# 2D -> 3D 身體骨架資訊

> 非平行照片，高度不同、仰角不同

## 流程
1. 給定 對應點 ，計算 Fundamental Matrix
2. 給定 對應點 ，計算 Essential Matrix
3. 給定 F / E ，計算 Rotation Matrix

## A. Fundamental Matrix

def Find_Fundamental_matrix(first_input, second_input, img1, img2):
  # Use The function to gain the fundamental matrix，in order to the next step extracting {R|T} from fundamental matrix
  Max_length_img1 = max(img1.shape[0],img1.shape[1]) # Extract max length from image sizes，in order to normalize our input getting results more stable
  Max_length_img2 = max(img2.shape[0],img2.shape[1])

  first_img_coordinate = [] # coordinates in first image
  second_img_coordinate = [] # coordinates in second image
  # Normalization
  for i in range(len(first_input)):
    first_img_coordinate.append([first_input[i][0]/Max_length_img1, first_input[i][1]/Max_length_img1,1/Max_length_img1])
  for i in range(len(second_input)):
    second_img_coordinate.append((second_input[i][0]/Max_length_img2, second_input[i][1]/Max_length_img2,1/Max_length_img2))
  
  # calculate kronecker 
  A = []
  for i in range(len(first_img_coordinate)):
    A.append(np.transpose(np.kron(first_img_coordinate[i], second_img_coordinate[i])))
    
  # singular value decomposition
  U, D, V = svd(np.array(A))

  # approximate F, possibly regular
  Fa = np.reshape(V[:,8],(3,3))
  return Fa