初学小白,注释的代码比较详细
import numpy as np
import scipy as sp
import scipy.linalg as sl
def ransac(data, model, n, k, t, d, debug = False, return_all = False):
"""
参考:http://scipy.github.io/old-wiki/pages/Cookbook/RANSAC
伪代码:http://en.wikipedia.org/w/index.php?title=RANSAC&oldid=116358182
输入:
data - 样本点
model - 假设模型:事先自己确定
n - 生成模型所需的最少样本点
k - 最大迭代次数
t - 阈值:作为判断点满足模型的条件
d - 拟合较好时,需要的样本点最少的个数,当做阈值看待
输出:
bestfit - 最优拟合解（返回nil,如果未找到）
iterations = 0
bestfit = nil #后面更新
besterr = something really large #后期更新besterr = thiserr
while iterations < k
{
maybeinliers = 从样本中随机选取n个,不一定全是局内点,甚至全部为局外点
maybemodel = n个maybeinliers 拟合出来的可能符合要求的模型
alsoinliers = emptyset #满足误差要求的样本点,开始置空
for (每一个不是maybeinliers的样本点)
{
if 满足maybemodel即error < t
将点加入alsoinliers
}
if (alsoinliers样本点数目 > d)
{
%有了较好的模型,测试模型符合度
bettermodel = 利用所有的maybeinliers 和 alsoinliers 重新生成更好的模型
thiserr = 所有的maybeinliers 和 alsoinliers 样本点的误差度量
if thiserr < besterr
{
bestfit = bettermodel
besterr = thiserr
}
}
iterations++
}
return bestfit
"""
iterations = 0
bestfit = None
besterr = np.inf #设置默认值
best_inlier_idxs = None
while iterations < k:
maybe_idxs, test_idxs = random_partition(n, data.shape[0])
maybe_inliers = data[maybe_idxs, :] #获取size(maybe_idxs)行数据(Xi,Yi)
test_points = data[test_idxs] #若干行(Xi,Yi)数据点
maybemodel = model.fit(maybe_inliers) #拟合模型
test_err = model.get_error(test_points, maybemodel) #计算误差:平方和最小
also_idxs = test_idxs[test_err < t]
also_inliers = 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(also_inliers)) )
if len(also_inliers > d):
betterdata = np.concatenate( (maybe_inliers, also_inliers) ) #样本连接
bettermodel = model.fit(betterdata)
better_errs = model.get_error(betterdata, bettermodel)
thiserr = np.mean(better_errs) #平均误差作为新的误差
if thiserr < besterr:
bestfit = bettermodel
besterr = thiserr
best_inlier_idxs = np.concatenate( (maybe_idxs, also_idxs) ) #更新局内点,将新点加入
iterations += 1
if bestfit is None:
raise ValueError("did't 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 the other len(data) - n rows"""
all_idxs = np.arange(n_data) #获取n_data下标索引
np.random.shuffle(all_idxs) #打乱下标索引
idxs1 = all_idxs[:n]
idxs2 = all_idxs[n:]
return idxs1, idxs2
class LinearLeastSquareModel:
#最小二乘求线性解,用于RANSAC的输入模型
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 = np.vstack( [data[:,i] for i in self.input_columns] ).T #第一列Xi-->行Xi
B = np.vstack( [data[:,i] for i in self.output_columns] ).T #第二列Yi-->行Yi
x, resids, rank, s = sl.lstsq(A, B) #residues:残差和
return x #返回最小平方和向量
def get_error(self, data, model):
A = np.vstack( [data[:,i] for i in self.input_columns] ).T #第一列Xi-->行Xi
B = np.vstack( [data[:,i] for i in self.output_columns] ).T #第二列Yi-->行Yi
B_fit = sp.dot(A, model) #计算的y值,B_fit = model.k*A + model.b
err_per_point = np.sum( (B - B_fit) ** 2, axis = 1 ) #sum squared error per row
return err_per_point
def test():
#生成理想数据
n_samples = 500 #样本个数
n_inputs = 1 #输入变量个数
n_outputs = 1 #输出变量个数
A_exact = 20 * np.random.random((n_samples, n_inputs))#随机生成0-20之间的500个数据:行向量
perfect_fit = 60 * np.random.normal( size = (n_inputs, n_outputs) ) #随机线性度即随机生成一个斜率
B_exact = sp.dot(A_exact, perfect_fit) # y = x * k
#加入高斯噪声,最小二乘能很好的处理
A_noisy = A_exact + np.random.normal( size = A_exact.shape ) #500 * 1行向量,代表Xi
B_noisy = B_exact + np.random.normal( size = B_exact.shape ) #500 * 1行向量,代表Yi
if 1:
#添加"局外点"
n_outliers = 100
all_idxs = np.arange( A_noisy.shape[0] ) #获取索引0-499
np.random.shuffle(all_idxs) #将all_idxs打乱
outlier_idxs = all_idxs[:n_outliers] #100个0-500的随机局外点
A_noisy[outlier_idxs] = 20 * np.random.random( (n_outliers, n_inputs) ) #加入噪声和局外点的Xi
B_noisy[outlier_idxs] = 50 * np.random.normal( size = (n_outliers, n_outputs)) #加入噪声和局外点的Yi
#setup model
all_data = np.hstack( (A_noisy, B_noisy) ) #形式([Xi,Yi]....) shape:(500,2)500行2列
input_columns = range(n_inputs) #数组的第一列x:0
output_columns = [n_inputs + i for i in range(n_outputs)] #数组最后一列y:1
debug = False
model = LinearLeastSquareModel(input_columns, output_columns, debug = debug) #类的实例化:用最小二乘生成已知模型
linear_fit,resids,rank,s = sp.linalg.lstsq(all_data[:,input_columns], all_data[:,output_columns])
#run RANSAC 算法
ransac_fit, ransac_data = ransac(all_data, model, 50, 1000, 7e3, 300, debug = debug, return_all = True)
if 1:
import pylab
sort_idxs = np.argsort(A_exact[:,0])
A_col0_sorted = A_exact[sort_idxs] #秩为2的数组
if 1:
pylab.plot( A_noisy[:,0], B_noisy[:,0], 'k.', label = 'data' ) #散点图
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],
np.dot(A_col0_sorted,ransac_fit)[:,0],
label='RANSAC fit' )
pylab.plot( A_col0_sorted[:,0],
np.dot(A_col0_sorted,perfect_fit)[:,0],
label='exact system' )
pylab.plot( A_col0_sorted[:,0],
np.dot(A_col0_sorted,linear_fit)[:,0],
label='linear fit' )
pylab.legend()
pylab.show()
if __name__ == "__main__":
test()
