1980 Preface * 1999 Preface * 1999 Acknowledgements * Introduction * 1 Circular Logic * 2 Phase Singularities (Screwy Results of Circular Logic) * 3 The Rules of the Ring * 4 Ring Populations * 5 Getting Off the Ring * 6 Attracting Cycles and Isochrons * 7 Measuring the Trajectories of a Circadian Clock * 8 Populations of Attractor Cycle Oscillators * 9 Excitable Kinetics and Excitable Media * 10 The Varieties of Phaseless Experience: In Which the Geometrical Orderliness of Rhythmic Organization Breaks Down in Diverse Ways * 11 The Firefly Machine 12 Energy Metabolism in Cells * 13 The Malonic Acid Reagent ('Sodium Geometrate') * 14 Electrical Rhythmicity and Excitability in Cell Membranes * 15 The Aggregation of Slime Mold Amoebae * 16 Numerical Organizing Centers * 17 Electrical Singular Filaments in the Heart Wall * 18 Pattern Formation in the Fungi * 19 Circadian Rhythms in General * 20 The Circadian Clocks of Insect Eclosion * 21 The Flower of Kalanchoe * 22 The Cell Mitotic Cycle * 23 The Female Cycle * References * Index of Names * Index of Subjects

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/596B270197FE27DE5FABB598B6210622/S0025557200150892a.pdf/div-class-title-span-class-italic-the-geometry-of-biological-time-span-by-a-t-winfree-pp-544-dm68-corrected-second-printing-1990-isbn-3-540-52528-9-springer-div.pdf

The geometry of biological time , by A. T. Winfree. Pp 544. DM68. Corrected Second Printing 1990. ISBN 3-540-52528-9 (Springer)

One of the more powerful impressions created by vision is that of a coherent, richly detailed world where everything is present simultaneously. Indeed, this impression is so compelling that we tend to ascribe these properties not only to the external world, but to our internal representations as well. But results from several recent experiments argue against this latter ascription. For example, changes in images of real-world scenes often go unnoticed when made during a saccade, flicker, blink, or movie cut. This “change blindness” provides strong evidence against the idea that our brains contain a picture-like representation of the scene that is everywhere detailed and coherent. How then do we represent a scene? It is argued here that focused attention provides spatiotemporal coherence for the stable representation of one object at a time. It is then argued that the allocation of attention can be co-ordinated to create a “virtual representation”. In such a scheme, a stable object representation is formed...

/pdf/the-dynamic-representation-of-scenes-4atslp6uen.pdf

The Dynamic Representation of Scenes

It is well known that visual cortical neurons respond vigorously to a limited range of stimulus orientations, while their primary afferent inputs, neurons in the lateral geniculate nucleus (LGN), respond well to all orientations. Mechanisms based on intracortical inhibition and/or converging thalamocortical afferents have previously been suggested to underlie the generation of cortical orientation selectivity; however, these models conflict with experimental data. Here, a 1:4 scale model of a 1700 microns by 200 microms region of layer IV of cat primary visual cortex (area 17) is presented to demonstrate that local intracortical excitation may provide the dominant source of orientation-selective input. In agreement with experiment, model cortical cells exhibit sharp orientation selectivity despite receiving strong iso-orientation inhibition, weak cross-orientation inhibition, no shunting inhibition, and weakly tuned thalamocortical excitation. Sharp tuning is provided by recurrent cortical excitation. As this tuning signal arises from the same pool of neurons that it excites, orientation selectivity in the model is shown to be an emergent property of the cortical feedback circuitry. In the model, as in experiment, sharpness of orientation tuning is independent of stimulus contrast and persists with silencing of ON-type subfields. The model also provides a unified account of intracellular and extracellular inhibitory blockade experiments that had previously appeared to conflict over the role of inhibition. It is suggested that intracortical inhibition acts nonspecifically and indirectly to maintain the selectivity of individual neurons by balancing strong intracortical excitation at the columnar level.

