Attachment 'Motion.tex'

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   1 %!TEX TS-program = pdflatex
   2 %!TEX encoding = Latin1
   3 %!TEX root = perrinet09int.tex
   4 %\section{Motion}%
   5 %\begin{frame}\frametitle{Outline}%: Decoding low-level neural information to track visual motion}%
   6 %\includegraphics<+>[width=.6\linewidth]{model_simple.pdf}%
   7 %  \end{frame}%
   8 %\begin{frame}\frametitle{Outline: Spatial and temporal integration}%
   9 %\includegraphics<+>[width=.6\linewidth]{model_rog.pdf}%
  10 %  \end{frame}%
  11 %\begin{frame}\frametitle{Outline: An integrated model of OFR}%
  12 %\includegraphics<+>[width=.94\linewidth]{summary.png}%
  13 %\end{frame}%
  14 \begin{frame}\frametitle{Outline}%
  15 %----------------------------------------------------------------------------------------------------%
  16 %\begin{columns}[c]%
  17 %\begin{column}{4cm}%
  18 %\only<2>{\includemovie[autoplay,loop,text={\includegraphics[width=.8\linewidth]{fig_cross.png}},repeat]{.8\linewidth}{.8\linewidth}{../../Motion/08-06-02_seminaire_ulm/figures/full_field.mp4}}%
  19 %\only<3>{\includemovie[autoplay,loop,text={\includegraphics[width=.8\linewidth]{fig_cross.png}},repeat]{.8\linewidth}{.8\linewidth}{../../Motion/08-06-02_seminaire_ulm/figures/grating_size.mp4}}%
  20 %\only<4>{\includemovie[autoplay,loop,repeat]{.8\linewidth}{.8\linewidth}{figures/moving_pink_low.mpg}}%
  21 %\end{column}%
  22 %\begin{column}{6cm}%
  23 \begin{itemize}%
  24     \item<1-> Context: coding of static natural images
  25 %    \item  toward coding of motion flows
  26     \item<1-> Decoding low-level neural information to track visual motion:
  27   	\begin{itemize}%
  28   		  \item<2-> Probabilistic representations
  29   		  \item<3-> General formulation for spatio-temporal integration
  30 		  \item<4> Dynamical recurrent models of motion estimation
  31   	\end{itemize}%
  32     \end{itemize}%
  33 %\end{column}%
  34 %\end{columns}%
  35 \end{frame}%
  36 %\frame{\includemovie[loop,text={\includegraphics[width=.8\linewidth]{fig_cross.png}},repeat]{.8\linewidth}{.8\linewidth}{../../Motion/08-06-02_seminaire_ulm/figures/full_field.mp4}}%
  37 %
  38 %\begin{frame}\frametitle{Outline: Probabilistic representations of motion}%
  39 %\includegraphics<+>[width=.6\linewidth]{model_simple.pdf}%
  40 %\end{frame}%
  41 %
  42 %\frame{\includemovie[autoplay,loop,text={\includegraphics[width=.8\linewidth]{fig_cross.png}},repeat]{.8\linewidth}{.8\linewidth}{../../Motion/08-06-02_seminaire_ulm/figures/grating_size.mp4}}%
  43 %
  44 %%\begin{frame}\frametitle{Outline: Spatial and temporal integration}%
  45 %\includegraphics<+>[width=.6\linewidth]{model_rog.png}%
  46 %\end{frame}%
  47 %
  48 % % TODO: find a better example
