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From: Rein van den Boomgaard (UvA) <rein@sc...>  20040707 07:45:08

Dear All, as i'm new to this list let me first introduce myself before posting a question. I'm working in the field of image processing and computer vision for a long time now and i am a long time matlab user. Up to now i didn't like any of the matlab clones but it seems that numarray+matplotlib might be a winner here. I started using numarray+matplotlib by coding the Gaussian derivative convolutions. Calculating a derivative (by convolving with the derivative of the Gaussian function) will lead to an image(array) with both positive and negative values. Although imshow should deal with that (as far as i understand the code: beware i am a Python beginner) the display turns black for all derivatives (except for the 'zero order' derivative of course). What is going on? Is it me (probably) or is it imshow? Attached you find the code. Regards Rein van den Boomgaard University of Amsterdam The Netherlands # ========================================================== # Gaussian Derivatives # # Copyright (c) Rein van den Boomgaard # Vision Consultancy & Training # rein@... # # ========================================================== import types from numarray import * from numarray.nd_image import * def gD( image, scales, orders, nscales=4, mode='reflect' ): scales = _normalize_sequence(scales,image) orders = _normalize_sequence(orders,image) result = image.copy() ndims = len( image.shape ) for i in range(0,ndims): N = ceil(scales[i]*nscales) x = arange( N, N ) w = GaussianDerivativeFunction( x, scales[i], orders[i] ) result = convolve1d( result, w, i, mode = mode ) return( result ) def HermiteH( n, x ): """ Hermite Poynomial """ if n==0: return 0*x + 1 elif n==1: return 2*x else: return 2*x*HermiteH( n1, x )  2*(n1)*HermiteH(n2,x) def GaussianDerivativeFunction( x, scale, order ): scale = float(scale) g = 1.0 / ( scale * sqrt(2*pi) ) * exp(  x**2 / (2*scale**2) ) return (1.0 / (scale*sqrt(2.0)))**order * \ HermiteH( order, x / (scale * sqrt(2)) ) * g # the _normalize_sequence function is copied from numarray # because i cant import it...??? def _normalize_sequence(input, array): """If input is a scalar, create a sequence of length equal to the rank of array by duplicating the input. If input is a sequence, check if its length is equalt to the lenght of array. """ if isinstance(array, ArrayType): rank = len(array.shape) else: rank = 1 if (isinstance(input, (types.IntType, types.LongType, types.FloatType))): normalized = [input] * rank else: if isinstance(input, numarray.numarraycore.NumArray): normalized = list(input) else: normalized = input if len(normalized) != rank: error = "sequence argument must have length equal to input rank" raise RuntimeError, error return normalized if __name__ == "__main__": from matplotlib import use, interactive from matplotlib.matlab import * PLOT_1D_GAUSS = 1 PLOT_GAUSSIAN_DERIVATIVES = 1 PLOT_TIMING = 1 if PLOT_1D_GAUSS: # testing the Gaussiand Derivatives x=arange(5,5,.01) figure(1) clf() plot(x,GaussianDerivativeFunction(x,1,0)) plot(x,GaussianDerivativeFunction(x,1,1)) plot(x,GaussianDerivativeFunction(x,1,2)) plot(x,GaussianDerivativeFunction(x,1,3)) plot(x,GaussianDerivativeFunction(x,1,4)) xlabel(r'$x$') ylabel(r'$G_n(x)$') title('Gaussian Derivatives') if PLOT_GAUSSIAN_DERIVATIVES: scale = 9 def _gDplot(n,ox,oy): subplot(4,4,n) axis('off') imshow( gD(a,scale,(ox,oy)) ) a = zeros( (64,64) ) * 1.0 a[32,32] = 1.0 figure(2) axis('off') title('Gaussian Derivatives') _gDplot(1,0,0) title(r'$G$') _gDplot(5,1,0) title(r'$G_x$') _gDplot(6,0,1) title(r'$G_y$') _gDplot(9,2,0) title(r'$G_{xx}$') _gDplot(10,1,1) title(r'$G_{xy}$') _gDplot(11,0,2) title(r'$G_{yy}$') _gDplot(13,3,0) title(r'$G_{xxx}$') _gDplot(14,2,1) title(r'$G_{xxy}$') _gDplot(15,1,2) title(r'$G_{xyy}$') _gDplot(16,0,3) title(r'$G_{yyy}$') if PLOT_TIMING: from timeit import Timer niter = 5 def time_gD(scale): t = Timer( "b=gD(a,%d, 0)" % scale, "from __main__ import gD,a" ) timing = t.timeit(number=niter ) print( timing/niter ) return( timing/niter ) a = zeros( (256,256) ) * 1.0 a[128,128] = 1.0 figure(3) scales = array([1,3,5,7,9,11,15,19, 25,31,41,51]) print(type(scales)) plot( scales, map( time_gD, scales ), 'x' ) xlabel('Scale (px)') ylabel('Time (s)') title('Gaussian Convolution Timings') 
