两个三维点云获取旋转矩阵

计算的python代码如下

def rigid_transform_3D(A, B, scale=False):
    assert A.shape == B.shape

    num_rows, num_cols = A.shape
    if num_rows != 3:
        A = A.transpose()
        num_rows, num_cols = A.shape
        if num_rows != 3:
            raise Exception(f"matrix A is not 3xN, it is {num_rows}x{num_cols}")

    num_rows, num_cols = B.shape
    if num_rows != 3:
        B = B.transpose()
        num_rows, num_cols = B.shape
        if num_rows != 3:
            raise Exception(f"matrix B is not 3xN, it is {num_rows}x{num_cols}")


    centroid_A = np.mean(A, axis=1)
    centroid_B = np.mean(B, axis=1)
    centroid_A = centroid_A.reshape(-1, 1)
    centroid_B = centroid_B.reshape(-1, 1)
    # subtract mean
    Am = A.copy() - centroid_A
    Bm = B.copy() - centroid_B

    if scale:
        scale = np.std(Bm) / np.std(Am)
        A = A * scale
    else:
        scale = -1

    # find mean column wise
    centroid_A = np.mean(A, axis=1)
    centroid_B = np.mean(B, axis=1)

    # import pdb
    # pdb.set_trace()

    # ensure centroids are 3x1
    centroid_A = centroid_A.reshape(-1, 1)
    centroid_B = centroid_B.reshape(-1, 1)

    # subtract mean
    Am = A - centroid_A
    Bm = B - centroid_B

    H = Am @ np.transpose(Bm)

    # sanity check
    #if linalg.matrix_rank(H) < 3:
    #    raise ValueError("rank of H = {}, expecting 3".format(linalg.matrix_rank(H)))

    # find rotation
    U, S, Vt = np.linalg.svd(H)
    R = Vt.T @ U.T

    # special reflection case
    if np.linalg.det(R) < 0:
        print("det(R) < R, reflection detected!, correcting for it ...")
        Vt[2,:] *= -1
        R = Vt.T @ U.T

    t = -R @ centroid_A + centroid_B

    if scale > 0:
        return R, t, scale
    else:
        return R, t