations can also impact cooperation over public goods, as diffusion of public goods and intentional motion of individuals towards regions with greater resources can interact with population and public goods dynamics to produce heterogeneous patterns in the spatial distribution of strategies and resources. In this paper, we build off a model introduced by Young and Belmonte for the reaction dynamics of interacting individuals and an explicit public good, deriving a system of PDEs that describes the spatial profiles of strategies and the public good in the presence of both diffusive motion of individuals and resources and chemotaxis-like directed motion of individuals in response to gradients in the concentration of public goods. Through linear stability analysis, we show that spatial patterns in strategic and public goods profiles can emerge due to either Turing instability with high defector diffusivity or a directed-motion instability through strong sensitivity of cooperators towards increasing resource concentration. We further explore the emergent spatial patterns with a mix of weakly nonlinear stability analysis and numerical simulation, showing that, for a wide range of reaction parameters, diffusion-driven instability appears to increase cooperation and public goods across the spatial domain, while directed motion of cooperators towards public goods tends to decrease cooperation and environmental quality across the environment.

Models, Biological

Component analysis of spatial and spectral patterns in multispectral images. I. Basis.

A new (to our knowledge) theory of component pattern analysis in multispectral images is developed by using the methods of principal component analysis and nonlinear optimization with a nonnegativity constraint. Given images of a scene in different color bands, we estimate both the spectral curves of components included in the image and the spatial pattern corresponding to each spectral curve. In this method, neither spatial nor spectral features of the components are necessary, but the physical rule of nonnegative absorptivity and density nonnegativity is used for any material of any optical frequency at any position in the image. Experimental results of component analysis with real microscopic image data are shown to demonstrate the effectiveness of the proposed method.

Form Perception

Pattern of epithelial cell cycling in hydra.

We have investigated the spatial pattern of epithelial cell cycling in a mutant strain of Hydra magnipapillata (sf-1). This strain has temperature sensitive interstitial stem cells and thus polyps containing only epithelial cells can be obtained by growth at the restrictive temperature. Epithelial animals were pulse labeled with the thymidine analog 5'-bromo-2'-deoxyuridine (Brdu) and stained with anti-Brdu antibody to visualize S phase cells. Our results indicate that Brdu-labeled cells are broadly and fairly evenly distributed along the body column. Feeding stimulates a rapid decrease and then an increase in labeled cells in gastric tissue; labeled cells in the head are not affected. Starvation leads to a twofold decrease in labeled cells in the gastric region; the density of labeled cells in head tissue remains similar to that in well-fed animals. During bud formation the number of labeled epithelial cells increases significantly in the evaginating bud. During head regeneration the number of labeled cells declines sharply during the first 12 hr and then increases to a density typical of head tissue by 24-36 hr of regeneration. The results indicate the release of signals by feeding and regeneration which inhibit mitosis. By contrast head tissue and developing buds express signals stimulating mitosis. Thus changes in epithelial cell cycling in hydra are closely correlated with morphogenetic events as well as with feeding stimuli.

Animals

Wavelike isomorphic prepatterns in development.

The patterns generated by these mechanisms are usually wavelike spatial patterns in the distribution of the chemical components and/or physical properties of the organism or tissue being considered. In this paper the range of patterns generated by one of these mechanisms, namely the reaction-diffusion (RD) system (Turing, 1952), is reviewed and its potential to function as a source of isomorphic prepatterns for the regulation of development in a wide range of organisms is illustrated. Examples have been chosen to show the capacity of an RD system to generate a single stationary spatial prepattern, as well as a travelling wavelike spatial prepattern. However, the full potential of an RD system to regulate development stems from its capacity to spontaneously generate a temporal sequence of isomorphic stationary wavelike spatial prepatterns, rather than just a single isomorphic stationary spatial prepattern. To demonstrate this point the examples presented include the morphogenesis of the skin and some of its appendages, as well as the early decisions in the embryogenesis of Drosophila leading to segmentation. The mini-review begins by comparing the concepts of positional information and a temporal sequence of isomorphic prepatterns, which represent two quite different approaches to understanding the spatial and temporal regulation of cellular differentiation.

Animals

Responses of olfactory bulb neurones to odour stimulation of small nasal areas in the salamander.

