将 SVD 代码从 MATLAB 转换为 Python

问：

我在MATLAB中有一些代码需要转换为Python，以SVD为中心。在相同的输入下，我无法得到相同的结果。有没有人知道我哪里出错了？

MATLAB代码

function v = homography_solve(pin, pout)
% HOMOGRAPHY_SOLVE finds a homography from point pairs
%   V = HOMOGRAPHY_SOLVE(PIN, POUT) takes a 2xN matrix of input vectors and
%   a 2xN matrix of output vectors, and returns the homogeneous
%   transformation matrix that maps the inputs to the outputs, to some
%   approximation if there is noise.
%
%   This uses the SVD method of
%   http://www.robots.ox.ac.uk/%7Evgg/presentations/bmvc97/criminispaper/node3.html
% David Young, University of Sussex, February 2008
if ~isequal(size(pin), size(pout))
    error('Points matrices different sizes');
end
if size(pin, 1) ~= 2
    error('Points matrices must have two rows');
end
n = size(pin, 2);
if n < 4
    error('Need at least 4 matching points');
end
% Solve equations using SVD
x = pout(1, :); y = pout(2,:); X = pin(1,:); Y = pin(2,:);
rows0 = zeros(3, n);
rowsXY = -[X; Y; ones(1,n)];
hx = [rowsXY; rows0; x.*X; x.*Y; x];
hy = [rows0; rowsXY; y.*X; y.*Y; y];
h = [hx hy];
if n == 4
    [U, ~, ~] = svd(h);
else
    [U, ~, ~] = svd(h, 'econ');
end
v = (reshape(U(:,9), 3, 3)).';
end

pin =

  [167.4787  300.2447  430.9681  114.3723  298.2021  479.9894;
  200.5000  199.1383  202.5426  226.3723  228.4149  228.4149]

pout = 
   [-3.0500         0    3.0500   -3.0500         0    3.0500;
    6.7050    6.7050    6.7050    1.9800    1.9800    1.9800]

This returns 

v =    

   [-0.0006   -0.0000    0.1934;
   -0.0000    0.0040   -0.9801;
    0.0000   -0.0004    0.0449]

我在 Python 中的当前代码如下，但没有给出类似的结果。它将返回一个 3x3 矩阵，但与 MATLAB 不同。

import numpy as np
from scipy import linalg

def homography_solve(pin, pout):
    # Check if input and output matrices have the same size
    if pin.shape != pout.shape:
        raise ValueError('Points matrices different sizes')
    
    # Check if the matrices have two rows
    if pin.shape[0] != 2:
        raise ValueError('Points matrices must have two rows')
    
    n = pin.shape[1]
    
    # Check if we have at least 4 matching points
    if n < 4:
        raise ValueError('Need at least 4 matching points')
    
    # Solve equations using SVD
    x = pout[0, :]
    y = pout[1, :]
    X = pin[0, :]
    Y = pin[1, :]
    
    rows0 = np.zeros((3, n))
    rowsXY = np.vstack((-X, -Y, -np.ones(n)))
    hx = np.vstack((rowsXY, rows0, x * X, x * Y, x))
    hy = np.vstack((rows0, rowsXY, y * X, y * Y, y))
    h = np.hstack((hx, hy))
    

    if n == 4:
        U, sdiag, VH = np.linalg.svd(h)
    else:
        U, sdiag, VH = np.linalg.svd(h, full_matrices=False)
        
    S = np.zeros((h.shape[0], h.shape[1]))
    np.fill_diagonal(S, sdiag)
    V = VH.T.conj() 
    
    v = (U[-1,:].reshape(3, 3)).T
    
    return v