python ransac拟合曲线,机器学习：RANSAC算法做直线拟合

# -*- coding: utf-8 -*-import numpy

import scipy # use numpy if scipy unavailableimport scipy.linalg # use numpy if scipy unavailableimport pylab

## Copyright (c) 2004-2007, Andrew D. Straw. All rights reserved.

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 # 可观测数据点集

model - a model that can be fitted to data points #

n - the minimum number of data values required to fit the model # 拟合模型所需的最小数据点数目

k - the maximum number of iterations allowed in the algorithm # 最大允许迭代次数

t - a threshold value for determining when a data point fits a model #确认某一数据点是否符合模型的阈值

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 = 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) ) # x坐标 perfect_fit = 60*numpy.random.normal(size=(n_inputs,n_outputs) ) # the model(斜率) B_exact = scipy.dot(A_exact,perfect_fit) # y坐标 assert B_exact.shape == (n_samples,n_outputs) #验证y坐标数组的大小 #pylab.plot( A_exact, B_exact, 'b.', label='data' ) #pylab.show()

# add a little gaussian noise (linear least squares alone should handle this well) A_noisy = A_exact + numpy.random.normal(size=A_exact.shape ) # x坐标添加高斯噪声 B_noisy = B_exact + numpy.random.normal(size=B_exact.shape ) # y坐标.... #pylab.plot( A_noisy, B_noisy, 'b.', label='data' )

if 1:

# add some outliers n_outliers = 100 # 500个数据点有100个是putliers all_idxs = numpy.arange( A_noisy.shape[0] )

numpy.random.shuffle(all_idxs) # 索引随机排列 outlier_idxs = all_idxs[:n_outliers] # 选取all_idxs前100个做outlier_idxs non_outlier_idxs = all_idxs[n_outliers:] # 后面的不是outlier_idxs A_noisy[outlier_idxs] = 20*numpy.random.random((n_outliers,n_inputs) ) # 外点的横坐标 B_noisy[outlier_idxs] = 50*numpy.random.normal(size=(n_outliers,n_outputs) ) # 外点的纵坐标 #pylab.plot( A_noisy, B_noisy, 'b.', label='data' ) #pylab.show()

# setup model

all_data = numpy.hstack( (A_noisy,B_noisy) ) # 组成坐标对 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]) # 对A_exact排序， sort_idxs为排序索引 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()