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])
ax1 = fig.add_subplot(1,2,1)
ax1.imshow(I1)
plt.axis('off')
ax2 = fig.add_subplot(1,2,2)
ax2.imshow(I2)
plt.axis('off')
# Plot the transformed points
ax2.plot(matches[:,2], matches[:,3], 'r+')
ax2.plot(Tr_coord2_R[0,:], Tr_coord2_R[1,:], 'b+')
ax1.plot(matches[:,0], matches[:,1], 'r+')
ax1.plot(Tr_coord1_R[0,:], Tr_coord1_R[1,:], 'b+')
### Homography Transformation ###
Homography_T = Transformations.Homography(Input_coord1, Input_coord2)
# Transformed coordinates
Tr_coord2_H = Transformations.HomographyTransformer(Homography_T, Input_coord1)
Tr_coord1_H = Transformations.HomographyTransformer(np.linalg.inv(Homography_T), Input_coord2)
# Display the image
fig = plt.figure('Homogrphy Transformation')
ax1 = fig.add_subplot(1,2,1)
ax1.imshow(I1)
plt.axis('off')
ax2 = fig.add_subplot(1,2,2)
ax2.imshow(I2)
plt.axis('off')
# Plot the transformed points