1. Previous experiments have suggested that one way odours may be discriminated is by different spatial patterns of response at both the olfactory bulb and receptor level. The present experiments were designed to test to what extent the position of an odour on the receptor mucosa can influence the activity of olfactory bulb neurones.2. To deliver odours to small areas on the nasal receptor sheet a new method for local application of odour was developed. The flow rate, concentration, and time course of the odour were controlled using the olfactometer described in the preceding paper.3. In thirty olfactory bulb units in the salamander it was found that if the response of a unit to odour delivered to the entire exposed receptor epithelium were suppression (type S), then the unit tended to be suppressed when odour was delivered to a number of localized epithelial regions. If the response were excitation (type E) to stimulation of the entire epithelium, then stimulation to only one or two localized regions would elicit the maximum response.4. Different epithelial regions had the ability to cause excitation in the same bulbar unit depending on the odour being used. Two odours, camphor and amyl acetate, elicited maximum excitation when they were presented to different mucosal areas. The areas at which presentation of these odours gave excitation were surprisingly consistent from unit to unit and animal to animal.5. The data presented here suggest the presence of restricted excitatory receptive fields for some olfactory bulb neurones for a particular odour.6. The presence of spatial response patterns using odour delivery to small nasal receptor regions and thus the presence of receptive fields is discussed with reference to bulbar neuronal circuitry.

Action Potentials

Metabolic labeling associated with index finger stimulation in monkey SI: between animal variability.

Four monkeys (Macaca fascicularis) were stimulated with an identical intermittent vertical displacement (flutter) stimulus on the tip of the index finger and received intravenous [14C]2-deoxyglucose (2-DG). The majority of metabolic labeling was found to exist in areas 3b and 1 of the anterior parietal cortex (SI) in the form of intermittent patches, which extended vertically across the cortical laminae. When the patches were traced through adjacent sections and reconstructed to produce a 2-dimensional map, it became evident that the patches of label combined to form a complex spatial pattern consisting of strips. Although the flutter stimulus was applied to a spatially restricted peripheral field, the metabolic pattern was always complex and widely distributed within SI. Nevertheless, the 2-DG patterns produced in the different animals stimulated with the same stimulus were strikingly similar. The relationships between descriptions of the SI index finger representation based on neurophysiological mapping data and the distribution of 2-DG uptake are described. The reproducibility of the 2-DG labeling pattern and relationship to neurophysiological maps suggests that the 2-DG mapping method provides a potent and useful tool for the investigation of stimulus representation in the somatosensory cortex.

Animals

Dopamine D1 receptor development in the rat striatum: early localization in striosomes.

The development of dopamine D1-receptors in rat striatum during the early postnatal period is examined, using autoradiography and [3H]SCH 23390 as ligand. Dopamine D1-receptors are present in striatum at birth and are more dense than in any adjacent region. The receptors are preferentially localized in striosomes and to some extent in a subcallosal streak. The density of D1-receptors in the matrix increases with age so that by two weeks postnatally the striosomal pattern is no longer evident, and the overall dense labelling is the same as seen in adults. Dopamine D1-receptor development seems to take place earlier than that of dopamine terminals but at the same time as or somewhat later than that of acetylcholinesterase. The D1-defined striosomes move from ventrolateral towards dorso-medial striatum with increasing age and from anterior to posterior striatum. This direction is nearly perpendicular to the direction of development of several other markers, including dopamine terminals and D2-receptors. The present studies indicate that for markers appearing in the striosomal compartment there are different patterns of development with respect to time and spatial pattern. Regulation of striatal development by interaction of neuronal systems with one another and with other factors is complex and will require extensive study to clarify the mechanisms involved.

Aging

Tactile sensing of surface features.

The tactile recognition of an object held in the hand involves characterizing its surface features. Recent neurophysiological studies point to a number of possible ways in which tactile primary afferents convey information about surface characteristics. The spatial pattern of the afferents that are activated probably underlies the unique recognition of patterns. Measures of afferent response intensity correlate well with overall surface texture and quantitatively encode variations in surface spatial parameters. The temporal patterns of afferent firing provide yet another potential mechanism by which surface features are signaled. Studies of somatosensory cortex have already begun to examine the central processing of these afferent signals, and this remains a fertile field for the future.

Afferent Pathways

Spatial and temporal patterning distinguishes the locomotor activating effects of dizocilpine and phencyclidine in rats.

