def find_inliers(x_0s, F, x_1s, threshold):
""" Find the inliers' indices for a given model.
There are multiple methods you could use for calculating the error
to determine your inliers vs outliers at each pass. CoHowever, we suggest
using the line to point distance function we wrote for the
optimization in part 2.
Args:
- x_0s: A numpy array of shape (N, 2) representing the coordinates
of possibly matching points from the left image
- F: The proposed fundamental matrix
- x_1s: A numpy array of shape (N, 2) representing the coordinates
of possibly matching points from the right image
- threshold: the maximum error for a point correspondence to be
considered an inlier
Each row in x_1s and x_0s is a proposed correspondence (e.g. row #42 of x_0s is a point that
corresponds to row #42 of x_1s)
Returns:
- inliers: 1D array of the indices of the inliers in x_0s and x_1s
"""
##############################
# TODO: Student code goes here
if x_0s.shape[1] == 2 and x_1s.shape[1] == 2:
x_0s, x_1s = two_view_data.preprocess_data(x_0s, x_1s)
errors = fundamental_matrix.signed_point_line_errors(x_0s, F, x_1s)
errors = np.absolute(errors)
inliers = []
for i in range(x_0s.shape[0]):
if errors[i * 2] < threshold and errors[i * 2 + 1] < threshold:
inliers.append(i)
##############################
return np.array(inliers)
def ransac_fundamental_matrix(x_0s, x_1s):
"""Find the fundamental matrix with RANSAC.
Use RANSAC to find the best fundamental matrix by
randomly sampling interest points. You will call your
solve_F() from part 2 of this assignment
and calculate_num_ransac_iterations().
You will also need to define a new function (see above) for finding
inliers after you have calculated F for a given sample.
Tips:
0. You will need to determine your P, k, and p values.
What is an acceptable rate of success? How many points
do you want to sample? What is your estimate of the correspondence
accuracy in your dataset?
1. A potentially useful function is numpy.random.choice for
creating your random samples
2. You will want to call your function for solving F with the random
sample and then you will want to call your function for finding
the inliers.
3. You will also need to choose an error threshold to separate your
inliers from your outliers. We suggest a threshold of 1.
Args:
- x_0s: A numpy array of shape (N, 2) representing the coordinates
of possibly matching points from the left image
- x_1s: A numpy array of shape (N, 2) representing the coordinates
of possibly matching points from the right image
Each row is a proposed correspondence (e.g. row #42 of x_0s is a point that
corresponds to row #42 of x_1s)
Returns:
- best_F: A numpy array of shape (3, 3) representing the best fundamental
matrix estimation
- inliers_x_0: A numpy array of shape (M, 2) representing the subset of
corresponding points from the left image that are inliers with
respect to best_F
- inliers_x_1: A numpy array of shape (M, 2) representing the subset of
corresponding points from the right image that are inliers with
respect to best_F
"""
number_of_iteration = calculate_num_ransac_iterations(0.999, 9, 0.7)
x0_concat, x1_concat = np.concatenate((x_0s, np.ones((len(x_0s), 1))),
axis=1), np.concatenate(
(x_1s, np.ones((len(x_1s), 1))),
axis=1)
minavgE = 99999
for _ in range(number_of_iteration):
rand_sample = np.random.choice(len(x_0s), 9, replace=False)
x0_process, x1_process = two_view_data.preprocess_data(
x_0s[rand_sample], x_1s[rand_sample])
F = solve_F(x_0s[rand_sample], x_1s[rand_sample])
found_inliers = find_inliers(x0_process, F, x1_process, 1)
if len(found_inliers) >= 0:
errors = fundamental_matrix.signed_point_line_errors(
x0_concat[found_inliers], F, x1_concat[found_inliers])
for i in range(len(errors)):
errors[i] = abs(errors[i])
average_error = sum(errors) / len(errors)
if average_error < minavgE:
minavgE, best_F, inliers_x_0, inliers_x_1 = average_error, F, x_0s[
found_inliers], x_1s[found_inliers]
##############################
return best_F, inliers_x_0, inliers_x_1
def ransac_fundamental_matrix(x_0s, x_1s):
"""Find the fundamental matrix with RANSAC.