  49 %\frame{\includemovie[autoplay,loop,text={\includegraphics[width=.8\linewidth]{fig_cross.png}},repeat]{.8\linewidth}{.8\linewidth}{../../Motion/08-06-02_seminaire_ulm/figures/aperture_barberpole.mp4}}%
  50 %\frame{\includemovie[autoplay,loop,repeat]{.8\linewidth}{.8\linewidth}{../../Motion/08-06-02_seminaire_ulm/figures/barberpole.mp4}}%
  51 %\begin{frame}\frametitle{Outline: An integrated model of OFR}%
  52 %\includegraphics<+>[width=.94\linewidth]{summary.png}%
  53 %  \end{frame}%
  54 %----------------------------------------------------------------------------------------------------%
  55 %\frame{\includemovie[autoplay,loop,repeat,attach=false]{.8\linewidth}{.8\linewidth}{figures/full_field.mp4}}
  56 %%
  57 %\frame{\includemovie[autoplay,loop,repeat,attach]{.8\linewidth}{.8\linewidth}{./figures/moving_pink.mp4}}%horizontal.mp4}}%
  58 %\begin{frame}%
  59 %%\begin{columns}%
  60 %%\begin{column}{.5\textwidth}%
  61 %%\begin{center}%text={\includegraphics[width=.4\linewidth]{fig_cross.png}},
  62 %\includemovie[autoplay,loop,repeat]{.8\linewidth}{.4\linewidth}{figures/full_field.mp4}%
  63 %%\end{center}%
  64 %%\end{column}%
  65 %%\begin{column}{.5\textwidth}%
  66 %%\begin{center}%
  67 %\includemovie[autoplay,loop,repeat]{.4\linewidth}{.4\linewidth}{figures/horizontal.mp4}%
  68 %%\end{center}%
  69 %%\end{column}%
  70 %%\end{columns}%
  71 %\end{frame}%
  72 
  73 \frame{\includemovie[autoplay,loop,text={\includegraphics[width=.8\linewidth]{fig_cross.png}},repeat]{.8\linewidth}{.8\linewidth}{../../Motion/08-06-02_seminaire_ulm/figures/full_field.mp4}%
  74 }%
  75 
  76 \section{Probabilistic representations of motion}%
  77 \begin{frame}%
  78 \frametitle{\insertsection}%
  79 \begin{columns}[t]%
  80 \begin{column}{4.5cm}%
  81 	\begin{center}%
  82 	\includegraphics[width=.9\columnwidth]{model_simple.png}%
  83 	\end{center}%
  84 \end{column}%
  85 \begin{column}{7.5cm}%
  86 	\begin{itemize}%
  87            	\item	$  \mathbf{I}(\vec{x} + \vec{v} . dt ,t+dt) = \mathbf{I}(\vec{x},t) + \nu$
  88 		\item<2-> A posteriori Probability%
  89 %\only<3-4>{%	
  90 		\begin{itemize}%
  91 			\item Bayes theorem : $P( \vec{v} |   \mathbf{I} ) \propto   P( \mathbf{I}  | \vec{v} ). P( \vec{v} )$%
  92 			\item Prior $ P(\vec{v} ) =\frac{1}{\sqrt{2 \pi}\sigma_p} e^{-\frac{\| \vec{v} \|^2}{2  \sigma_p^2}}$%
  93 			\item Likelihood $ P( \mathbf{I}  | \vec{v} ) =\frac{1}{\sqrt{2 \pi}\sigma_m} e^{-\frac{\mathcal{T}(\mathbf{I})}{2  \sigma_m^2}}$%
  94 			\item with $\mathcal{T}(\mathbf{I}) = \| \mathbf{I}(\vec{x},t) -  \mathbf{I}(\vec{x} - \vec{v} . dt ,t-dt) \|^2$ and $\mathbf{I}=C.\mathbf{I}_{100}$,%
  95 		\end{itemize}%
  96 %}%
  97 		\item<3->[] \framebox{$ P( \vec{v} |   \mathbf{I} ) \propto \exp(- \frac{C^2 . \mathcal{T}(\mathbf{I}_{100})^2}{2 \sigma_m^2} - \frac{ \| \vec{v} \|^2}{2 \sigma_p^2 })$}%
