papers available on stereo and learning

[Ning Qian]

Dear Colleagues,

The following papers can be downloaded from the web site:

http://brahms.cpmc.columbia.edu/

All papers are in Unix-compressed PostScript format.  A limited number
of hard copies are available for those who cannot download or decode.

Best regards,
Ning Qian

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Relationship between Phase and Energy Methods for Disparity
Computation, Neural Computation (in press)

Ning Qian and Sam Mikaelian

The phase and energy methods for computing binocular disparity maps
from stereograms are motivated differently, have different
physiological relevances, and involve different computational
steps. Nevertheless, we demonstrate that at the final stages where
disparity values are made explicit, the simplest versions of the two
methods are exactly equivalent. The equivalence also holds when the
quadrature-pair construction in the energy method is replaced with a
more physiologically plausible phase-averaging step. The equivalence
fails, however, when the phase-difference receptive field model is
replaced by the position-shift model.  Additionally, intermediate
results from the two methods are always quite distinctive. In
particular, the energy method generates a distributed disparity
representation similar to that found in the visual cortex while the
phase method does not. Finally, more elaborate versions of the two
methods are in general not equivalent. We also briefly compare these
two methods with some other stereo models in the literature.

http://brahms.cpmc.columbia.edu/publications/compare.ps.Z


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On the Momentum Term in Gradient Descent Learning Algorithms,
Neural Networks, 1999, 12:145-151

Ning Qian

A momentum term is usually included in the simulations of
connectionist learning algorithms. Although it is well known that such
a term greatly improves the speed of learning, there have been few
rigorous studies of its mechanisms. In this paper, I show that in the
limit of continuous time, the momentum parameter is analogous to the
mass of Newtonian particles that move through a viscous medium in a
conservative force field. The behavior of the system near a local
minimum is equivalent to a set of coupled and damped harmonic
oscillators. The momentum term improves the speed of convergence by
bringing some eigen components of the system closer to critical
damping. Similar results can be obtained for the discrete time case
used in computer simulations. In particular, I derive the bounds for
convergence on learning-rate and momentum parameters, and demonstrate
that the momentum term can increase the range of learning rate over
which the system converges. The optimal condition for convergence is
also analyzed.

http://brahms.cpmc.columbia.edu/publications/momentum.ps.Z


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Perceptual Learning on Orientation and Direction Discrimination, 
Vision Research (in press)

Nestor Matthews, Zili Liu, Bard J. Geesaman, and Ning Qian

Two experiments were conducted to determine the extent to which
perceptual learning transfers between orientation and direction
discrimination. Naive observers were trained to discriminate
orientation differences between two single-line stimuli, and direction
differences between two single-moving-dot stimuli. In the first
experiment, observers practiced the orientation and direction tasks
along orthogonal axes in the fronto-parallel plane. In the second
experiment, a different group of observers practiced both tasks along
a single axis. Perceptual learning was observed on both tasks in both
experiments. Under the same-axis condition, the observers' orientation
sensitivity was found to be significantly elevated after the direction
training, indicating a transfer of learning from direction to
orientation. There was no evidence of transfer in any other cases
tested. In addition, the rate of learning on the orientation task was
much higher than the rate on the direction task. The implications of
these findings on the neural mechanisms subserving orientation and
direction discrimination are discussed.

http://brahms.cpmc.columbia.edu/publications/pl.ps.Z