ift6266: writeup/nips2010_submission.tex comparison

comparison writeup/nips2010_submission.tex @ 551:8f365abf171d

separete the transmo image

author	Frederic Bastien <nouiz@nouiz.org>
date	Wed, 02 Jun 2010 17:00:11 -0400
parents	662299f265ab
children	35c611363291

comparison

equal deleted inserted replaced

-:662299f265ab
+:8f365abf171d
 the self-taught learning framework.
 \vspace*{-1mm}
 \section{Perturbation and Transformation of Character Images}
 \label{s:perturbations}
-\vspace*{-1mm}
+{\large\bf Transformations}
+\vspace*{-1mm}
+\begin{minipage}[b]{0.14\linewidth}
+\centering
+\includegraphics[scale=.45]{images/Original.PNG}
+\label{fig:Original}
+\vspace{1.2cm}
+\end{minipage}%
+\hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
+{\bf Original:}
 This section describes the different transformations we used to stochastically
 transform source images in order to obtain data from a larger distribution which
 covers a domain substantially larger than the clean characters distribution from
 which we start. Although character transformations have been used before to
 improve character recognizers, this effort is on a large scale both
 amount of deformation or noise introduced.
 There are two main parts in the pipeline. The first one,
 from slant to pinch below, performs transformations. The second
 part, from blur to contrast, adds different kinds of noise.
+\end{minipage}
-\begin{figure}[ht]
-\vspace*{-2mm}
-\centerline{\resizebox{.9\textwidth}{!}{\includegraphics{images/transfo.png}}}
+\begin{minipage}[b]{0.14\linewidth}
-% TODO: METTRE LE NOM DE LA TRANSFO A COTE DE CHAQUE IMAGE
+\centering
-\caption{Illustration of each transformation applied alone to the same image
+\includegraphics[scale=.45]{images/Slant_only.PNG}
-of an upper-case h (top left). First row (from left to right) : original image, slant,
+\label{fig:Slant}
-thickness, affine transformation (translation, rotation, shear),
+\end{minipage}%
-local elastic deformation; second row (from left to right) :
+\hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
-pinch, motion blur, occlusion, pixel permutation, Gaussian noise; third row (from left to right) :
+%\centering
-background image, salt and pepper noise, spatially Gaussian noise, scratches,
+{\bf Slant:}
-grey level and contrast changes.}
-\label{fig:transfo}
-\vspace*{-2mm}
-\end{figure}
-{\large\bf Transformations}
-\vspace*{0.5mm}
-{\bf Slant.}
 Each row of the image is shifted
 proportionally to its height: $shift = round(slant \times height)$.
 $slant \sim U[-complexity,complexity]$.
-\vspace*{-1mm}
+\vspace{1.2cm}
+\end{minipage}
-{\bf Thickness.}
+\begin{minipage}[b]{0.14\linewidth}
+\centering
+\includegraphics[scale=.45]{images/Thick_only.PNG}
+\label{fig:Think}
+\vspace{.9cm}
+\end{minipage}%
+\hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
+{\bf Thinkness:}
 Morphological operators of dilation and erosion~\citep{Haralick87,Serra82}
 are applied. The neighborhood of each pixel is multiplied
 element-wise with a {\em structuring element} matrix.
 The pixel value is replaced by the maximum or the minimum of the resulting
 matrix, respectively for dilation or erosion. Ten different structural elements with
 randomly sample the operator type (dilation or erosion) with equal probability and one structural
 element from a subset of the $n=round(m \times complexity)$ smallest structuring elements
 where $m=10$ for dilation and $m=6$ for erosion (to avoid completely erasing thin characters).
 A neutral element (no transformation)
 is always present in the set. is applied.
-\vspace*{-1mm}
+\vspace{.4cm}
+\end{minipage}
-{\bf Affine Transformations.}
