Opencv 如何在考虑摄像机标定的情况下进行二维到三维重建

我试图重建摄像机捕捉到的物体的三维位置，使其位置在二维平面上，并具有所有摄像机校准参数。 我正在使用Python和OpenCV

我已经搜索并尝试了多种解决方案，但我无法实现我想要的转变。我的主要问题是，我在图形方面没有足够的背景知识来理解和执行所需的确切步骤

<?xml version="1.0"?>
<opencv_storage>
<intrinsic type_id="opencv-matrix">
  <rows>3</rows>
  <cols>3</cols>
  <dt>f</dt>
  <data>
    4.04310596e+003 0. 9.15485046e+002
    0. 4.03170264e+003 4.26480865e+002
    0. 0. 1.</data></intrinsic>
<rotation_vector type_id="opencv-matrix">
  <rows>1</rows>
  <cols>3</cols>
  <dt>f</dt>
  <data>
    -4.56216574e-001 1.76409543e+000 2.05966163e+000</data></rotation_vector>
<rotation_matrix type_id="opencv-matrix">
  <rows>3</rows>
  <cols>3</cols>
  <dt>f</dt>
  <data>
    -8.71332586e-001 -4.90659207e-001 5.74691826e-003 8.10814202e-002
    -1.32417098e-001 9.87872243e-001 -4.83947605e-001 8.61231267e-001
    1.55162677e-001</data></rotation_matrix>
<translation type_id="opencv-matrix">
  <rows>1</rows>
  <cols>3</cols>
  <dt>f</dt>
  <data>
    3.16912168e+004 -1.31297791e+003 8.73433125e+004</data></translation>
<distortion type_id="opencv-matrix">
  <rows>1</rows>
  <cols>4</cols>
  <dt>f</dt>
  <data>
    4.86164242e-001 -3.57553625e+000 -1.77373271e-002 -3.11793620e-003</data></distortion>
<points_2d type_id="opencv-matrix">
  <rows>10</rows>
  <cols>1</cols>
  <dt>"2f"</dt>
  <data>
    1454. 223. 463. 375. 742. 461. 1163. 588. 1704. 755. 646. 550. 129.
    497. 567. 690. 196. 738. 546. 935.</data></points_2d>
<points_3d type_id="opencv-matrix">
  <rows>10</rows>
  <cols>3</cols>
  <dt>f</dt>
  <data>
    0. 34000. 0. 36000. 20160. 0. 36000. 7.31248877e+003 0. 36000.
    -7.31248877e+003 0. 36000. -20160. 0. 41500. 0. 0. 47000. 9160. 0.
    47000. -9160. 0. 52500. -9160. 0. 52500. -20160. 0.</data></points_3d>
<reprojection_errors type_id="opencv-matrix">
  <rows>1</rows>
  <cols>20</cols>
  <dt>f</dt>
  <data>
    19. -2. -9. -2. 0. 1. -1. -1. 3. 1. 0. 1. -19. 0. -8. 0. -4. 2. 9.
    1.</data></reprojection_errors>
</opencv_storage>

3.
3.
F
4.04310596e+003 0。9.15485046e+002
04.03170264e+003 4.26480865e+002
001.
1.
3.
F
-4.56216574e-001 1.76409543e+000 2.05966163e+000
3.
3.
F
-8.71332586e-001-4.90659207e-001 5.74691826e-003 8.10814202e-002
-1.32417098e-001 9.87872243e-001-4.83947605e-001 8.61231267e-001
1.55162677e-001
1.
3.
F
3.16912168e+004-1.3129791E+003 8.73433125e+004
1.
4.
F
4.86164242e-001-3.57553625e+000-1.77373271e-002-3.11793620e-003
10
1.
“2f”
145422346337574246111635881704755646550129
497567690196738546935
10
3.
F
034000036000201600360007.31248877e+003 0。36000
-7.31248877e+003 0。36000. -20160041500004700091600
47000. -9160052500. -9160052500. -201600
1.
20
F
19. -2. -9. -2.01. -1. -1.3.1.01. -190. -8.0. -4.2.9
1.

这就是我所拥有的，以2d和3d点为例，以及所有相机校准参数：固有、失真等

执行2d到3d转换需要什么操作顺序？看数据，我想转换（1454，223）到（0，34000，0）等等。< /P> < P>在第二部分中，你可以找到一些数学来解决你的问题，并用C++实现解决方案。 无论如何，我已经在Python中实现了类似的解决方案，如下所示：

matrices = [
    "intrinsic",
    "rotation_vector",
    "rotation_matrix",
    "translation",
    "distortion",
    "points_2d",
    "points_3d",
    "reprojection_errors"
]

# Load data from persistent storage
dic = {}
data = cv2.FileStorage(storage_file, cv2.FILE_STORAGE_READ)
for m in matrices:
    dic[m] = data.getNode(m).mat()

# Prepare matrices
rotation_matrix = np.mat(dic["rotation_matrix"])
translation_vector = np.mat(dic["translation"])
intrinsic_matrix = np.mat(dic["intrinsic"])

# Extrinsic Parameters Matrix
translation_vector_transposed = np.transpose(translation_vector)
extrinsic_matrix = np.concatenate((rotation_matrix, translation_vector_transposed), axis=1)

# Projection Matrix
projection_matrix = intrinsic_matrix * extrinsic_matrix

# Homography Matrix
p11 = projection_matrix[0,0]
p12 = projection_matrix[0,1]
p14 = projection_matrix[0,3]
p21 = projection_matrix[1,0]
p22 = projection_matrix[1,1]
p24 = projection_matrix[1,3]
p31 = projection_matrix[2,0]
p32 = projection_matrix[2,1]
p34 = projection_matrix[2,3]
homography_matrix = np.array([[p11,p12,p14], [p21,p22,p24], [p31,p32,p34]], dtype=np.float)
homography_matrix_inverse = inv(homography_matrix)

for i in range(0,10):

    # Prepare points
    np.set_printoptions(suppress=True)
    point_2D = np.append(np.array(dic["points_2d"][i]), np.array([[1]]), axis=1)
    print("\nPoint2D:", end=" ")
    print_point(point_2D)
    point_3d_expected = dic["points_3d"][i]
    print("\nPoint3D Exptected:", end=" ")
    print_point_simple(point_3d_expected)

    # Projection
    point_3D_w = np.mat(homography_matrix_inverse) * np.mat(np.transpose(point_2D))

    # Normalization
    point_3D = np.divide(point_3D_w,point_3D_w[2])
    point_3D[2] = 0

    # Show Result
    print("\nPoint3D:", end=" ")
    print_point(point_3D)
    print('')

希望这对你有帮助