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\begin{abstract} |
\begin{abstract} |
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%NO NEED FOR PERFECT RECALL - JUST A CUE |
%NO NEED FOR PERFECT RECALL - JUST A CUE |
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%In addition to being drawn by hand or scanned, |
%In addition to being drawn by hand or scanned, |
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Textures have been synthesized in several ways: procedurally\cite{perlin-noise-intro}, |
Textures have been synthesized in several ways: procedurally\cite{perlin-noise-intro}, |
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using |
using |
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other textures as a starting point |
other textures as a starting point\cite{heeger95pyramid}, |
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(see, e.g., Heeger\cite{heeger95pyramid}), |
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perceptually, for visualizing surface orientation\cite{schweitzer83texturing,interrante97illustrating} and scalar or vector fields\cite{ware95texture}, |
perceptually, for visualizing surface orientation\cite{schweitzer83texturing,interrante97illustrating} and scalar or vector fields\cite{ware95texture}, |
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and statistically, as samples from a probability distribution on a random field |
and statistically, as samples from a probability distribution on a random field |
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\cite{cross83markov,geman84stochastic}. |
\cite{cross83markov,geman84stochastic}. |
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% XXX: there's overlap between the enumerated cases |
% XXX: there's overlap between the enumerated cases |
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%Textures have also been modeled statistically, |
%Textures have also been modeled statistically, |
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In these models, a bank of linear filters is applied to the texture followed |
In these models, a bank of linear filters is applied to the texture followed |
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by a nonlinearity and then another set of filters to extract features |
by a nonlinearity and then another set of filters to extract features |
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(see, e.g., Heeger\cite{heeger95pyramid}). |
(see, e.g., Heeger\cite{heeger95pyramid}). |
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There is also physiological evidence of the filtering processes: |
There is also physiological evidence of the filtering processes: |
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%The first stages |
%The first stages |
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%of visual perception |
%of visual perception |
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%are fairly well known |
%are fairly well known |
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in the visual cortex, there are cells sensitive to different |
in the visual cortex, there are cells sensitive to different |
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frequencies, orientations, and locations in the visual field |
frequencies, orientations, and locations in the visual field |
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(see, e.g.,~Bruce et al\cite{bruce96visualperception}). |
%(see, e.g.,~Bruce et al |
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\cite{bruce96visualperception}. |
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On a higher level, the correlations between local features are combined |
On a higher level, the correlations between local features are combined |
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by forming contours and possibly |
by forming contours and possibly |
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other higher-level constructions (see, e.g., \cite{saarinen97integration}). |
other higher-level constructions %(see, e.g., |
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\cite{saarinen97integration}. |
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These higher levels are not yet thoroughly understood; |
These higher levels are not yet thoroughly understood; |
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some theories |
some theories |
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(see, e.g., Biederman\cite{biederman87}) |
%(see, e.g., Biederman% |
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\cite{biederman87} |
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assume certain primitive shapes whose |
assume certain primitive shapes whose |
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structure facilitates recognition. |
structure facilitates recognition. |
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with the selected repeating unit. For example, a texture can |
with the selected repeating unit. For example, a texture can |
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repeat multiple times inside the repeating unit, or can be skewed |
repeat multiple times inside the repeating unit, or can be skewed |
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w.r.t.~the repeating unit. |
w.r.t.~the repeating unit. |
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Again, a heuristic distribution is used which does not skew or scale |
Again, a heuristic distribution is used which does not skew or scale |
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the basis texture too much too often. |
the basis texture too much too often. |
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