  98 %\item<5->[$\ast$] Quadratic approximation [Weiss et al., 2002] of $\mathcal{T}(\mathbf{I}_{100})^2$% 
  99 %\item<5->[] CRF is a  Slope-2 Naka Rushton curve  \framebox{$\gamma (C) \propto \frac{C^2}{C_{50}^2+C^2}$} with $C_{50} \propto \frac{\sigma_p}{\sigma_m}$%
 100 		\item<4-> Decision (eye's acceleration gain): $\gamma \propto \vec{v}^\ast $%
 101 		\item<4->[] $\vec{v}^\ast =  E( \vec{v} |   \mathbf{I} ) = \int \vec{v}  dP( \vec{v} |   \mathbf{I} )$%
 102 	\end{itemize}%
 103 \end{column}%
 104 \end{columns}%
 105 \end{frame}%
 106 
 107 \begin{frame}\frametitle{\insertsection}%
 108 \only<1>{%
 109 \begin{columns}%
 110 \begin{column}{.5\textwidth}%
 111 \begin{center}%
 112 \includemovie[%
 113 autoplay,loop,repeat%text={\includegraphics[width=.95\columnwidth]{fig_cross.png}},
 114 ]{.95\columnwidth}{.95\columnwidth}{../../Motion/08-06-02_seminaire_ulm/figures/full_field.mp4}%\\%
 115 \end{center}%\input
 116 \end{column}%
 117 \begin{column}{.5\textwidth}%
 118 \begin{center}%
 119 \includemovie[%
 120 autoplay,loop,repeat%,text={\includegraphics[width=.95\columnwidth]{fig_cross.png}}
 121 ]{.95\columnwidth}{.95\columnwidth}{figures/moving_pink.mpg}%{../../Motion/08-06-02_seminaire_ulm/figures/moving_pink.mp4}%horizontal.mp4}\\%
 122 \end{center}%
 123 \end{column}%
 124 \end{columns}%
 125 }%
 126 \only<2>{%
 127 \begin{columns}%
 128 \begin{column}{.5\textwidth}%
 129 \begin{center}%
 130 \includegraphics[width=.95\columnwidth]{likelihood_1D_H.pdf}\\%
 131 Grating%
 132 \end{center}%
 133 \end{column}%
 134 \begin{column}{.5\textwidth}%
 135 \begin{center}%
 136 \includegraphics[width=.95\columnwidth]{likelihood_2D_H.pdf}\\%
 137 Cloud%
 138 \end{center}%
 139 \end{column}%
 140 \end{columns}%
 141 }%
 142 \only<3>{%
 143 \begin{columns}%
 144 \begin{column}{.5\textwidth}%
 145 \begin{center}%
 146 \includemovie[%
 147 autoplay,loop,repeat%text={\includegraphics[width=.95\columnwidth]{fig_cross.png}},
 148 ]{.95\columnwidth}{.95\columnwidth}{../../Motion/08-06-02_seminaire_ulm/figures/full_field_low.mp4}\\%
 149 \end{center}%
 150 \end{column}%
 151 \begin{column}{.5\textwidth}%
 152 \begin{center}%
 153 \includemovie[%
 154 autoplay,loop,repeat%text={\includegraphics[width=.95\columnwidth]{fig_cross.png}},
 155 ]{.95\columnwidth}{.95\columnwidth}{figures/moving_pink_low.mpg}%horizontal.mp4}\\%
 156 \end{center}%
 157 \end{column}%
 158 \end{columns}%
 159 }%
 160 \only<4>{%
 161 \begin{columns}%full_field_low
 162 \begin{column}{.5\textwidth}%
 163 \begin{center}%
 164 \includegraphics[width=.95\columnwidth]{likelihood_1D_L.pdf}\\%
 165 Grating%
 166 \end{center}%
 167 \end{column}%
 168 \begin{column}{.5\textwidth}%
 169 \begin{center}%
 170 \includegraphics[width=.95\columnwidth]{likelihood_2D_L.pdf}\\%
 171 Cloud%
 172 \end{center}%
 173 \end{column}%
 174 \end{columns}%
 175 }%
 176 \end{frame}%
