Alistair J. Bray

A learning rule for extracting spatio-temporal invariances

The inputs to photoreceptors tend to change rapidly over time, whereas physical parameters (e.g. surface depth) underlying these changes vary more slowly. Accordingly, if a neuron codes for a physical parameter then its output should also change slowly, despite its rapidly fluctuating inputs. We demonstrate that a model neuron which adapts to make its output vary smoothly over time can learn to extract invariances implicit in its input. This learning consists of a linear combination of Hebbian and anti-Hebbian synaptic changes, operating simultaneously upon the same connection weights but at different time scales. This is shown to be sufficient for the unsupervised learning of simple spatio-temporal invariances.

Tracking objects using image disparities

Abstract A method and results are presented for a system that finds and tracks known polyhedral objects in 3-space, given a sequence of grey-level images. The object is located in the first frame using model-based search. Image features are then tracked into the next frame using optic flow techniques, and their disparities are used to invert the perspective transform. The system can recognise when it is getting lost during the tracking stage. It recaptures its position through another model search that uses the reduced disparity information, and a ‘best guess’ at position, to constrain the size of the search space. To do this the system integrates three established algorithms in a novel way: model matching is done using modified Goad-search1,2; edgelets are tracked between images using a flow algorithm such as that of Barnard and Thomson3; and the perspective transform is inverted using Lowes formulation of the projection equations4,5.

A self-organizing model of “color blob” formation

This paper explores the possibility that the formation of color blobs in primate striate cortex can be partly explained through the process of activity-based self-organization. We present a simulation of a highly simplified model of visual processing along the parvocellular pathway, that combines precortical color processing, excitatory and inhibitory cortical interactions, and Hebbian learning. The model self-organizes in response to natural color images and develops islands of unoriented, color-selective cells within a sea of contrast-sensitive, orientation-selective cells. By way of understanding this topography, a principal component analysis of the color inputs presented to the network reveals that the optimal linear coding of these inputs keeps color information and contrast information separate.

A Model of Adaptive Development of Complex Cortical Cells

We present in this paper some initial results from a model of activity-dependent development of complex cortical cell receptive fields. We hypothesize that, in general, cortical layers II and III may be the locus of classical conditioning, and that complex cells in primary visual cortex may develop through conditioning to low-level visual information. We demonstrate that an unsupervised time-derivative adaptation rule can yield characteristics of complex cell fields, in both a simplified abstract model and a more detailed, large-scale model with 57,000 cells.

Properties of Local Geometric Constraints

Formal analysis shows that the relationship between 2D line segments which is rotationally and translationally invariant can be expressed using four independent variables (five if scale is included). The formalism leads to a language for defining local geometric constraints and describing their properties. This terminology allows us to establish a criterion for evaluating the quality of a constraint set. Finally, a 2D constraint set is described that is deemed useful in light of the criterion proposed.

Object recognition using local geometric constraints: a robust alternative to tree-search

A new algorithm is presented for recognising 3D polyhedral objects in a 2D segmented image using local geometric constraints between 2D line segments. Results demonstrate the success of the algorithm at coping with poorly segmented images that would cause substantial problems for many current algorithms. The algorithm adapts to use with either 3D line data or 2D polygonal objects; either case increases its efficiency. The conventional approach of searching an interpretation tree and pruning it using local constraints is discarded; the new approach accumulates the information available from the local constraints and forms match hypotheses subject to two global constraints that are enforced using the competitive paradigm. All stages of processing consist of many extremely simple and intrinsically parallel operations. This parallelism means that the algorithm is potentially very fast, and contributes to its robustness. It also means that the computation can be guaranteed to complete after a known time.

Unsupervised discovery of invariances

The grey level profiles of adjacent image regions tend to be different, whilst the ‘hidden’ physical parameters associated with these regions (e.g. surface depth, edge orientation) tend to have similar values. We demonstrate that a network in which adjacent units receive inputs from adjacent image regions learns to code for hidden parameters. The learning rule takes advantage of the spatial smoothness of physical parameters in general to discover particular parameters embedded in grey level profiles which vary rapidly across an input image. We provide examples in which networks discover stereo disparity and feature orientation as invariances underlying image data.

An Adaptive Neural Model of Early Visual Processing

We describe an adaptive computer model of the mammalian visual system, from retina to primary visual cortex. With real world images as input, the basic model robustly develops oriented receptive field patterns, Gabor-function-like fields, and smoothly-varying orientation preference. Extensions of the model show: simultaneous development of oriented receptive fields, retinotopic mapping, and ocular dominance columns; development of “color blobs”; and development of “complex” cells.

Tracking Curved Objects by Perspective Inversion

A method is presented for tracking general curved objects through 3-space, given a sequence of grey-level images. The explicit recovery of 3D features is avoided and results demonstrate the method to be stable, accurate and robust. The object model has two parts — a tracking model and a grey-level model; the former specifies which features of the object are tracked, and the latter determines the appearance of these features. The method assumes initial position is known. Visible features are tracked using correlation between their rendered appearance and the next frame, to give a set of disparities. These disparities are used to invert the perspective transform and give the new position of the object.

Activity-Induced “Colour Blob” Formation

Abstract Principal Component Analysis of patterns taken from a natural colour image shows that only one of the main components is significantly colour selective, and it is unoriented. This result suggests an activity-based explanation of the formation of “colour blobs” in primary visual cortex. We describe a network simulation of processing in the retina, lateral geniculate nucleus and adaptive visual cortex which self-organizes in response to natural colour images and produces “featuremaps” in which islands of a few unoriented colour-sensitive cells are surrounded by a sea of oriented non-colour-selective cells.