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March 28, 2022 07:43
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fit plane
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import numpy as np | |
import scipy.optimize | |
def fitPLaneLTSQ(XYZ): | |
# Fits a plane to a point cloud, | |
# Where Z = aX + bY + c ----Eqn #1 | |
# Rearanging Eqn1: aX + bY -Z +c =0 | |
# Gives normal (a,b,-1) | |
# Normal = (a,b,-1) | |
[rows,cols] = XYZ.shape | |
G = np.ones((rows,3)) | |
G[:,0] = XYZ[:,0] #X | |
G[:,1] = XYZ[:,1] #Y | |
Z = XYZ[:,2] | |
(a,b,c),resid,rank,s = np.linalg.lstsq(G,Z) | |
normal = (a,b,-1) | |
nn = np.linalg.norm(normal) | |
normal = normal / nn | |
return normal | |
def fitPlaneSVD(XYZ): | |
[rows,cols] = XYZ.shape | |
# Set up constraint equations of the form AB = 0, | |
# where B is a column vector of the plane coefficients | |
# in the form b(1)*X + b(2)*Y +b(3)*Z + b(4) = 0. | |
p = (np.ones((rows,1))) | |
AB = np.hstack([XYZ,p]) | |
[u, d, v] = np.linalg.svd(AB,0) | |
B = v[3,:]; # Solution is last column of v. | |
nn = np.linalg.norm(B[0:3]) | |
B = B / nn | |
return B[0:3] | |
def fitPlaneEigen(XYZ): | |
# Works, in this case but don't understand! | |
average=sum(XYZ)/XYZ.shape[0] | |
covariant=np.cov(XYZ - average) | |
eigenvalues,eigenvectors = np.linalg.eig(covariant) | |
want_max = eigenvectors[:,eigenvalues.argmax()] | |
(c,a,b) = want_max[3:6] # Do not understand! Why 3:6? Why (c,a,b)? | |
normal = np.array([a,b,c]) | |
nn = np.linalg.norm(normal) | |
return normal / nn | |
def fitPlaneSolve(XYZ): | |
X = XYZ[:,0] | |
Y = XYZ[:,1] | |
Z = XYZ[:,2] | |
npts = len(X) | |
A = np.array([ [sum(X*X), sum(X*Y), sum(X)], | |
[sum(X*Y), sum(Y*Y), sum(Y)], | |
[sum(X), sum(Y), npts] ]) | |
B = np.array([ [sum(X*Z), sum(Y*Z), sum(Z)] ]) | |
normal = np.linalg.solve(A,B.T) | |
nn = np.linalg.norm(normal) | |
normal = normal / nn | |
return normal.ravel() | |
def fitPlaneOptimize(XYZ): | |
def residiuals(parameter,f,x,y): | |
return [(f[i] - model(parameter,x[i],y[i])) for i in range(len(f))] | |
def model(parameter, x, y): | |
a, b, c = parameter | |
return a*x + b*y + c | |
X = XYZ[:,0] | |
Y = XYZ[:,1] | |
Z = XYZ[:,2] | |
p0 = [1., 1.,1.] # initial guess | |
result = scipy.optimize.leastsq(residiuals, p0, args=(Z,X,Y))[0] | |
normal = result[0:3] | |
nn = np.linalg.norm(normal) | |
normal = normal / nn | |
return normal | |
if __name__=="__main__": | |
XYZ = np.array([ | |
[0,0,1], | |
[0,1,2], | |
[0,2,3], | |
[1,0,1], | |
[1,1,2], | |
[1,2,3], | |
[2,0,1], | |
[2,1,2], | |
[2,2,3] | |
]) | |
print "Solve: ", fitPlaneSolve(XYZ) | |
print "Optim: ",fitPlaneOptimize(XYZ) | |
print "SVD: ",fitPlaneSVD(XYZ) | |
print "LTSQ: ",fitPLaneLTSQ(XYZ) | |
print "Eigen: ",fitPlaneEigen(XYZ) |
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