 177 %-------------------------------------------------------------------------------------------%
 178 %\begin{frame}%
 179 %\includegraphics[height=.71\linewidth]{../../Motion/SpatialSummation/06-10_NeuroComp_talk/figures/fig_2bayesian_grating.png}
 180 %\end{frame}%
 181 \begin{frame}%
 182 \includegraphics[width=\linewidth]{Contrast_human.pdf}
 183 \vskip 1cm
 184 \framebox{$\gamma (C) \propto \frac{C^2}{C_{50}^2+C^2}$} with $C_{50} \propto \frac{\sigma_p}{\sigma_m}$\\%
 185 $\lambda(C) = \lambda_0 +  \frac{1}{\gamma (C)}$%
 186 \end{frame}%
 187 %\begin{frame}%
 188 %\includegraphics[width=.5\columnwidth]{naka-rushton.pdf}%
 189 %\includegraphics[width=.5\columnwidth]{naka-rushton_n.pdf}\\%
 190 %\vskip 1cm
 191 %$\gamma (C) = \frac{C^n}{C_{50}^n+C^n} = \frac{1}{1+  \frac{C_{50}^n}{C^n}}$
 192 %\end{frame}%
 193 %\begin{frame}%
 194 %\includegraphics[width=\linewidth]{figures/eye_walker.pdf}
 195 %\end{frame}%
 196 %-------------------------------------------------------------------------------------------%
 197 \frame{\includemovie[autoplay,loop,text={\includegraphics[width=.8\linewidth]{fig_cross.png}},repeat]{.8\linewidth}{.8\linewidth}{../../Motion/08-06-02_seminaire_ulm/figures/grating_size.mp4}%
 198 }%
 199 \begin{frame}
 200 \includegraphics<+>[width=.6\linewidth]{model_simple.pdf}%
 201 \includegraphics<+>[width=.6\linewidth]{model_rog.pdf}%
 202 \end{frame}%
 203 \section{General formulation for spatio-temporal integration}%
 204 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 205 \begin{frame}
 206 \frametitle{\insertsection}%
 207 \begin{columns}%[t]%
 208 \begin{column}{4.5cm}%
 209 \begin{center}%
 210 %TODO change model_rog for disk grating
 211 \includegraphics[width=.9\columnwidth]{model_rog.pdf}%
 212 \end{center}%
 213 \end{column}%
 214 \begin{column}{7.5cm}%
 215 \begin{block}{How is probabilistic information pooled?}%
 216 %\begin{itemize}%
 217 $\mathcal{N} (\vec{v}_{{\bf n}},C_{{\bf n}})=\frac{1}{\sqrt{det(2 \pi C_{{\bf n}})}} e^{-\frac{(\vec{v}-\vec{v}_{{\bf n}})^T C_{{\bf n}}^{-1} (\vec{v} - \vec{v}_{{\bf n}})}{2}}$%
 218 \begin{eqnarray*}%
 219 C_{{\bf n}} = %
 220 \left( \begin{array}{cc}%
 221 \cos(\theta) & -\sin(\theta) \\%
 222 \sin(\theta) & \cos(\theta)%
 223 \end{array} \right)%
 224 \left( \begin{array}{cc}%
 225 \sigma_1^2 & 0 \\%
 226 0 & \sigma_2^2%
 227 \end{array} \right)%
 228 \end{eqnarray*}%
 229 %\end{itemize}%
 230 \end{block}%
 231 \begin{block}<2->{Independence of measurement noise}%
 232 %\begin{itemize}%
 233 %\item 
 234 $ P( \vec{v} |   \mathbf{I} ) = \Pi_{{\bf n}}  P( \vec{v} |   \mathbf{I} , {\bf n})=\mathcal{N} (\vec{v}_m,C)$ with%%\item 
 235 \begin{eqnarray*}\fbox{$
 236 \left\{
 237 \begin{array}{rcl}
 238 C^{-1}              &=& \sum C^{-1}_{{\bf n}}\\
 239 C^{-1} . \vec{v}_m &=& \sum C^{-1}_{{\bf n}} \vec{v}_{{\bf n}}
 240  \end{array}
 241  \right. 
