--- a/writeup/techreport.tex	Fri Apr 30 16:24:35 2010 -0400
+++ b/writeup/techreport.tex	Fri Apr 30 16:29:17 2010 -0400
@@ -118,13 +118,6 @@
 
 $\sigma$ and $\alpha$ were linked to complexity through the formulas $\alpha = \sqrt[3]{complexity} \times 10.0$ and $\sigma = 10 - 7 \times \sqrt[3]{complexity}$.
 
-\subsection{Motion Blur}
-
-This is a GIMP filter we applied, a "linear motion blur" in GIMP terminology. The description will be brief as it is a well-known filter.
-
-This algorithm has two input parameters, $length$ and $angle$. The value of a pixel in the final image is the mean value of the $length$ first pixels found by moving in the $angle$ direction. An approximation of this idea is used, as we won't fall onto precise pixels by following that direction. This is done using the Bresenham line algorithm.
-
-The angle, in our case, is chosen from a uniform distribution over $[0,360]$ degrees. The length, though, depends on the complexity; it's sampled from a Gaussian distribution of mean 0 and standard deviation $\sigma = 3 \times complexity$.
 
 \subsection{Pinch}
 
@@ -138,12 +131,13 @@
 
 The value for $pinch$ in our case was given by sampling from an uniform distribution over the range $[-complexity, 0.7 \times complexity]$.
 
+\subsection{Motion Blur}
 
-\subsection{Distorsion gauss}
-This filter simply adds, to each pixel of the image independently, a gaussian noise of mean $0$ and standard deviation $\frac{complexity}{10}$.
+This is a GIMP filter we applied, a "linear motion blur" in GIMP terminology. The description will be brief as it is a well-known filter.
 
-It has has a probability of not being applied, at all, of 70\%.
+This algorithm has two input parameters, $length$ and $angle$. The value of a pixel in the final image is the mean value of the $length$ first pixels found by moving in the $angle$ direction. An approximation of this idea is used, as we won't fall onto precise pixels by following that direction. This is done using the Bresenham line algorithm.
 
+The angle, in our case, is chosen from a uniform distribution over $[0,360]$ degrees. The length, though, depends on the complexity; it's sampled from a Gaussian distribution of mean 0 and standard deviation $\sigma = 3 \times complexity$.
 
 \subsection{Occlusion}
 
@@ -161,6 +155,14 @@
 
 This filter has a probability of not being applied, at all, of 60\%.
 
+
+\subsection{Distorsion gauss}
+
+This filter simply adds, to each pixel of the image independently, a gaussian noise of mean $0$ and standard deviation $\frac{complexity}{10}$.
+
+It has has a probability of not being applied, at all, of 70\%.
+
+
 \subsection{Background Images}
 
 This transformation adds a random background behind the letter. The background is chosen by first selecting, at random, an image from a set of images. Then we choose a 32x32 subregion of that image as the background image (by sampling x and y positions uniformly while making sure not to cross image borders).
@@ -178,6 +180,7 @@
 This filter also has a probability of not being applied, at all, of 75\%.
 
 \subsection{Spatially Gaussian Noise}
+
 The aim of this transformation is to filter, with a gaussian kernel, different regions of the image. In order to save computing time 
 we decided to convolve the whole image only once with a symmetric gaussian kernel of size and variance choosen uniformly in the ranges:
 $[12,12 + 20 \times complexity]$ and $[2,2 + 6 \times complexity]$. The result is normalized between $0$ and $1$.
@@ -191,8 +194,9 @@
 
 
 \subsection{Color and Contrast Changes}
+
 This filter changes the constrast and may invert the image polarity (white on black to black on white). The contrast $C$ is defined here as the difference 
-between the maximum and the minimum pixel value of the image. A contrast value is sampled uniformly between $1$ and $1-0.85 \times complexity}$
+between the maximum and the minimum pixel value of the image. A contrast value is sampled uniformly between $1$ and $1-0.85 \times complexity$
 (this insure a minimum constrast of $0.15$). We then simply normalize the image to the range $[\frac{1-C}{2},1-\frac{1-C}{2}]$. The polarity 
 is inverted with $0.5$ probability.