+\vspace{-.7cm}
+\begin{minipage}[b]{0.14\linewidth}
+\centering
+\includegraphics[scale=.45]{images/Affine_only.png}
+\label{fig:Affine}
+\end{minipage}%
+\hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
+{\bf Affine Transformations:}
 A $2 \times 3$ affine transform matrix (with
 6 parameters $(a,b,c,d,e,f)$) is sampled according to the $complexity$ level.
 Output pixel $(x,y)$ takes the value of input pixel
 nearest to $(ax+by+c,dx+ey+f)$,
 producing scaling, translation, rotation and shearing.
 forbid large rotations (not to confuse classes) but to give good
 variability of the transformation: $a$ and $d$ $\sim U[1-3 \times
 complexity,1+3 \times complexity]$, $b$ and $e$ $\sim[-3 \times complexity,3
 \times complexity]$ and $c$ and $f$ $\sim U[-4 \times complexity, 4 \times
 complexity]$.
-\vspace*{-1mm}
+\end{minipage}
-{\bf Local Elastic Deformations.}
+\begin{minipage}[b]{0.14\linewidth}
+\centering
+\includegraphics[scale=.45]{images/Localelasticdistorsions_only.PNG}
+\label{fig:Elastic}
+\end{minipage}%
+\hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
+{\bf Local Elastic Deformations:}
 This filter induces a ``wiggly'' effect in the image, following~\citet{SimardSP03-short},
 which provides more details.
 The intensity of the displacement fields is given by
 $\alpha = \sqrt[3]{complexity} \times 10.0$, which are
 convolved with a Gaussian 2D kernel (resulting in a blur) of
 standard deviation $\sigma = 10 - 7 \times\sqrt[3]{complexity}$.
-\vspace*{-1mm}
+\vspace{.4cm}
+\end{minipage}
-{\bf Pinch.}
+\vspace{-.7cm}
+\begin{minipage}[b]{0.14\linewidth}
+\centering
+\includegraphics[scale=.45]{images/Pinch_only.PNG}
+\label{fig:Pinch}
+\vspace{.6cm}
+\end{minipage}%
+\hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
+{\bf Pinch:}
 This is the ``Whirl and pinch'' GIMP filter but with whirl was set to 0.
 A pinch is ``similar to projecting the image onto an elastic
 surface and pressing or pulling on the center of the surface'' (GIMP documentation manual).
 For a square input image, this is akin to drawing a circle of
 radius $r$ around a center point $C$. Any point (pixel) $P$ belonging to
 and $C$. $d_2$ is given by $d_2 = sin(\frac{\pi{}d_1}{2r})^{-pinch} \times
 d_1$, where $pinch$ is a parameter to the filter.
 The actual value is given by bilinear interpolation considering the pixels
 around the (non-integer) source position thus found.
 Here $pinch \sim U[-complexity, 0.7 \times complexity]$.
+%\vspace{1.5cm}
-\vspace*{0.5mm}
+\end{minipage}
+\vspace{.1cm}
 {\large\bf Injecting Noise}
-\vspace*{0.5mm}
+\vspace*{-.2cm}
+\begin{minipage}[b]{0.14\linewidth}
-{\bf Motion Blur.}
+\centering
+\includegraphics[scale=.45]{images/Original.PNG}
+\label{fig:Original}
+\end{minipage}%
+\hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
+{\bf Motion Blur:}
 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 first $length$ pixels
 found by moving in the $angle$ direction.
 Here $angle \sim U[0,360]$ degrees, and $length \sim {\rm Normal}(0,(3 \times complexity)^2)$.
-\vspace*{-1mm}
+\vspace{.7cm}
+\end{minipage}
-{\bf Occlusion.}
+\vspace*{-5mm}
+\begin{minipage}[b]{0.14\linewidth}
+\centering
+\includegraphics[scale=.45]{images/Original.PNG}
+\label{fig:Original}
+\end{minipage}%
+\hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
+{\bf Occlusion:}
 Selects a random rectangle from an {\em occluder} 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 (more details in~\citet{ift6266-tr-anonymous}).
 This filter is skipped with probability 60\%.
-\vspace*{-1mm}
+\vspace{.4cm}
+\end{minipage}
-{\bf Pixel Permutation.}
-This filter permutes neighbouring pixels. It first selects