Use RANSAC to find the best fundamental matrix by
randomly sampling interest points. You will call your
solve_F() from part 2 of this assignment
and calculate_num_ransac_iterations().
You will also need to define a new function (see above) for finding
inliers after you have calculated F for a given sample.
Tips:
0. You will need to determine your P, k, and p values.
What is an acceptable rate of success? How many points
do you want to sample? What is your estimate of the correspondence
accuracy in your dataset?
1. A potentially useful function is numpy.random.choice for
creating your random samples
2. You will want to call your function for solving F with the random
sample and then you will want to call your function for finding
the inliers.
3. You will also need to choose an error threshold to separate your
inliers from your outliers. We suggest a threshold of 1.
Args:
- x_0s: A numpy array of shape (N, 2) representing the coordinates
of possibly matching points from the left image
- x_1s: A numpy array of shape (N, 2) representing the coordinates
of possibly matching points from the right image
Each row is a proposed correspondence (e.g. row #42 of x_0s is a point that
corresponds to row #42 of x_1s)
Returns:
- best_F: A numpy array of shape (3, 3) representing the best fundamental
matrix estimation
- inliers_x_0: A numpy array of shape (M, 2) representing the subset of
corresponding points from the left image that are inliers with
respect to best_F
- inliers_x_1: A numpy array of shape (M, 2) representing the subset of
corresponding points from the right image that are inliers with
respect to best_F
"""
P = 0.999
k = 30
p = 0.9
threshold = 1
num_points = x_0s.shape[0]
iterations = calculate_num_ransac_iterations(P, k, p)
max_inliers = 0
best_inlier_indices = None
best_F = None
for _ in range(iterations):
sample_indices = np.random.choice(a=num_points, size=k, replace=False)
sample_x0 = x_0s[sample_indices]
sample_x1 = x_1s[sample_indices]
F = solve_F(sample_x0, sample_x1)
sample_x0, sample_x1 = two_view_data.preprocess_data(
sample_x0, sample_x1)
inlier_indices = find_inliers(sample_x0, F, sample_x1, threshold)
if (inlier_indices.shape[0] > max_inliers):
max_inliers = inlier_indices.shape[0]
best_inlier_indices = inlier_indices
best_F = F
inliers_x_0 = x_0s[best_inlier_indices]
inliers_x_1 = x_1s[best_inlier_indices]
return best_F, inliers_x_0, inliers_x_1
def solve_F(x_0s, x_1s):
x_0s, x_1s = two_view_data.preprocess_data(x_0s, x_1s)
p0 = (skew(1, 0, 0)).flatten() # stereo
result = optimize(p0, x_0s, x_1s)
F = np.reshape(result, (3, 3))
return F
def ransac_fundamental_matrix(x_0s, x_1s):
"""Find the fundamental matrix with RANSAC.
Use RANSAC to find the best fundamental matrix by
randomly sampling interest points. You will call your
solve_F() from part 2 of this assignment
and calculate_num_ransac_iterations().
You will also need to define a new function (see above) for finding
inliers after you have calculated F for a given sample.
Tips:
0. You will need to determine your P, k, and p values.
What is an acceptable rate of success? How many points
do you want to sample? What is your estimate of the correspondence
accuracy in your dataset?
1. A potentially useful function is numpy.random.choice for
creating your random samples
2. You will want to call your function for solving F with the random
sample and then you will want to call your function for finding
the inliers.
3. You will also need to choose an error threshold to separate your
inliers from your outliers. We suggest a threshold of 1.
Args:
- x_0s: A numpy array of shape (N, 2) representing the coordinates
of possibly matching points from the left image
- x_1s: A numpy array of shape (N, 2) representing the coordinates
of possibly matching points from the right image
Each row is a proposed correspondence (e.g. row #42 of x_0s is a point that
corresponds to row #42 of x_1s)
Returns:
- best_F: A numpy array of shape (3, 3) representing the best fundamental
matrix estimation
- inliers_x_0: A numpy array of shape (M, 2) representing the subset of
corresponding points from the left image that are inliers with
respect to best_F
- inliers_x_1: A numpy array of shape (M, 2) representing the subset of
corresponding points from the right image that are inliers with
respect to best_F
"""
##############################
# TODO: Student code goes here
# raise NotImplementedError
# make coordinates homogeneous
x_0s_3d, x_1s_3d = two_view_data.preprocess_data(x_0s, x_1s)
# solve_F(x_0s, x_1s) takes in two lists of paired homogenuous coordinates and returns an estimated fundamental matrix
prob_success = 0.999 # pick one yourself
sample_size = 9 # ?