 242 $} %
 243 \end{eqnarray*}%
 244 %\begin{eqnarray*}%
 245 %C_{{\bf n}}^{-1} = %
 246 %\left( \begin{array}{cc}
 247 %\cos(\theta) & \sin(\theta) \\
 248 %-\sin(\theta) & \cos(\theta)
 249 %\end{array} \right)
 250 %\left( \begin{array}{cc}
 251 %\sigma_{{\bf n}}^{-2}  & 0 \\
 252 %0 & \sigma_2^{-2}
 253 %\end{array} \right)
 254 %\end{eqnarray*}
 255 %\end{itemize}%
 256 \end{block}%
 257 \end{column}%
 258 \end{columns}%
 259 \end{frame}%
 260 
 261 \begin{frame}
 262 \includegraphics[width=.5\columnwidth]{../../Motion/SpatialSummation/08-06_areadne08/figures/fit_BRF.pdf}%
 263 \begin{eqnarray*}%
 264 \gamma(C,d) = \frac{ \frac{C^2}{C_e^2} (1- \exp(-\frac{d^2}{2.\omega^2})) }{ 1 + \frac{C^2}{C_e^2}.(1- \exp(-\frac{d^2}{2.\omega^2})) + \frac{C^2}{C_i^2}.(1- \exp(-\frac{d^2}{2.\omega_i^2})) } %
 265 \end{eqnarray*}%
 266 \end{frame}%
 267 %\begin{frame}%<+>
 268 %\includegraphics[height=.35\linewidth]{../../Motion/SpatialSummation/08-06_areadne08/figures/bipartite_labeled.pdf}
 269 %\includegraphics[height=.35\linewidth]{fit_CRF_bipartite.pdf}%
 270 %\end{frame}%
 271 
 272 %-------------------------------------------------------------------------------------------% 
 273 %: dynamical particles
 274 \section{Dynamical recurrent models of motion estimation}%
 275 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 276 \frame{\includemovie[autoplay,loop,text={\includegraphics[width=.8\linewidth]{fig_cross.png}},repeat]{.8\linewidth}{.8\linewidth}{../../Motion/08-06-02_seminaire_ulm/figures/barberpole.mp4}}%
 277 %
 278 
 279 \frame{%
 280 \includegraphics[width=.6\linewidth]{bp.pdf}\\%
 281 \uncover<2>{\includegraphics<2>[width=.6\linewidth]{plaid.pdf}}%
 282 }
 283 %%
 284 %\begin{frame}
 285 %\includegraphics<+>[width=.6\linewidth]{model_rog.pdf}%
 286 %\includegraphics<+>[width=.6\linewidth]{model.pdf}%
 287 %\end{frame}%
 288 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 289 \begin{frame}
 290 \frametitle{\insertsection}%
 291 %\begin{columns}%[t]%
 292 %\begin{column}{7.5cm}%
 293 	\includegraphics<1>[width=.9\linewidth]{model_navier.png}%
 294 	\includegraphics<2>[width=.9\linewidth]{model_navier_markov.png}%
 295 %\end{column}%
 296 %\begin{column}{4.5cm}%
 297 %\begin{center}%
 298 %	\includegraphics[width=\linewidth]{model.pdf}%
 299 %\end{center}%
 300 %\end{column}%
 301 %\end{columns}%
 302 \end{frame}%
 303 
 304 
 305 \begin{frame}\frametitle{\insertsection}%
 306 \only<1>{%
 307 \begin{columns}%
 308 \begin{column}{.5\textwidth}%
 309 \begin{center}%
 310 \includemovie[%
 311 controls,loop,repeat%
 312 ]{.95\columnwidth}{.95\columnwidth}{../../Motion/particles/figures/virtualdot_noparticles.mpg}%\\%
 313 \end{center}%\input
 314 \end{column}%
 315 \begin{column}{.5\textwidth}%
 316 \begin{center}%
 317 \includemovie[%
 318 controls,loop,repeat%
 319 ]{.95\columnwidth}{.95\columnwidth}{../../Motion/particles/figures/virtualdot_particles.mpg}%
 320 \end{center}%
 321 \end{column}%
