From: <jd...@us...> - 2007-10-26 19:48:15
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Revision: 4024 http://matplotlib.svn.sourceforge.net/matplotlib/?rev=4024&view=rev Author: jdh2358 Date: 2007-10-26 12:48:03 -0700 (Fri, 26 Oct 2007) Log Message: ----------- updates to workbook Modified Paths: -------------- trunk/py4science/doc/linkfest trunk/py4science/examples/convolution_demo.py trunk/py4science/examples/fft_imdenoise.py trunk/py4science/examples/stock_records.py trunk/py4science/workbook/main.tex Added Paths: ----------- trunk/py4science/workbook/fft_imdenoise.tex trunk/py4science/workbook/fig/fft_imdenoise.eps trunk/py4science/workbook/fig/fft_imdenoise.png Modified: trunk/py4science/doc/linkfest =================================================================== --- trunk/py4science/doc/linkfest 2007-10-26 19:46:12 UTC (rev 4023) +++ trunk/py4science/doc/linkfest 2007-10-26 19:48:03 UTC (rev 4024) @@ -62,9 +62,9 @@ ipython: svn co http://ipython.scipy.org/svn/ipython/ipython/trunk ipython - matplotlib: svn co https://svn.sourceforge.net/svnroot/matplotlib/trunk/matplotlib matplotlib + matplotlib: svn co https://matplotlib.svn.sourceforge.net/svnroot/matplotlib/trunk/matplotlib - py4science: svn co https://svn.sourceforge.net/svnroot/matplotlib/trunk/py4science py4science + py4science: svn co https://matplotlib.svn.sourceforge.net/svnroot/matplotlib/trunk/py4science Important commands: Modified: trunk/py4science/examples/convolution_demo.py =================================================================== --- trunk/py4science/examples/convolution_demo.py 2007-10-26 19:46:12 UTC (rev 4023) +++ trunk/py4science/examples/convolution_demo.py 2007-10-26 19:48:03 UTC (rev 4024) @@ -71,4 +71,6 @@ ax2.plot(t, yi, label='fft') ax2.legend(loc='best') +fig.savefig('convolution_demo.png', dpi=150) +fig.savefig('convolution_demo.eps') show() Modified: trunk/py4science/examples/fft_imdenoise.py =================================================================== --- trunk/py4science/examples/fft_imdenoise.py 2007-10-26 19:46:12 UTC (rev 4023) +++ trunk/py4science/examples/fft_imdenoise.py 2007-10-26 19:48:03 UTC (rev 4024) @@ -73,4 +73,6 @@ P.title('Reconstructed Image') P.imshow(im_new, P.cm.gray) +P.savefig('fft_imdenoise.png', dpi=150) +P.savefig('fft_imdenoise.eps') P.show() Modified: trunk/py4science/examples/stock_records.py =================================================================== --- trunk/py4science/examples/stock_records.py 2007-10-26 19:46:12 UTC (rev 4023) +++ trunk/py4science/examples/stock_records.py 2007-10-26 19:48:03 UTC (rev 4024) @@ -37,7 +37,7 @@ r.sort() return r -tickers = 'INTC', 'MSFT', 'YHOO', 'GOOG', 'GE', 'WMT', 'AAPL' +tickers = 'SPY', 'QQQQ', 'INTC', 'MSFT', 'YHOO', 'GOOG', 'GE', 'WMT', 'AAPL' # we want to compute returns since 2003, so define the start date startdate = datetime.datetime(2003,1,1) Added: trunk/py4science/workbook/fft_imdenoise.tex =================================================================== --- trunk/py4science/workbook/fft_imdenoise.tex (rev 0) +++ trunk/py4science/workbook/fft_imdenoise.tex 2007-10-26 19:48:03 UTC (rev 4024) @@ -0,0 +1,47 @@ +Convolution of an input with with a linear filter in the termporal or +spatial domain is equivalent to multiplication by the fourier +transforms of the input and the filter in the spectral domain. This +provides a conceptually simple way to think about filtering: transform +your signal into the frequency domain, dampen the frequencies you are +not interested in by multiplying the frequency spectrum by the desired +weights, and then inverse transform the multiplies