https://www.jneurosci.org/content/jneuro/15/8/5448.full.pdf

An emergent model of orientation selectivity in cat visual cortical simple cells

The author extends a previous review and focuses on feed-forward neural-net classifiers for static patterns with continuous-valued inputs. He provides a taxonomy of neural-net classifiers, examining probabilistic, hyperplane, kernel, and exemplar classifiers. He then discusses back-propagation and decision-tree classifiers; matching classifier complexity to training data; GMDH (generalized method of data handling) networks and high-order nets; K nearest-neighbor classifiers; the feature-map classifier; the learning vector quantizer; hypersphere classifiers; and radial-basis function classifiers. >

Pattern classification using neural networks

The detection and recognition of objects in images is a key research topic in the computer vision community Within this area, face recognition and interpretation has attracted increasing attention owing to the possibility of unveiling human perception mechanisms, and for the development of practical biometric systems This book and the accompanying website, focus on template matching, a subset of object recognition techniques of wide applicability, which has proved to be particularly effective for face recognition applications Using examples from face processing tasks throughout the book to illustrate more general object recognition approaches, Roberto Brunelli: examines the basics of digital image formation, highlighting points critical to the task of template matching; presents basic and advanced template matching techniques, targeting grey-level images, shapes and point sets; discusses recent pattern classification paradigms from a template matching perspective; illustrates the development of a real face recognition system; explores the use of advanced computer graphics techniques in the development of computer vision algorithms Template Matching Techniques in Computer Vision is primarily aimed at practitioners working on the development of systems for effective object recognition such as biometrics, robot navigation, multimedia retrieval and landmark detection It is also of interest to graduate students undertaking studies in these areas

Template Matching Techniques in Computer Vision: Theory and Practice

A space-variant sensor design based on the conformal mapping of the half disk, w=log (z+a), with real a>0, which characterizes the anatomical structure of the primate and human visual systems is discussed. There are three relevant parameters: the circumferential index kappa which is defined as the number of pixels around the periphery of the sensor, the visual field radius R (of the half-disk to be mapped), and the map parameter a, which displaces the logarithm's singularity at the origin out of the domain of the mapping. It is shown that the log sensor requires O( kappa /sup 2/log (R/a)) pixels. An analysis is presented which makes it possible to compare directly the space complexity of different sensor designs in the complex logarithmic family. In particular, rough estimates can be obtained of the parameters necessary to duplicate the field width/resolution performance of the human visual system. >

Design considerations for a space-variant visual sensor with complex-logarithmic geometry

A simple algorithm based on bandpass-filtering of white noise images provides good quality computer reconstruction of the cat and monkey ocular dominance and orientation column patterns. A small number of parameters control the frequency, orientation, "branchedness", and "regularity" of the column patterns. An oriented (anisotropic) bandpass filter followed by a threshold operation models the macaque ocular dominance column pattern and cat orientation column system. An unoriented (isotropic) bandpass filter models the cat ocular dominance column pattern and the macaque orientation column system. The resemblance of computer graphic simulations produced by this algorithm and histological pattern data, is strong. Since this algorithm is very fast, we have been able to extensively explore its parameter space in order to determine filter parameters which closely match the structure of the various cortical systems. In particular, we have applied spectral analysis to our recent computer reconstruction of the macaque ocular dominance column system, and the model produced by the present algorithm is in close agreement with this detailed data analysis.