 322 \end{columns}%
 323 }%
 324 \only<2>{%
 325 \begin{columns}%
 326 \begin{column}{.5\textwidth}%
 327 \begin{center}%
 328 \includegraphics[width=.95\columnwidth]{../../Motion/particles/figures/virtualdot_noparticles.png}\\%
 329 %Without%
 330 \end{center}%
 331 \end{column}%
 332 \begin{column}{.5\textwidth}%
 333 \begin{center}%
 334 \includegraphics[width=.95\columnwidth]{../../Motion/particles/figures/virtualdot_particles.png}\\%
 335 %With Navier-Stokes%
 336 \end{center}%
 337 \end{column}%
 338 \end{columns}%
 339 }%
 340 \end{frame}%
 341 
 342 
 343 %%%: dynamical particles
 344 \begin{frame}
 345 \frametitle{\insertsection}%
 346 %\begin{columns}%
 347 %	\begin{column}[c]{.66\textwidth}%
 348 %		\includegraphics\includegraphics[width=\linewidth]{model.pdf}%
 349 %	\end{column}%
 350 %	\begin{column}[c]{.28\textwidth}%
 351 %		\includegraphics[width=\linewidth]{Spontaneous_particles}%
 352 %	\end{column}%
 353 %\end{columns}%
 354 %\begin{frame} 
 355 \begin{center}
 356 \begin{tabular}{ccccc}
 357 input & early & motion & late & OFR \\
 358 \includegraphics[width=.14\columnwidth]{dot_steps_init}&%
 359 \includegraphics[width=.14\columnwidth]{dot_steps_readout_init}&%
 360 %\includegraphics[width=.14\columnwidth]{dot_steps_spatial_field}&%
 361 \uncover<2->{\includegraphics[width=.14\columnwidth]{dot_steps_particles}&%
 362 \includegraphics[width=.14\columnwidth]{dot_steps_readout}&}%
 363 \uncover<3->{\includegraphics[width=.14\columnwidth]{dot_steps_ofr}}%
 364 \end{tabular}%
 365 \end{center}%
 366 
 367 \uncover<4->{\begin{center}
 368 \includegraphics[width=.15\columnwidth]{dot-blur0_particles}%
 369 \includegraphics[width=.15\columnwidth]{dot-blur1_particles}%
 370 \includegraphics[width=.15\columnwidth]{dot-blur2_particles}%
 371 \includegraphics[width=.15\columnwidth]{dot-blur3_particles}%
 372 \includegraphics[width=.15\columnwidth]{dot-blur4_particles}%
 373 \includegraphics[width=.15\columnwidth]{dot-blur5_particles}%
 374 \end{center}}
 375 \end{frame}%
 376 
 377 
 378 
 379 \begin{frame}%
 380 \frametitle{\insertsection}%
 381 \begin{columns}%
 382 \begin{column}{.5\textwidth}%
 383 \begin{center}%
 384 	\includemovie[%
 385 	autoplay,controls,loop,repeat%
 386 	]{.95\columnwidth}{.95\columnwidth}{../../Motion/particles/figures/trans_image.mpg}%
 387 \end{center}%\input
 388 \end{column}%
 389 \begin{column}{.5\textwidth}%
 390 \begin{center}%
 391 	\includemovie[%
 392 	autoplay,controls,loop,repeat%
 393 	]{.95\columnwidth}{.95\columnwidth}{../../Motion/particles/figures/trans_particles.mpg}%
 394 \end{center}%
 395 \end{column}%
 396 \end{columns}%
 397 \end{frame}%
 398 
 399 \begin{frame}\frametitle{\insertsection}%
 400 \begin{columns}%
 401 \begin{column}{.5\textwidth}%
 402 \begin{center}%
 403 \includemovie[%
 404 autoplay,controls,loop,repeat%
 405 ]{.95\columnwidth}{.95\columnwidth}{../../Motion/particles/figures/line_image.mpg}%
 406 \end{center}%\input