A behavioral pattern monitor was used to assess the effects of dizocilpine (MK-801) and phencyclidine on the spatial and temporal patterns of locomotion and investigatory behavior in rats. The monitor provided both quantitative measures of crossovers, rearings and holepokes and qualitative measurement of the spatial and temporal patterns of locomotion. Dizocilpine (0.004-0.5 mg/kg) and phencyclidine (0.25-5.0 mg/kg) produced similar, dose-dependent increases in locomotor activity. At small doses, dizocilpine and phencyclidine increased investigatory holepokes, while at larger doses, both drugs significantly decreased the number of holepokes. Rearings were reduced similarly by the larger doses of each drug. Both dizocilpine and phencyclidine produced perseverative spatial patterns of locomotion, especially at larger doses. However, the locomotor patterns produced by these drugs were found to be dissimilar in spatial quality. After phencyclidine, animals frequently circled the perimeter of the monitor chamber or moved repetitively in horseshoe or figure-8 patterns. By contrast, rats given dizocilpine completed small rotations about either end of the chamber. Pretreatment with a small dose (0.02 mg/kg) of haloperidol, prior to either dizocilpine (0.5 mg/kg) or phencyclidine (5.0 mg/kg) had no effect on the increase in locomotor activity or the decreases in investigatory holepokes produced by the drugs. However, haloperidol altered the effects of phencyclidine on the spatial and temporal patterns of locomotion, suggesting that sigma receptors or other haloperidol-sensitive binding sites, may influence the quality but not the quantity of phencyclidine-induced hyperactivity.

Animals

Spatial low frequency pattern analysis in positron emission tomography: a study between normals and schizophrenics.

Using the two-dimensional Fourier transform and the brain's centroidal principal axis, a method is developed for the analysis of PET metabolic brain images without the use of predefined anatomic regions of interest. We applied the method to images from a group of 11 normal and 12 medicated schizophrenics tested under resting conditions and under a visual task. A cortical/subcortical spatial pattern was found to be significant in two directions; anterior/posterior and chiasmatic (left-anterior/right-posterior). The best individual clinical classification (Jackknife classification) occurred under visual task at two axial brain levels: at the basal ganglia with correct classification rates of 91% and 84%, while the cerebellum had rates of 82% and 92%. These high classification rates were obtained using only the four coefficients of the lowest spatial frequency. These results point to the generalized brain dysfunction of regional glucose metabolism in chronic medicated schizophrenics both at rest and at a visual image-tracking task.

Analysis of Variance

Source density analysis of scalp potentials during linguistic and non-linguistic processing of visual stimuli.

Event-related potentials (ERPs) were recorded from 40 locations, covering most of the scalp, during repeated tasks in which the observer (O) had to judge either the tense of a printed verb (V) or the symmetry of a spatial pattern (S). Stimuli were drawn at random from large ensembles. A simplified method of Laplacean analysis (MacKay 1983, 1984) allowed the corresponding source densities to be mapped at up to 28 locations, relatively free of artefacts due to eye movements or tongue movements. O signalled his judgement in each case by pressing one of two buttons on a given cue. The decision time allowed was kept short (about 1 s) but long enough for the task to be handled successfully. When stimuli 'V' and 'S' were drawn from geometrically different ensembles, the source-density distributions for the two tasks differed significantly at a number of locations. When 'V' and 'S' were drawn from a common ensemble, however, and O was instructed on each trial (in random order) to assess each stimulus as a word or as a geometrical pattern, the similarities in the source-density maps were more striking than the differences. It would seem that during sufficiently rapid verbal and spatial judgments, little sign of hemispheric specialization or task-specific differences may appear in the spatiotemporal profile of ERP source densities. More salient differences, some lateralized, appeared during the preparation interval prior to verbal and spatial tasks; but their pattern varied widely from subject to subject.

Cerebral Cortex

MPTP produces a mosaic-like pattern of terminal degeneration in the caudate nucleus of dog.

This paper describes the spatial pattern of terminal degeneration in the caudate nucleus and putamen of the dog following an injection of 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine (MPTP). Marked inhomogeneities in the filed of terminal degeneration were found in the head of the caudate nucleus, which are reminiscent of the fundamental patch/matrix organization of the striatum. Using MPTP as a selective lesioning method, our results provide further evidence that the dopaminergic, nigrostriatal projection has a heterogeneous organization.

1-Methyl-4-phenyl-1,2,3,6-tetrahydropyridine