--- a/writeup/techreport.tex	Wed Apr 28 11:45:14 2010 -0400
+++ b/writeup/techreport.tex	Wed Apr 28 14:35:01 2010 -0400
@@ -72,10 +72,27 @@
 
 \section{Perturbation and Transformation of Character Images}
 
+\subsection{Adding Slant}
+In order to mimic a slant effect, we simply shift each row of the image proportionnaly to its height.
+The coefficient is randomly sampled according to the complexity level and can be negatif or positif with equal probability.
+
+\subsection{Changing Thickness}
+To change the thickness of the characters we used morpholigical operators: dilation and erosion~\cite{Haralick87,Serra82}.
+The basic idea of such transform is, for each pixel, to multiply in the element-wise manner its neighbourhood with a matrix called the structuring element.
+Then for dilation we remplace the pixel value by the maximum of the result, or the minimum for erosion.
+This will dilate or erode objects in the image, the strength of the transform only depends on the structuring element.
+We used ten different structural elements with various shapes (the biggest is $5\times5$).
+for each image, we radomly sample the operator type (dilation or erosion) and one structural element
+from a subset depending of the complexity (the higher the complexity, the biggest the structural element can be).
+Erosion allows only the five smallest structural elements because when the character is too thin it may erase it completly.
+
 \subsection{Affine Transformations}
-\subsection{Adding Slant}
+We generate an affine transform matrix according to the complexity level, then we apply it directly to the image.
+This allows to produce scaling, translation, rotation and shearing variances. We took care that the maximum rotation applied
+to the image is low enough not to confuse classes.
+
 \subsection{Local Elastic Deformations}
-\subsection{Changing Thickness}
+\subsection{GIMP transformation}
 \subsection{Occlusion}
 \subsection{Background Images}
 \subsection{Salt and Pepper Noise}
@@ -140,7 +157,7 @@
 
 \section{Conclusions}
 
-\bibliography{strings,ml,aigaion}
+\bibliography{strings,ml,aigaion,specials}
 \bibliographystyle{mlapa}
 
-\end{document}
\ No newline at end of file
+\end{document}