spectrum back into +the original domain. In the example below, we will simply set the +weights of the frequencies we are uninterested in (the high frequency +noise) to zero rather than dampening them with a smoothly varying +function. Although this is not usually the best thing to do, since +sharp edges in one domain usually introduce artifacts in another (eg +high frequency ``ringing''), it is easy to do and sometimes provides +satisfactory results. + +The image in the upper left panel of Figure~\ref{fig:fft_imdenoise} is +a grayscale photo of the moon landing. There is a banded pattern of +high frequency noise polluting the image. In the upper right panel we +see the 2D spatial frequency spectrum. The FFT output in +\texttt{scipy} is packed with the lower freqeuencies starting in the +upper left, and proceeding to higher frequencies as one moves to the +center of the spectrum (this is the most efficient way numerically to +fill the output of the FFT algorithm). Because the input signal is +real, the output spectrum is complex and symmetrical: the +transformation values beyond the midpoint of the frequency spectrum +(the Nyquist frequency) correspond to the values for negative +frequencies and are simply the mirror image of the positive +frequencies below the Nyquist (this is true for the 1D, 2D and ND FFTs +in \texttt{numpy}). + +In this exercise we will compute the 2D spatial frequency spectra of +the luminance image, zero out the high frequency components, and +inverse transform back into the time domain. We can plot the input +and output images with the \texttt{pylab.imshow} function, but the +images must first be scaled to be withing the 0..1 luminance range. +For best results, it helps to \textit{amplify} the image by some scale +factor, and then \textit{clip} it to set all values greater than one +to one. This serves to enhance contrast among the darker elements of +the image, so it is not completely dominated by the brighter segments + +\lstinputlisting[label=code:fft_imdenoise_skel,caption={IGNORED}]{skel/fft_imdenoise_skel.py} + +\begin{figure} +\begin{centering}\includegraphics[width=3in]{fig/fft_imdenoise}\par\end{centering} + +\caption{\label{fig:fft_imdenoise}High freqeuency noise filtering of a 2D image in the Fourier domain. The upper panels show the original image (left) and spectral power (right) and the lower panels show the same data with the high frequency power set to zero. Although the input and output images are grayscale, you can provide colormaps to \texttt{pylab.imshow} to plot them in psudo-color} +\end{figure} Added: trunk/py4science/workbook/fig/fft_imdenoise.eps =================================================================== --- trunk/py4science/workbook/fig/fft_imdenoise.eps (rev 0) +++ trunk/py4science/workbook/fig/fft_imdenoise.eps 2007-10-26 19:48:03 UTC (rev 4024) @@ -0,0 +1,9710 @@ +%!PS-Adobe-3.0 EPSF-3.0 +%%Title: fft_imdenoise.eps +%%Creator: matplotlib version 0.90.1, http://matplotlib.sourceforge.net/ +%%CreationDate: Fri Oct 26 13:30:19 2007 +%%Orientation: portrait +%%BoundingBox: 11 173 600 618 +%%EndComments +%%BeginProlog +/mpldict 7 dict def +mpldict begin +/m { moveto } bind def +/l { lineto } bind def +/r { rlineto } bind def +/box { +m +1 index 0 r +0 exch r +neg 0 r +closepath +} bind def +/clipbox { +box +clip +newpath +} bind def +/ellipse { +newpath +matrix currentmatrix 7 1 roll +translate +scale +0 0 1 5 3 roll arc +setmatrix +closepath +} bind def +%!PS-Adobe-3.0 Resource-Font +%%Title: Bitstream Vera Sans +%%Copyright: Copyright (c) 2003 by Bitstream, Inc. 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