From: John Hunter <jdhunter@ac...>  20040707 12:37:18

>>>>> "Rein" == Rein van den Boomgaard (UvA) <rein@...> writes: Rein> Dear All, as i'm new to this list let me first introduce Rein> myself before posting a question. Rein> I'm working in the field of image processing and computer Rein> vision for a long time now and i am a long time matlab Rein> user. Up to now i didn't like any of the matlab clones but Rein> it seems that numarray+matplotlib might be a winner here. I've worked some with octave in the past and found it unsatisfying (though a very impressive one man feat!), in part because I wasn't happy with gnuplot, which it used for graphics at the time (and perhaps still does), and in part because it really aimed at being a matlab clone but very few of my mfiles ran w/o alteration. matplotlib tries to solve the first problem by producing better graphics than matlab and the second by not trying to be a drop in replacement for matlab. I'm curious about your experiences, what you tried, and what you found lacking. Rein> I started using numarray+matplotlib by coding the Gaussian Rein> derivative convolutions. Calculating a derivative (by Rein> convolving with the derivative of the Gaussian function) Rein> will lead to an image(array) with both positive and negative Rein> values. Although imshow should deal with that (as far as i Rein> understand the code: beware i am a Python beginner) the Rein> display turns black for all derivatives (except for the Rein> 'zero order' derivative of course). Rein> What is going on? Is it me (probably) or is it imshow? In matplotlib0.54.2, the images must be normalized to the unit interval before color mapping or plotting. For example, in examples/image_demo2.py, notice that I do A *= 1.0/max(A) Your images are black, I think, because you haven't normalized them. I've done a lot of work on matplotlib images since 0.54.2, with new fixes and features. Normalization is handled by default in the 0.60 release candidate. When I run your (very nice) example with my development version of matplotlib, it produces this image for figure 2 ( I added "show" at the end of your script, but it was otherwise unaltered) http://nitace.bsd.uchicago.edu:8080/files/share/fig2.png which looks right to me. I'm always interested in nice screenshots for the web site, so please consider donating this example! I've uploaded the 0.60d release candidate to http://nitace.bsd.uchicago.edu:8080/files/share/matplotlib0.60d.tar.gz Can you compile matplotlib yourself or are you using a binary distribution? If you can try the development version linked above, that would solve two problems: you'll get enhanced image support and I'll get a tester for my image changes. If you do so, see the updated help for the image related commands: imshow, figimage, clim, jet, gray and the new matplotlibrc parameters image.* In the figure 2 image from your script, I notice that there the titles overlap the images above. Here is how you can control this (requires matplotlib 0.60d) # pass in these keywor args to title. The y location is the y # text coordinate in axes coords (0,0 is lower left, 1,1 is # upper right). You can use **somedict in place of keyword # args in python offsets = {'y':1.0, 'fontsize':10} _gDplot(1,0,0) title(r'$G$', **offsets) _gDplot(5,1,0) title(r'$G_x$', **offsets) _gDplot(6,0,1) title(r'$G_y$', **offsets) _gDplot(9,2,0) title(r'$G_{xx}$', **offsets) _gDplot(10,1,1) title(r'$G_{xy}$', **offsets) _gDplot(11,0,2) title(r'$G_{yy}$', **offsets) _gDplot(13,3,0) title(r'$G_{xxx}$', **offsets) _gDplot(14,2,1) title(r'$G_{xxy}$', **offsets) _gDplot(15,1,2) title(r'$G_{xyy}$', **offsets) _gDplot(16,0,3) title(r'$G_{yyy}$', **offsets) Cheers, JDH 
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