def Ransac(Matches, TYPE, N, Epsilon):
# Random sample consensus(RANSAC) is an iterative method to estimate parameters
# of a mathematical model from a set of observed data that contains outliers.
# By iteratively fitting a model to the data we find the best model by its ability
# to characterize a threshold of inlier points.
# Input: Corresponding Image coordinates in the two images (Matches)
# Threshold number of inlier points (N)
# Threshold value for Sum of Squared differences (Epsilon)
# TYPE determines the model to compute (1=Affine, 2=Homography)
# Outputs: Number of inlier points
# Affine or Homography transformation matrix
# Inlier count
In_count = 0
# Inlier array
Inlier_Data = []
while (In_count < N):
# Randomly pick out points from the matches
r = np.round((len(Matches) - 1)*np.random.random(np.int(np.round(len(Matches)/2)) + 1)).astype(int)
Subsample = Matches[r,:]
# Keep track of the inliers
if (In_count > 0):
Subsample = np.concatenate((Subsample, np.asarray(Inlier_Data)), axis=0)
# Isolate the matches
Image_Coords_1 = np.asarray(Subsample)[:,0:2]
Image_Coords_2 = np.asarray(Subsample)[:,2:4]
# Homography
if (TYPE == 2):
# Compute the homography matrix
H = Transformations.Homography(Image_Coords_1, Image_Coords_2)
# Compute the transformation and the inverse transformation
X2 = Transformations.HomographyTransformer(H, Matches[:, 0:2])
X1 = Transformations.HomographyTransformer(np.linalg.inv(H), Matches[:, 2:4])
# Compute the euclidean distance
ssd = SumEucDistance(X1, Matches[:, 0:2], X2, Matches[:, 2:4])
# Affine
elif (TYPE == 1):
# Compute the affine matrix
A = Transformations.AffineTransformer(Image_Coords_1, Image_Coords_2)
# Compute the transformation coordinates and inverse transformation coordinates
X2 = np.matmul(A, np.transpose(np.hstack((np.asarray(Matches[:,0:2]), np.ones(shape=(len(Matches),1))))))
X1 = np.matmul(np.linalg.inv(A), np.transpose(np.hstack((np.asarray(Matches[:,2:4]), np.ones(shape=(len(Matches),1))))))
# Compute the euclidean distance
ssd = SumEucDistance(X1[0:2].T, Matches[:, 0:2], X2[0:2].T, Matches[:, 2:4])
else:
raise ValueError("Incorrect Type")
# Extract the outliers
for i in range(0, len(ssd)):
if (ssd[i] < Epsilon):
if [Matches[i,0],Matches[i,1],Matches[i,2],Matches[i,3]] not in np.asarray(Inlier_Data).tolist():
Inlier_Data.append(Matches[i,:])
In_count += 1
print(In_count)
# Compute the transformation using the inliers
Inlier_Data = np.asarray(Inlier_Data, dtype=float)
if (TYPE == 1):
return Inlier_Data, Transformations.AffineTransformer(Inlier_Data[:, 0:2], Inlier_Data[:, 2:4])
elif (TYPE == 2):
return Inlier_Data, Transformations.Homography(Inlier_Data[:, 0:2], Inlier_Data[:, 2:4])
import Ransac
import Transformations
import numpy as np
import matplotlib.pyplot as plt
I1 = plt.imread('library1.jpg')
I2 = plt.imread('library2.jpg')
matches = np.loadtxt('library_matches.txt')
Input_coord1 = matches[:,0:2]
Input_coord2 = matches[:,2:4]
### LS Affine transformation ###
Affine_T = Transformations.AffineTransformer(Input_coord1, Input_coord2)
# Generate a pseudo z-axis
PS_Input_coord1 = np.hstack((Input_coord1, np.ones(shape=(len(Input_coord1), 1))))
PS_Input_coord2 = np.hstack((Input_coord2, np.ones(shape=(len(Input_coord2), 1))))
# Transformed coordinates
Tr_coord1 = np.matmul(np.linalg.inv(Affine_T),np.transpose(PS_Input_coord2))
Tr_coord2 = np.matmul(Affine_T,np.transpose(PS_Input_coord1))
# Residuals and mean error
Residuals_IC1 = Tr_coord2.T-PS_Input_coord2
Residuals_IC2 = Tr_coord1.T-PS_Input_coord1
Mean_Res_IC1 = np.mean(Residuals_IC1)
Mean_Res_IC2 = np.mean(Residuals_IC2)
