Biomedical subjects
Publications and source records attributed to Eric L Schwartz.
Spectral graph partitioning provides a powerful approach to image segmentation. We introduce an alternate idea that finds partitions with a small isoperimetric constant, requiring solution to a linear system rather than an eigenvector problem. This approach produces the high quality segmentations of spectral methods, but with improved speed and stability.
Neurons in macaque primary visual cortex are spatially arranged by their global topographic position and in at least three overlapping local modular systems: ocular dominance columns, orientation pinwheels, and cytochrome oxidase (CO) blobs. Individual neurons in the blobs are not tuned to orientation, and populations of neurons in the pinwheel center regions show weak orientation tuning, suggesting a close relation between pinwheel centers and CO blobs. However, this hypothesis has been challenged by a series of optical recording experiments. In this report, we show that the statistical error associated with photon scatter and absorption in brain tissue combined with the blurring introduced by the optics of the imaging system has typically been in the range of 250 microm. These physical limitations cause a systematic error in the location of pinwheel centers because of the vectorial nature of these patterns, such that the apparent location of a pinwheel center measured by optical recording is never (on average) in the correct in vivo location. The systematic positional offset is approximately 116 microm, which is large enough to account for the claimed misalignment of CO blobs and pinwheel centers. Thus, optical recording, as it has been used to date, has insufficient spatial resolution to accurately locate pinwheel centers. The earlier hypothesis that CO blobs and pinwheel centers are coterminous remains the only hypothesis currently supported by reliable observation.
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The mapping function w = k log(z + a) is a widely accepted approximation to the topographic structure of primate V1 foveal and parafoveal regions. A better model, at the cost of an additional parameter, captures the full field topographic map in terms of the dipole map function w = k log[(z + a)/(z + b)]. However, neither model describes topographic shear since they are both explicitly complex-analytic or conformal. In this paper, we adopt a simple ansatz for topographic shear in V1, V2, and V3 that assumes that cortical topographic shear is rotational, i.e. a compression along iso-eccentricity contours. We model the constant rotational shear with a quasiconformal mapping, the wedge mapping. Composing this wedge mapping with the dipole mapping provides an approximation to V1, V2, and V3 topographic structure, effectively unifying all three areas into a single V1-V2-V3 complex using five independent parameters. This work represents the first full-field, multi-area, quasiconformal model of striate and extra-striate topographic map structure.