 407 \end{column}%
 408 \begin{column}{.5\textwidth}%
 409 \begin{center}%
 410 \includemovie[%
 411 autoplay,controls,loop,repeat%
 412 ]{.95\columnwidth}{.95\columnwidth}{../../Motion/09-02-28_cosyne/figures/line_particles.mpg}%
 413 \end{center}%
 414 \end{column}%
 415 \end{columns}%
 416 \end{frame}%
 417 
 418 
 419 \begin{frame}%
 420 \frametitle{\insertsection}%
 421 \begin{tabular}{ccccc}%
 422 input & early  & motion & late & OFR \\
 423 \includegraphics[width=.14\columnwidth]{trans_steps_init}&%
 424 \includegraphics[width=.14\columnwidth]{trans_steps_readout_init}&%
 425 %\includegraphics[width=.14\columnwidth]{trans_steps_spatial_field}&%
 426 \includegraphics[width=.14\columnwidth]{trans_steps_particles}&%
 427 \includegraphics[width=.14\columnwidth]{trans_steps_readout}&%
 428 \includegraphics[width=.14\columnwidth]{trans_steps_ofr}\\%
 429 &&&&\\%
 430 \uncover<2->{\includegraphics[width=.14\columnwidth]{line_steps_init}&%
 431 \includegraphics[width=.14\columnwidth]{line_steps_readout_init}&%
 432 %\includegraphics[width=.14\columnwidth]{line_steps_spatial_field}&%
 433 \includegraphics[width=.14\columnwidth]{line_steps_particles}&%
 434 \includegraphics[width=.14\columnwidth]{line_steps_readout}&%
 435 \includegraphics[width=.14\columnwidth]{line_steps_ofr}\\}%
 436 &&&&\\%
 437 \uncover<3->{\includegraphics[width=.14\columnwidth]{plaid_steps_init}&%
 438 \includegraphics[width=.14\columnwidth]{plaid_steps_readout_init}&%
 439 %\includegraphics[width=.14\columnwidth]{plaid_steps_spatial_field}&%
 440 \includegraphics[width=.14\columnwidth]{plaid_steps_particles}&%
 441 \includegraphics[width=.14\columnwidth]{plaid_steps_readout}&%
 442 \includegraphics[width=.14\columnwidth]{plaid_steps_ofr}\\}%
 443 &&&&\\%
 444 \uncover<4->{\includegraphics[width=.14\columnwidth]{grating_steps_init}&%
 445 \includegraphics[width=.14\columnwidth]{grating_steps_readout_init}&%
 446 %\includegraphics[width=.14\columnwidth]{grating_steps_spatial_field}&%
 447 \includegraphics[width=.14\columnwidth]{grating_steps_particles}&%
 448 \includegraphics[width=.14\columnwidth]{grating_steps_readout}&%
 449 \includegraphics[width=.14\columnwidth]{grating_steps_ofr}}%
 450 \end{tabular}%
 451 \end{frame}%
 452 
 453 
 454 
 455 
 456 
 457 \begin{frame}%
 458 \frametitle{\insertsection}%
 459 \begin{tabular}{ccc}%
 460 latency & \uncover<2->{sharpening} & \uncover<3->{surround} \\
 461  effect & \uncover<2->{of CRF} & \uncover<3->{suppression} \\
 462 \includegraphics[width=.21\columnwidth]{dot-latency}&%
 463 \uncover<2->{\includegraphics[width=.21\columnwidth]{CRF_ofr}}&%
 464 \uncover<3->{\includegraphics[width=.21\columnwidth]{surround-sup}}%
 465 \end{tabular}%
 466 \end{frame}%
 467 %-------------------------------------------------------------------------------------------%
 468 %\frame{\includegraphics[width=.99\linewidth]{summary.png}}%
 469 %
 470 

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