[Gzz-commits] gzz/Documentation/Manuscripts/Paper paper.tex

[Tuomas J. Lukka]

CVSROOT:        /cvsroot/gzz
Module name:    gzz
Changes by:     Tuomas J. Lukka <address@hidden>        02/11/29 04:18:22

Modified files:
        Documentation/Manuscripts/Paper: paper.tex 

Log message:
        Getting there

CVSWeb URLs:
http://savannah.gnu.org/cgi-bin/viewcvs/gzz/gzz/Documentation/Manuscripts/Paper/paper.tex.diff?tr1=1.89&tr2=1.90&r1=text&r2=text

Patches:
Index: gzz/Documentation/Manuscripts/Paper/paper.tex
diff -u gzz/Documentation/Manuscripts/Paper/paper.tex:1.89 
gzz/Documentation/Manuscripts/Paper/paper.tex:1.90
--- gzz/Documentation/Manuscripts/Paper/paper.tex:1.89  Fri Nov 29 03:25:47 2002
+++ gzz/Documentation/Manuscripts/Paper/paper.tex       Fri Nov 29 04:18:22 2002
@@ -291,11 +291,25 @@
 % an easily distinguishable unique background from a
 % distribution based on 
 
-We use a very rough, qualitative model of visual perception,
+We use a very rough, qualitative model of visual perception
+(see Fig.~\ref{fig-perceptual}).
 %providing an infinite source of unique backgrounds.
 %generating textures based on seed numbers [identity]
-The basic assumption of the model is that an image
-is perceived as a set of features (see Fig.~\ref{fig-perceptual}).
+Current knowledge of the first stages
+of visual perception 
+(see, e.g.~Bruce et al\cite{bruce96visualperception})
+is fairly precise:
+in the visual cortex, there are cells sensitive to different 
+frequencies, orientations, and locations in the visual field.
+On a higher level, correlating local features are combined 
+to global perception, by forming contours and possibly
+other higher-level constructions. 
+These higher levels are not yet thoroughly understood;
+theories of structural object perception 
+(see e.g. Biederman\cite{biederman87})
+propose certain primitive shapes whose 
+structure facilities recognition.
+
 
 \begin{figure}
 \centering
@@ -308,24 +322,39 @@
 }
 \end{figure}
 
-Current knowledge of the first stages
-of visual perception (see, e.g.~\cite{bruce96visualperception})
-supports this view:
-in the visual cortex, there are cells sensitive to different 
-frequencies, orientations, and locations in the visual field.
-On a higher level, correlating local features are combined 
-to global perception, by forming contours and possibly
-other higher-level constructions. 
-These higher levels are not yet thoroughly understood;
-theories of structural object perception (e.g. \cite{biederman87})
-propose certain primitive shapes whose 
-structure facilities recognition.
+% The basic assumption of the model is that an image
+% is perceived as a set of features 
 
 We make the assumption
-that the intensities of different features,
+that at some point,
+the intensities of different features,
 such as local and global shapes and colors, 
-form a \emph{feature vector},
-which facilitates recognition and memorization of images.
+combine to form an abstract \emph{feature vector},
+as used in neural computation.
+This feature vector is then used as an input to the
+networks which linearly compute which concept the particular
+input corresponds to, in a perceptron-like 
+fashion\cite{widrow60adaptive,rosenblatt62neurodynamics}.
+
+From this picture, we can formulate the following points:
+To be distinguishable,
+\begin{itemize}
+\item A feature vector for a given texture should be always the
+    same, and not a smudged distribution; 
+    therefore, a repeating texture should be easier to recognize
+    than one that does not repeat, even if local features
+    are similar. Our anecdotal observations confirm this.
+\item There should be as many potential features in the distribution
+    as possible. For example, if there were no yellow textures,
+    or if there were no curved lines, we would be wasting
+    a lot of recognition potential by leaving some elements
+    of the feature vector always zero.
+\item (Most abstractly) 
+    The entropy of the feature vectors
+    over the distribution of textures, should be maximized.
+\end{itemize}
+
+% which facilitates recognition and memorization of images.
 % The structure of the features is assumed to be irrelevant.
 
 % A good mathematical model for the excitatory and inhibitory
@@ -336,11 +365,17 @@
 % of adjacent receptive fields and different objects are 
 % perceived.
 
-For the backgrounds to be distinguishable, they should produce
-distinct feature vectors in brain. 
-To achieve this, the model should maximize the entropy of the feature vector.
+% For the backgrounds to be distinguishable, they should produce
+% distinct feature vectors in brain. 
+% To achieve this, the model should maximize the entropy of the feature vector.
 %We call this the principle of saving bits.
-Features orthogonal to human perception 
+
+The last part means essentially
+that if all square-like shapes were green, we would again be
+wasting recognitive power.
+Indeed, entropy is maximized when the features are distributed
+independently from each other:
+features orthogonal to human perception 
 (e.g.~color, direction of fastest luminance change)
 should be independently random, and features not orthogonal 
 (e.g. colors of neighbouring pixels) 
@@ -349,10 +384,12 @@
 (e.g. pixels on a small area should correlate enough to
 facilitate perception of contours).
 
-In a sense, the perception model should invert the
+In a sense, the perception model should {\em invert} the
 visual processing to produce a unique background from 
 a random vector seeded by the identity.
-This type of approach has been used by Ware and Knight\cite{ware95texture}, 
for inverting the earliest stage of the visual system, 
+This type of approach has been used 
+by Ware and Knight\cite{ware95texture}, for inverting 
+the earliest stage of the visual system, 
 the spatial frequency detectors, in order to place 
 information
 in the texture channel. Their goals are in more conventional