Cat and monkey cortical columnar patterns modeled by bandpass-filtered 2D white noise

A characteristic feature of vertebrate sensory cortex (and midbrain) is the existence of multiple two-dimensional map representations. Some workers have considered single-map classification (e.g. Kohonen 1984) but little work has focused on the use of multiple maps. We have constructed a multiple-map classifier, which permits abstraction of the computational properties of a multiple-map architecture. We identify three problems which characterize a multiple-map classifier: classification in two dimensions, mapping from high dimensions to two dimensions, and combination of multiple maps. We demonstrate component solutions to each of the problems, using Parzen-window density estimation in two dimensions, a generalized Fisher discriminant function for dimensionality reduction, and split/merge methods to construct a “tree of maps” for the multiple-map representation. The combination of components is modular and each component could be improved or replaced without affecting the other components. The classifier training procedure requires time linear in the number of training examples; classification time is independent of the number of training examples and requires constant space. Performance of this classifier on Fisher's iris data, Gaussian clusters on a five-dimensional simplex, and digitized speech data is comparable to competing algorithms, such as nearest-neighbor, back-propagation and Gaussian classifiers. This work provides an example of the computational utility of multiple-map representations for classification. It is one step towards the goal of understanding why brain areas such as visual cortex utilize multiple map-like representations of the world.

A multiple-map model for pattern classification

Smoothing a random pattern of orientations causes the appearance of orientation "vortices." These patterns are similar to the hypercolumn pattern of orientation tuning in monkey visual cortex, and to the "pinwheels" that have been observed in cat area 18. The generic presence of such patterns in continuous orientation maps is a consequence of a basic topological theorem (nonretraction of R/sup 2/->S/sup 1/), together with the stochastic properties of random orientation distributions. There as a close correspondence between experimental results from cat area 18 and computer simulations based on smoothed random orientations. Several of the qualitative features of cortical hypercolumn patterns, including the "puff-extra" structure of monkey V-1, are evident in our simulations. There are two important conclusions from this work. (1) Experimental observation of orientation "vortex" structure in any visually excitable neural tissue must be evaluated in the light of the null hypothesis that these patterns are readily formed from smoothed, random orientation distributions, (2) The underlying explanation for the "vortex" patterns which likely exist in primate and cat visual cortex is fundamentally topological, and follows directly from the definition of orientation, and the existence of local correlation of orientation in cortex.

Cortical hypercolumns and the topology of random orientation maps

The complex logarithm as a conformal mapping has drawn interest as a sensor architecture for computer vision due to its psuedo-invariance with respect to rotation and scaling, its high ratio of field width to resolution for a given number of pixels, and its utilization in biological vision as the topographic mapping from the retina to primary visual cortex. This thesis extends the computer vision applications of the complex-logarithmic geometry. Sensor design is based on the complex log mapping "w = log (z + a)," with real a $>$ 0, which smoothly removes the singularity in the log at the origin. Previous applications of the complex-logarithmic geometry to computer vision, graphics and sensory neuroscience are surveyed. A quantitative analysis of the space complexity of a complex-logarithmic sensor as a function of map geometry, field width and angular resolution is presented. The computer-graphic problems of warping uniform scenes according to the complex logarithm and inversion of log-mapping scenes to recover the original uniform scene are considered, as is the problem of blending the resulting inverse log maps to reconstruct the original (uniform) scene. A series of simple algorithms for segmentation of log scenes by contour completion and region filling are presented. A heuristic algorithm for figure/ground segmentation using the log geometry is also shown. The problem of fixation-point selection (visual attention) is considered. Random selection of fixation points, inhibition around previous fixations, spatial and temporal derivatives in the sensor periphery, and regions found by segmentation are all examined as heuristic attentional algorithms. For the special case where targets can be parametrically defined, a theory of model-based attention based on the Hough transform is introduced. A priori knowledge about the consistency between potential objects in the scene and measured features in the scene is used to select fixation points. The exponential storage requirements of the usual Hough transform are avoided.

Alan Rojer

Papers

Design considerations for a space-variant visual sensor with complex-logarithmic geometry

Cat and monkey cortical columnar patterns modeled by bandpass-filtered 2D white noise

A multiple-map model for pattern classification

Cortical hypercolumns and the topology of random orientation maps

Space-variant computer vision with a complex-logarithmic sensor geometry