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POScipy leastsq() function overhead
 

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    <p>I am working on an image analysis program and I have narrowed down my bottleneck to attempts to fit a 2D gaussian to a small window (20x20) pixels many times. 90% of the execution time is spent in this code.</p> <p>I am using the code given in the scipy cookbook for this problem:</p> <pre><code> def gaussian(height, center_x, center_y, width_x, width_y): """Returns a gaussian function with the given parameters""" width_x = float(width_x) width_y = float(width_y) return lambda x,y: height*exp( -(((center_x-x)/width_x)**2+((center_y-y)/width_y)**2)/2) def moments(data): """Returns (height, x, y, width_x, width_y) the gaussian parameters of a 2D distribution by calculating its moments """ total = data.sum() X, Y = indices(data.shape) x = (X*data).sum()/total y = (Y*data).sum()/total col = data[:, int(y)] width_x = sqrt(abs((arange(col.size)-y)**2*col).sum()/col.sum()) row = data[int(x), :] width_y = sqrt(abs((arange(row.size)-x)**2*row).sum()/row.sum()) height = data.max() return height, x, y, width_x, width_y def fitgaussian(data): """Returns (height, x, y, width_x, width_y) the gaussian parameters of a 2D distribution found by a fit""" params = moments(data) errorfunction = lambda p: ravel(gaussian(*p)(*indices(data.shape)) - data) p, success = optimize.leastsq(errorfunction, params, maxfev=50, ftol=1.49012e-05) return p </code></pre> <p>I was able to cut the execution time in half by combining the errorfunction() and gaussian() functions so every time leastsq() calls errorfunction() there is one function call instead of two. </p> <p>This leads me to believe that most of the remaining execution time is spent tied up in function call overhead as the leastsq() algorithm calls errorfunction().</p> <p>Is there any way to reduce this function call overhead? I am at a loss since leastsq() takes a function as an input. </p> <p>I apologize in advance if my description is confusing, I am a mechanical engineer by training and I'm learning Python as I go. Please let me know if there is any other information that would be helpful. </p>
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    1. COif what you fit is really a gaussian, do you actually need a call to `leastsq`--- can't you just calculate the moments, which you already do.
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    2. COI can't believe I hadn't checked this, thank you for the suggestion! A quick look suggests that most of the time the calculated moments and final fitted gaussian differ by less then 10%. I'm going to try just using those in my algorithm to see how well it works and I'll check back in.
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    3. COWell, I'm back. Seems that using the moments is good enough. Thanks Zhenya!
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