Matlab calculate 3D similarity transformation. fitgeotrans for 3D -

Matlab calculate 3D similarity transformation. fitgeotrans for 3D -

how can calculate in matlab similarity transformation between 4 points in 3d? can calculate transform matrix from

t*x = xp,

but give me affine matrix due little errors in points coordinates. how can fit matrix similarity one? need fitgeotrans, in 3d

thanks

if interpreting question correctly, seek find coefficients in 3d transformation matrix best warp 1 point another. have set problem linear scheme , solve. recall warping 1 point in 3d simply:

a*s = t

s = (x,y,z) source point, t = (x',y',z') target point , a 3 x 3 transformation matrix formatted such that:

a = [a00 a01 a02] [a10 a11 a12] [a20 a21 a22]

writing out actual scheme of equations of a*s = t, get:

a00*x + a01*y + a02*z = x' a10*x + a11*y + a12*z = y' a20*x + a21*y + a22*z = z'

the coefficients in a need solve for. re-writing in matrix form, get:

[x y z 0 0 0 0 0 0] [a00] [x'] [0 0 0 x y z 0 0 0] * [a01] = [y'] [0 0 0 0 0 0 x y z] [a02] [z'] [a10] [a11] [a12] [a20] [a21] [a22]

given have 4 points, concatenate rows of matrix on left side , vector on right

[x1 y1 z1 0 0 0 0 0 0] [a00] [x1'] [0 0 0 x1 y1 z1 0 0 0] [a01] [y1'] [0 0 0 0 0 0 x1 y1 z1] [a02] [z1'] [x2 y2 z2 0 0 0 0 0 0] [a10] [x2'] [0 0 0 x2 y2 z2 0 0 0] [a11] [y2'] [0 0 0 0 0 0 x2 y2 z2] [a12] [z2'] [x3 y3 z3 0 0 0 0 0 0] * [a20] = [x3'] [0 0 0 x3 y3 z3 0 0 0] [a21] [y3'] [0 0 0 0 0 0 x3 y3 z3] [a22] [z3'] [x4 y4 z4 0 0 0 0 0 0] [x4'] [0 0 0 x4 y4 z4 0 0 0] [y4'] [0 0 0 0 0 0 x4 y4 z4] [z4'] s * = t

s matrix contains 4 source points in format shown above, a vector of transformation coefficients in matrix want solve (ordered in row-major format), , t vector of target points in format shown above.

to solve parameters, have utilize mldivide operator or \ in matlab, compute to the lowest degree squares estimate you. therefore:

a = s^{-1} * t

as such, build matrix above, utilize \ operator solve transformation parameters in matrix. when you're done, reshape t 3 x 3 matrix. therefore:

s = ... ; %// come in in source points here above t = ... ; %// come in in target points in right hand side vector above = s \ t; similarity_matrix = reshape(a, 3, 3).';

with regards error in little perturbations of each of co-ordinates, more points have better. using 4 give solution, isn't plenty mitigate errors in opinion.

minor note: (more or less) fitgeotrans under hood. computes best homography given bunch of source , target points, , determines using to the lowest degree squares.

hope answered question!

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