[Time] 2019.09.04 
 [Title] Transform.similalicytransform () of the Skimage libraryI. SimiLARITYTRANSFORMSimilar transformation: Waiting transformation+uniform scale zoom, the so -called equivalent transformation is translation+rotation transformation.

transform matrix:

transform effect: angle, parallelism and verticality do not change.

2, transform.similalicytransform () usage

Reference: Help (TF.SIMILARITYTRANSFORM)

Input parameters:

• matrix : (3, 3) array, optional , Homogeneous transformation matrix.

optional, that is, the (3,3) change matrix in the above (3,3), depending on the description below.

• scale: float, optional (zoom factor, S)
• rotation : float, optional  Rotation angle in counter-clockwise direction as radians.

(Rotating angle θ, counterclockwise, expressed from the angle from the arc)

• translation : (tx, ty) as array, list or tuple, optional ，x, y translation parameters.

Transfer parameters (TX, TY)

Return:

A SKIMAGE.TRANSFORM._Geometric.similalicytransform Object

(3,3) Quality change matrix: 

       [[A0 B0 A1] 
        [B0 A0 B1] 
        [0 0 1]] 
 Compared with the transformation matrix, we can see: A0 = S * cos (rotation), B0 = s * sin (rotation), A1 = TX, B1 = TY.

The final similar transformation result of this is:

 X = a0 * x - b0 * y + a1 =
   = s * x * cos(rotation) - s * y * sin(rotation) + a1

 Y = b0 * x + a0 * y + b1 =
   = s * x * sin(rotation) + s * y * cos(rotation) + b1

3. Related methods:

3.1 ESTIMATE (SELF, SRC, DST): From a set of corresponding points (source point, target point), estimate change matrixinput parameters: 
  | src: (n, 2) array 
  | Source Coordinates. (Source coordinates) 
  | dst: (n, 2) array 
  | Destination Coordinates. 
  return: 
  | Success: BOOL 
  | True, if Model Estimation Succeeds.3.2 INVERSE (Self, Coords): From the target coordinates, the source coordinates| Apply Inverse Transformation. 
 Input parameters:     

  | Coords: (n, 2) array 
  | Destination Coordinates. 
 return:  
  | Coords: (n, 2) array 
  | Source Coordinates.3.3 Residuals (SELF, SRC, DST): Determine the residues of the target coordinates after the conversion, and determine the distance between Eujide with each source coordinates to each target coordinate.Input parameters: 
  | src: (n, 2) array 
  | Source Coordinates. 
  | dst: (n, 2) array 
  | Destination Coordinates. 
 return: 
  | Residuals: (n,) array 
  | Residual for coordinal. 
  | |

4, example

4.1

from skimage import transform as trans
import numpy as np
src = np.array([
    [38.2946, 51.6963],
    [73.5318, 51.5014],
    [56.0252, 71.7366],
    [41.5493, 92.3655],
    [70.7299, 92.2041] ], dtype=np.float32)
dst = np.array([
    [38.2946, 51.6963],
    [73.5318, 51.5014],
    [56.0252, 71.7366],
    [41.5493, 92.3655],
    [70.7299, 92.2041] ], dtype=np.float32)
tform = trans.SimilarityTransform()
res =tform.estimate(dst, src)
M = tform.params
print(res)
print(M)

[Run results]:

4.2

from skimage import io,data
from skimage import transform as tf
img = data.camera()
io.imshow(img)
tform = tf.SimilarityTransform(scale=1.5,rotation=np.deg2rad(10),translation=(10,12))
img1 = tf.warp(img,tform)
io.imshow(img1)

Original mapThe picture after similar transformation