* Applied changes suggested by reviewer #1:

-Page 3:
    The Latex "\noindent" could be added
    after equations (1) and (2).
    -Page 3, paragraph 3:
    gaussian -> Gaussian
    -Page 3 (two times):
    Experiment shows -> Experiments show  ??


git-svn-id: file:///srv/caca.zoy.org/var/lib/svn/research@2289 92316355-f0b4-4df1-b90c-862c8a59935f

2008-displacement/paper/paper.tex

@@ -101,7 +101,7 @@ value based on that model. One such algorithm is direct binary seach (DBS)
 (LSMB) \cite{lsmb}.
 
 HVS models are usually low-pass filters. Nasanen \cite{nasanen}, Analoui
-and Allebach \cite{allebach} found that using gaussian models gave visually
+and Allebach \cite{allebach} found that using Gaussian models gave visually
 pleasing results, an observation confirmed by independent visual perception
 studies \cite{mcnamara}.
 
@@ -140,8 +140,8 @@ mean square error between modified versions of the images, in the form:
   E(h,b) = \frac{(||v * h_{i,j} - v * b_{i,j}||_2)^2}{wh}
 \end{equation}
 
-where $w$ and $h$ are the image dimensions, $*$ denotes the convolution and $v$
-is a model for the human visual system.
+\noindent where $w$ and $h$ are the image dimensions, $*$ denotes the
+convolution and $v$ is a model for the human visual system.
 
 To compensate for the slight translation experienced in the halftone, we
 use the following error metric instead:
@@ -150,10 +150,10 @@ use the following error metric instead:
   E_{dx,dy}(h,b) = \frac{(||v * h_{i,j} - v * t_{dx,dy} * b_{i,j}||_2)^2}{wh}
 \end{equation}
 
-where $t_{dx,dy}$ is an operator which translates the image along the $(dx,dy)$
-vector.
+\noindent where $t_{dx,dy}$ is an operator which translates the image along the
+$(dx,dy)$ vector.
 
-A simple example can be given using a gaussian HVS model:
+A simple example can be given using a Gaussian HVS model:
 
 \begin{equation}
   v(x,y) = e^{\frac{x^2+y^2}{2\sigma^2}}
@@ -165,7 +165,7 @@ Finding the second filter is then straightforward:
   (v * t_{dx,dy})(x,y) = e^{\frac{(x-dx)^2+(y-dy)^2}{2\sigma^2}}
 \end{equation}
 
-Experiment shows that for a given image and a given corresponding halftone,
+Experiments show that for a given image and a given corresponding halftone,
 $E_{dx,dy}$ has a local minimum almost always away from $(dx,dy) = (0,0)$ (Fig.
 \ref{fig:lena-min}). Let $E$ be an error metric where this remains true. We
 call the local minimum $E_{min}$:
@@ -178,7 +178,7 @@ call the local minimum $E_{min}$:
   \begin{center}
    \input{lena-min}
    \caption{Mean square error for the \textit{Lena} image. $v$ is a simple
-            $11\times11$ gaussian convolution kernel with $\sigma = 1.2$ and
+            $11\times11$ Gaussian convolution kernel with $\sigma = 1.2$ and
             $(dx,dy)$ vary in $[-1,1]\times[-1,1]$.}
    \label{fig:lena-min}
   \end{center}
@@ -190,7 +190,7 @@ taking the displacement into account, the error becomes $7.77\times10^{-4}$
 for $(dx,dy) = (0.167709,0.299347)$. The new, corrected error is significantly
 smaller, with the exact same input and output images.
 
-Experiment shows that the corrected error is always noticeably smaller except
+Experiments show that the corrected error is always noticeably smaller except
 in the case of images that are already mostly pure black and white. The
 experiment was performed on a database of 10,000 images from common computer
 vision sets and from the image board \textit{4chan}, providing a representative
@@ -299,7 +299,7 @@ to be unstable \cite{stability}, and diffusing less than 100\% of the error is
 known to cause important error in shadow and highlight areas of the image.
 
 First we studied all possible coefficients on a pool of 250 images with an
-error metric $E$ based on a standard gaussian HVS model. Since we are studying
+error metric $E$ based on a standard Gaussian HVS model. Since we are studying
 algorithms on different images but error values are only meaningful for a given
 image, we chose a Condorcet voting scheme to determine winners. $E_{min}$ is
 only given here as an indication and had no role in the computation: