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\loch\af4\hich\af4\dbch\f4\cgrid \snext0 Normal;}{\*\cs10 \additive Default Paragraph Font;}}{\info{\author Marc Talusan}{\operator Marc Talusan}{\creatim\yr2003\mo9\dy23\hr22\min27}{\revtim\yr2003\mo9\dy23\hr22\min33}{\version1}{\edmins6}{\nofpages2}
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\pnlcrm\pnstart1\pnindent720\pnhang{\pntxtb (}{\pntxta )}}\pard\plain \widctlpar\tx560\tx1120\tx1680\tx2240\tx2800\tx3360\tx3920\tx4480\tx5040\tx5600\tx6160\tx6720\adjustright \loch\af4\hich\af4\dbch\f4\cgrid {\tab \tab \tab \tab \tab \tab \tab \tab \tab 
\tab \tab }{\hich\af4\dbch\af4\loch\f4 Notes by Philip Meier
\par \tab \tab \tab \tab \tab \tab \tab \tab \tab \tab \tab \hich\af4\dbch\af4\loch\f4 pmmeier@mit.edu
\par \tab \tab \tab \tab \tab \tab \tab \tab \tab \tab \tab \hich\af4\dbch\af4\loch\f4 9-23-03
\par 
\par \tab \tab \tab \tab \tab }{\scaps\fs28 \hich\af4\dbch\af4\loch\f4 Neural \hich\af4\dbch\af4\loch\f4 R\hich\af4\dbch\af4\loch\f4 epresentations}{\scaps\fs28 
\par }{
\par What is a representation?
\par 
\par -Some internal state related to the external world
\par -numbers can describe the internal and external world
\par -we can describe representations as some relation 
\par between an internal set of numbers that capture information about an external set of numbers
\par 
\par Question:  }{what sorts of questions would}{ you need to decide before working with a format of an image.
\par 
\par Continuous vs. sampled
\par Analog vs. digital world 
\par Analog vs digital computation (ie. spikes vs. voltage integration)
\par 
\par If the set of all possible signals is}{ infinite in at least one dimens}{ion, then the total number of possible images is no longer countable, and so making probablis
tic statements about the ratios becomes difficult.  i.e.  what is the ratio (signals that are natural images: total number of possible signals)  
\par 
\par Of course, it does not matter if the world is analog or not, so long as all sampling is discrete, and thus fi}{nite.  }{
\par 
\par PCM }{\tab \tab \tab \tab }{Pulse Code Modulation}{  (251,252,250,251)}{
\par DCPM }{\tab \tab \tab \tab }{Differential Pulse Code Modulation}{  (+1,-2,+1)}{
\par Sum/Diff Transform
\par Fourier  }{\tab \tab \tab \tab }{Sum of a bunch of sinusoidal gratings
\par PCA    }{\tab \tab \tab \tab }{Sum of a bunch of the best N basis functions  
\par }{\tab \tab \tab \tab \tab (determimed with training set}{s and minimizing error)
\par Subbands, pyramids,}{
\par and}{ waves
\par 
\par }{\i "The only aspect of vision science that really works is color..."}{\i   -T. Adelson}{\i 
\par }{
\par PCA with three components does a good job in capturing the spectral distribution of a signal.
\par 
\par Physiology and }{ideal component seem to align; }{use the dot product of the activation values of cones
\par 
\par 
\par }{\i "The rest of vision science is harder."
\par }{
\par }{It is hard to detect an impul}{se edge in a signal.
\par For example, consider a sharp bounda}{r}{y of a dye in a flower.  This is a step edge.  You cannot detect a step edge without an infinite number of components in PCA.  Of course, with enough components you can get a very good approximation.  
\par 
\par Thus, vision science may be good at describing sampling methods of a spectral distribution at a point, but it has a harder time explaining how we see sharp color boundaries, when spectral distributions vary over space.
\par }\pard \widctlpar\adjustright {
\par }}