+\vspace*{-5mm}
+\begin{minipage}[b]{0.14\linewidth}
+\centering
+\includegraphics[scale=.45]{images/Original.PNG}
+\label{fig:Original}
+\end{minipage}%
+\hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
+{\bf Pixel Permutation:}
+This filter permutes neighbouring pixels. It first selects
 fraction $\frac{complexity}{3}$ of pixels randomly in the image. Each of them are then
 sequentially exchanged with one other in as $V4$ neighbourhood.
 This filter is skipped with probability 80\%.
-\vspace*{-1mm}
+\vspace{.8cm}
+\end{minipage}
-{\bf Gaussian Noise.}
+\begin{minipage}[b]{0.14\linewidth}
+\centering
+\includegraphics[scale=.45]{images/Original.PNG}
+\label{fig:Original}
+\end{minipage}%
+\hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
+{\bf Gaussian Noise:}
 This filter simply adds, to each pixel of the image independently, a
 noise $\sim Normal(0,(\frac{complexity}{10})^2)$.
 This filter is skipped with probability 70\%.
-\vspace*{-1mm}
+\vspace{1.1cm}
+\end{minipage}
-{\bf Background Images.}
+\vspace{-.7cm}
+\begin{minipage}[b]{0.14\linewidth}
+\centering
+\includegraphics[scale=.45]{images/Original.PNG}
+\label{fig:Original}
+\end{minipage}%
+\hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
+{\bf Background Images:}
 Following~\citet{Larochelle-jmlr-2009}, this transformation adds a random
 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}
+\vspace{.8cm}
+\end{minipage}
-{\bf Salt and Pepper Noise.}
+\vspace{-.7cm}
+\begin{minipage}[b]{0.14\linewidth}
+\centering
+\includegraphics[scale=.45]{images/Original.PNG}
+\label{fig:Original}
+\end{minipage}%
+\hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
+{\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 is skipped with probability 75\%.
-\vspace*{-1mm}
+\vspace{.9cm}
+\end{minipage}
-{\bf Spatially Gaussian Noise.}
+\vspace{-.7cm}
+\begin{minipage}[b]{0.14\linewidth}
+\centering
+\includegraphics[scale=.45]{images/Original.PNG}
+\label{fig:Original}
+\vspace{.5cm}
+\end{minipage}%
+\hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
+{\bf Spatially Gaussian Noise:}
 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
 initialize to zero a mask matrix of the image size. For each selected pixel
 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 is skipped with probability 75\%.
-\vspace*{-1mm}
+\end{minipage}
+\vspace{-.7cm}
-{\bf Scratches.}
+\begin{minipage}[b]{0.14\linewidth}
+\centering
+\includegraphics[scale=.45]{images/Original.PNG}
+\label{fig:Original}
+\end{minipage}%
+\hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
+\vspace{.4cm}
+{\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 500 such 1 images,
 randomly cropped and rotated by an angle $\sim Normal(0,(100 \times
 complexity)^2$, 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 skipped with probability 85\%. The probabilities
 of applying 1, 2, or 3 patches are (50\%,30\%,20\%).
-\vspace*{-1mm}
+\end{minipage}
+\vspace{-.7cm}
-{\bf Grey Level and Contrast Changes.}
+\begin{minipage}[b]{0.14\linewidth}
+\centering
+\includegraphics[scale=.45]{images/Original.PNG}
+\label{fig:Original}
+\end{minipage}%
+\hspace{0.3cm}\begin{minipage}[b]{0.86\linewidth}
+{\bf Grey Level and Contrast Changes:}
 This filter changes the contrast and may invert the image polarity (white
 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\%.
+\vspace{.7cm}
+\end{minipage}
+\vspace{-.7cm}
 \iffalse
 \begin{figure}[ht]
 \centerline{\resizebox{.9\textwidth}{!}{\includegraphics{images/example_t.png}}}\\
 \caption{Illustration of the pipeline of stochastic

Mercurial > ift6266

comparison writeup/nips2010_submission.tex @ 551:8f365abf171d