Alan Rojer

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

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 logarithms 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.<<ETX>>

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

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.

A multiple-map model for pattern classification

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 Fishers 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.

Visualizing and Understanding Patterns of Brain Architecture

We illustrate application of computer science to neuroscience at three levels: measuring, modeling, and understanding the computational function of the columnar pattern of ocular dominance in primate visual cortex. We review our methods for the quantitative reconstruction of the pattern of binocular input to the visual cortex of monkeys. We show that an oriented bandpass filter, applied to white noise, provides a simple parametric characterization of the observed pattern. We suggest a computational motivation for the columnar architecture as a “brain data structure” for a stereo vision algorithm based on the properties of a nonlinear filter, the cepstrum. This work illustrates some of the algorithmic difficulties and novel research problems encountered when computational approaches are used to visualize the patterns of neural architecture of the primate visual system.

Fusion of multiple fixations with a space-variant sensor: conditional optimality of maximum-resolution blending

In previous work by ourselves and others it has been argued that the best algorithm for fusing multiple fixations of the same scene is to simply choose the maximum resolution information available at each position in the reconstructed scene. We can show under simple assumptions of pixel distributions that this algorithm is indeed optimal in a least-squared-error sense. In the presence of noise however optimality no longer holds a certain degree of averaging of lower resolution information is required to obtain optimal reconstruction. We also present empirical demonstrations of fused images using maximum-resolution and averaged blending techniqes and we illustrate the effects of noise on the quality of reconstruction.