ransac.py

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.
## Copyright (c) 2013, Nico Weber
## Jun 2013: Changed to true classical ransac and optional msac.

## Redistribution and use in source and binary forms, with or without
## modification, are permitted provided that the following conditions are
## met:

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##       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
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##       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
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def ransac(data,model,n,k,t,d,debug=False,return_all=False,msac=True):
    """fit model parameters to data using the RANSAC algorithm
    -    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
    """
    iterations = 0
    bestfit = None
    bestcost = numpy.infty
    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
        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 'number of inliers', len(also_idxs)
        if len(also_idxs) > d:
            thiscost = (data.shape[0] - n - len(also_idxs)) * t
            if msac:
                thiscost += numpy.sum(test_err[test_err < t])
            if thiscost < bestcost:
                if debug:
                    print '    new best fit',thiscost,bestcost
                bestcost = thiscost
                best_inlier_idxs = numpy.concatenate((maybe_idxs, also_idxs))
        iterations+=1

    if best_inlier_idxs is None:
        raise ValueError("did not meet fit acceptance criteria")
    bestfit = model.fit(data[best_inlier_idxs,:])

    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,
                                     2, 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()