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ransac.py
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ransac.py
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import numpy
import scipy # use numpy if scipy unavailable
import scipy.linalg # use numpy if scipy unavailable
## Copyright (c) 2004-2007, Andrew D. Straw. All rights reserved.
## Redistribution and use in source and binary forms, with or without
## modification, are permitted provided that the following conditions are
## met:
## * Redistributions of source code must retain the above copyright
## notice, this list of conditions and the following disclaimer.
## * Redistributions in binary form must reproduce the above
## copyright notice, this list of conditions and the following
## disclaimer in the documentation and/or other materials provided
## with the distribution.
## * Neither the name of the Andrew D. Straw nor the names of its
## contributors may be used to endorse or promote products derived
## from this software without specific prior written permission.
## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
## "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
## LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
## A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
## OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
## SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
## LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
## DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
## THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
## (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
def ransac(data,model,n,k,t,d,debug=False,return_all=False):
"""fit model parameters to data using the RANSAC algorithm
This implementation written from pseudocode found at
http://en.wikipedia.org/w/index.php?title=RANSAC&oldid=116358182
{{{
Given:
data - a set of observed data points
model - a model that can be fitted to data points
n - the minimum number of data values required to fit the model
k - the maximum number of iterations allowed in the algorithm
t - a threshold value for determining when a data point fits a model
d - the number of close data values required to assert that a model fits well to data
Return:
bestfit - model parameters which best fit the data (or nil if no good model is found)
iterations = 0
bestfit = nil
besterr = something really large
while iterations < k {
maybeinliers = n randomly selected values from data
maybemodel = model parameters fitted to maybeinliers
alsoinliers = empty set
for every point in data not in maybeinliers {
if point fits maybemodel with an error smaller than t
add point to alsoinliers
}
if the number of elements in alsoinliers is > d {
% this implies that we may have found a good model
% now test how good it is
bettermodel = model parameters fitted to all points in maybeinliers and alsoinliers
thiserr = a measure of how well model fits these points
if thiserr < besterr {
bestfit = bettermodel
besterr = thiserr
}
}
increment iterations
}
return bestfit
}}}
"""
iterations = 0
bestfit = None
besterr = numpy.inf
best_inlier_idxs = None
while iterations < k:
maybe_idxs, test_idxs = random_partition(n,data.shape[0])
maybeinliers = data[maybe_idxs,:]
test_points = data[test_idxs]
maybemodel = model.fit(maybeinliers)
test_err = model.get_error( test_points, maybemodel)
also_idxs = test_idxs[test_err < t] # select indices of rows with accepted points
alsoinliers = data[also_idxs,:]
if debug:
print 'test_err.min()',test_err.min()
print 'test_err.max()',test_err.max()
print 'numpy.mean(test_err)',numpy.mean(test_err)
print 'iteration %d:len(alsoinliers) = %d'%(
iterations,len(alsoinliers))
if len(alsoinliers) > d:
betterdata = numpy.concatenate( (maybeinliers, alsoinliers) )
bettermodel = model.fit(betterdata)
better_errs = model.get_error( betterdata, bettermodel)
thiserr = numpy.mean( better_errs )
if thiserr < besterr:
bestfit = bettermodel
besterr = thiserr
best_inlier_idxs = numpy.concatenate( (maybe_idxs, also_idxs) )
iterations+=1
if bestfit is None:
raise ValueError("did not meet fit acceptance criteria")
if return_all:
return bestfit, {'inliers':best_inlier_idxs}
else:
return bestfit
def random_partition(n,n_data):
"""return n random rows of data (and also the other len(data)-n rows)"""
all_idxs = numpy.arange( n_data )
numpy.random.shuffle(all_idxs)
idxs1 = all_idxs[:n]
idxs2 = all_idxs[n:]
return idxs1, idxs2
class LinearLeastSquaresModel:
"""linear system solved using linear least squares
This class serves as an example that fulfills the model interface
needed by the ransac() function.
"""
def __init__(self,input_columns,output_columns,debug=False):
self.input_columns = input_columns
self.output_columns = output_columns
self.debug = debug
def fit(self, data):
A = numpy.vstack([data[:,i] for i in self.input_columns]).T
B = numpy.vstack([data[:,i] for i in self.output_columns]).T
x,resids,rank,s = scipy.linalg.lstsq(A,B)
return x
def get_error( self, data, model):
A = numpy.vstack([data[:,i] for i in self.input_columns]).T
B = numpy.vstack([data[:,i] for i in self.output_columns]).T
B_fit = scipy.dot(A,model)
err_per_point = numpy.sum((B-B_fit)**2,axis=1) # sum squared error per row
return err_per_point
def test():
# generate perfect input data
n_samples = 500
n_inputs = 1
n_outputs = 1
A_exact = 20*numpy.random.random((n_samples,n_inputs) )
perfect_fit = 60*numpy.random.normal(size=(n_inputs,n_outputs) ) # the model
B_exact = scipy.dot(A_exact,perfect_fit)
assert B_exact.shape == (n_samples,n_outputs)
# add a little gaussian noise (linear least squares alone should handle this well)
A_noisy = A_exact + numpy.random.normal(size=A_exact.shape )
B_noisy = B_exact + numpy.random.normal(size=B_exact.shape )
if 1:
# add some outliers
n_outliers = 100
all_idxs = numpy.arange( A_noisy.shape[0] )
numpy.random.shuffle(all_idxs)
outlier_idxs = all_idxs[:n_outliers]
non_outlier_idxs = all_idxs[n_outliers:]
A_noisy[outlier_idxs] = 20*numpy.random.random((n_outliers,n_inputs) )
B_noisy[outlier_idxs] = 50*numpy.random.normal(size=(n_outliers,n_outputs) )
# setup model
all_data = numpy.hstack( (A_noisy,B_noisy) )
input_columns = range(n_inputs) # the first columns of the array
output_columns = [n_inputs+i for i in range(n_outputs)] # the last columns of the array
debug = False
model = LinearLeastSquaresModel(input_columns,output_columns,debug=debug)
linear_fit,resids,rank,s = scipy.linalg.lstsq(all_data[:,input_columns],
all_data[:,output_columns])
# run RANSAC algorithm
ransac_fit, ransac_data = ransac(all_data,model,
50, 1000, 7e3, 300, # misc. parameters
debug=debug,return_all=True)
if 1:
import pylab
sort_idxs = numpy.argsort(A_exact[:,0])
A_col0_sorted = A_exact[sort_idxs] # maintain as rank-2 array
if 1:
pylab.plot( A_noisy[:,0], B_noisy[:,0], 'k.', label='data' )
pylab.plot( A_noisy[ransac_data['inliers'],0], B_noisy[ransac_data['inliers'],0], 'bx', label='RANSAC data' )
else:
pylab.plot( A_noisy[non_outlier_idxs,0], B_noisy[non_outlier_idxs,0], 'k.', label='noisy data' )
pylab.plot( A_noisy[outlier_idxs,0], B_noisy[outlier_idxs,0], 'r.', label='outlier data' )
pylab.plot( A_col0_sorted[:,0],
numpy.dot(A_col0_sorted,ransac_fit)[:,0],
label='RANSAC fit' )
pylab.plot( A_col0_sorted[:,0],
numpy.dot(A_col0_sorted,perfect_fit)[:,0],
label='exact system' )
pylab.plot( A_col0_sorted[:,0],
numpy.dot(A_col0_sorted,linear_fit)[:,0],
label='linear fit' )
pylab.legend()
pylab.show()
if __name__=='__main__':
test()