--- a/writeup/nips2010_submission.tex	Wed Jun 02 10:23:33 2010 -0400
+++ b/writeup/nips2010_submission.tex	Wed Jun 02 10:33:37 2010 -0400
@@ -227,8 +227,8 @@
 \vspace*{0.5mm}
 
 {\bf Motion Blur.}
-This is a ``linear motion blur'' in GIMP
-terminology, with two parameters, $length$ and $angle$. The value of
+This is GIMP's ``linear motion blur'' 
+with parameters $length$ and $angle$. The value of
 a pixel in the final image is approximately the  mean value of the $length$ first pixels
 found by moving in the $angle$ direction. 
 Here $angle \sim U[0,360]$ degrees, and $length \sim {\rm Normal}(0,(3 \times complexity)^2)$.
@@ -236,55 +236,44 @@
 
 {\bf Occlusion.}
 Selects a random rectangle from an {\em occluder} character
-images and places it over the original {\em occluded} character
+image and places it over the original {\em occluded}
 image. Pixels are combined by taking the max(occluder,occluded),
 closer to black. The rectangle corners
 are sampled so that larger complexity gives larger rectangles.
 The destination position in the occluded image are also sampled
-according to a normal distribution (see more details in~\citet{ift6266-tr-anonymous}).
-This filter has a probability of 60\% of not being applied.
+according to a normal distribution (more details in~\citet{ift6266-tr-anonymous}).
+This filter is skipped with probability 60\%.
 \vspace*{-1mm}
 
 {\bf Pixel Permutation.}
 This filter permutes neighbouring pixels. It selects first
 $\frac{complexity}{3}$ pixels randomly in the image. Each of them are then
-sequentially exchanged with one other pixel in its $V4$ neighbourhood. The number
-of exchanges to the left, right, top, bottom is equal or does not differ
-from more than 1 if the number of selected pixels is not a multiple of 4.
-% TODO: The previous sentence is hard to parse
-This filter has a probability of 80\% of not being applied.
+sequentially exchanged with one other in as $V4$ neighbourhood. 
+This filter is skipped with probability 80\%.
 \vspace*{-1mm}
 
 {\bf Gaussian Noise.}
 This filter simply adds, to each pixel of the image independently, a
 noise $\sim Normal(0(\frac{complexity}{10})^2)$.
-It has a probability of 70\% of not being applied.
+This filter is skipped with probability 70\%.
 \vspace*{-1mm}
 
 {\bf Background Images.}
 Following~\citet{Larochelle-jmlr-2009}, 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 a 32$\times$32 sub-region
-of that image is chosen as the background image (by sampling position
-uniformly while making sure not to cross image borders).
-To combine the original letter image and the background image, contrast
-adjustments are made. We first get the maximal values (i.e. maximal
-intensity) for both the original image and the background image, $maximage$
-and $maxbg$. We also have a parameter $contrast \sim U[complexity, 1]$.
-Each background pixel value is multiplied by $\frac{max(maximage -
-  contrast, 0)}{maxbg}$ (higher contrast yield darker
-background). The output image pixels are max(background,original).
+background behind the letter, from a randomly chosen natural image,
+with contrast adjustments depending on $complexity$, to preserve
+more or less of the original character image.
 \vspace*{-1mm}
 
 {\bf Salt and Pepper Noise.}
 This filter adds noise $\sim U[0,1]$ to random subsets of pixels.
 The number of selected pixels is $0.2 \times complexity$.
-This filter has a probability of not being applied at all of 75\%.
+This filter is skipped with probability 75\%.
 \vspace*{-1mm}
 
 {\bf Spatially Gaussian Noise.}
-Different regions of the image are spatially smoothed.
-The image is convolved with a symmetric Gaussian kernel of
+Different regions of the image are spatially smoothed by convolving
+the image is convolved with a symmetric Gaussian kernel of
 size and variance chosen uniformly in the ranges $[12,12 + 20 \times
 complexity]$ and $[2,2 + 6 \times complexity]$. The result is normalized
 between $0$ and $1$.  We also create a symmetric averaging window, of the
@@ -295,32 +284,27 @@
 we add to the mask the averaging window centered to it.  The final image is
 computed from the following element-wise operation: $\frac{image + filtered
   image \times mask}{mask+1}$.
-This filter has a probability of not being applied at all of 75\%.
+This filter is skipped with probability 75\%.
 \vspace*{-1mm}
 
 {\bf Scratches.}
 The scratches module places line-like white patches on the image.  The
 lines are heavily transformed images of the digit ``1'' (one), chosen
-at random among five thousands such 1 images. The 1 image is
+at random among 500 such 1 images,
 randomly cropped and rotated by an angle $\sim Normal(0,(100 \times
-complexity)^2$, using bi-cubic interpolation,
+complexity)^2$, using bi-cubic interpolation.
 Two passes of a grey-scale morphological erosion filter
 are applied, reducing the width of the line
 by an amount controlled by $complexity$.
-This filter is only applied only 15\% of the time. When it is applied, 50\%
-of the time, only one patch image is generated and applied. In 30\% of
-cases, two patches are generated, and otherwise three patches are
-generated. The patch is applied by taking the maximal value on any given
-patch or the original image, for each of the 32x32 pixel locations.
+This filter is skipped with probability 85\%. The probabilities
+of applying 1, 2, or 3 patches are (50\%,30\%,20\%).
 \vspace*{-1mm}
 
 {\bf Grey Level and Contrast Changes.}
 This filter changes the contrast 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. 
-Contrast $\sim U[1-0.85 \times complexity,1]$ (so contrast $\geq 0.15$). 
-The image is normalized into $[\frac{1-C}{2},1-\frac{1-C}{2}]$. The
-polarity is inverted with $0.5$ probability.
+to black and black to white). The contrast is $C \sim U[1-0.85 \times complexity,1]$ 
+so the image is normalized into $[\frac{1-C}{2},1-\frac{1-C}{2}]$. The
+polarity is inverted with probability 50\%.
 
 \iffalse
 \begin{figure}[ht]