ind_prob_correct = 0.9 # get this for SIFT
num_samples = calculate_num_ransac_iterations(prob_success, sample_size,
ind_prob_correct)
print('\n\n{}\n\n'.format(num_samples))
best_F = None
best_F_inliers_num = -1
inliers_x_0 = None
inliers_x_1 = None
indices = np.arange(len(x_0s))
for each in range(num_samples):
sample = np.random.choice(indices, sample_size, replace=False)
F_candidate = solve_F(x_0s[sample], x_1s[sample])
inliers_indices = find_inliers(x_0s_3d, F_candidate, x_1s_3d, 1)
num_inliers = len(inliers_indices)
if num_inliers > best_F_inliers_num:
best_F_inliers_num = num_inliers
best_F = F_candidate
inliers_x_0 = x_0s[inliers_indices]
inliers_x_1 = x_1s[inliers_indices]
##############################
return best_F, inliers_x_0, inliers_x_1
def ransac_fundamental_matrix(x_0s, x_1s):
"""Find the fundamental matrix with RANSAC.
Use RANSAC to find the best fundamental matrix by
randomly sampling interest points. You will call your
solve_F() from part 2 of this assignment
and calculate_num_ransac_iterations().
You will also need to define a new function (see above) for finding
inliers after you have calculated F for a given sample.
Tips:
0. You will need to determine your P, k, and p values.
What is an acceptable rate of success? How many points
do you want to sample? What is your estimate of the correspondence
accuracy in your dataset?
1. A potentially useful function is numpy.random.choice for
creating your random samples
2. You will want to call your function for solving F with the random
sample and then you will want to call your function for finding
the inliers.
3. You will also need to choose an error threshold to separate your
inliers from your outliers. We suggest a threshold of 1.
Args:
- x_0s: A numpy array of shape (N, 2) representing the coordinates
of possibly matching points from the left image
- x_1s: A numpy array of shape (N, 2) representing the coordinates
of possibly matching points from the right image
Each row is a proposed correspondence (e.g. row #42 of x_0s is a point that
corresponds to row #42 of x_1s)
Returns:
- best_model: A numpy array of shape (3, 3) representing the best fundamental
matrix estimation
- inliers_x_0: A numpy array of shape (M, 2) representing the subset of
corresponding points from the left image that are inliers with
respect to best_model
- inliers_x_1: A numpy array of shape (M, 2) representing the subset of
corresponding points from the right image that are inliers with
respect to best_model
"""
##############################
# TODO: Student code goes here
best_model = np.zeros((3, 3))
num_inliers = 0
iterations = calculate_num_ransac_iterations(.97, 9, .68)
for i in range(iterations):
length = x_0s.shape[0]
p_idx = np.random.choice(length, 11, replace=False)
p_x0s = []
p_x1s = []
for idx in p_idx:
p_x0s.append(x_0s[idx])
p_x1s.append(x_1s[idx])
p_x0s = np.array(p_x0s)
p_x1s = np.array(p_x1s)
curr_inliers = find_inliers(
two_view_data.preprocess_data(x_0s, x_1s)[0],
solve_F(p_x0s, p_x1s),
two_view_data.preprocess_data(x_0s, x_1s)[1], 1)
if (curr_inliers.shape[0] > num_inliers):
num_inliers = curr_inliers.shape[0]
best_model = solve_F(p_x0s, p_x1s)
inliers_x_0 = []
inliers_x_1 = []
for inlier in curr_inliers:
inliers_x_0.append(x_0s[inlier])
inliers_x_1.append(x_1s[inlier])
inliers_x_0 = np.array(inliers_x_0)
inliers_x_1 = np.array(inliers_x_1)
best_F = best_model
inliers_x_0 = np.array(inliers_x_0)
inliers_x_1 = np.array(inliers_x_1)
##############################
return best_F, inliers_x_0, inliers_x_1