In [129]:
#perform imports, set display size for images.
import numpy as np
import numpy.linalg as linalg
%matplotlib inline
import cv2
import matplotlib.image as mpimg
import matplotlib.pyplot as plt
import matplotlib
matplotlib.rcParams['figure.figsize'] = (20.0, 10.0)
In [130]:
#read in and display images
road1 = cv2.imread("hw1data/190HW1.png")
road2 = cv2.imread("hw1data/190HW2.png")
road1 = cv2.cvtColor(road1, cv2.COLOR_BGR2RGB)
road2 = cv2.cvtColor(road2, cv2.COLOR_BGR2RGB)
plt.subplot(121)
plt.imshow(road1)
plt.subplot(122)
plt.imshow(road2)
Out[130]:
In [131]:
#generate keypoints and their descriptors, as described in OpenCV guide for SIFT.
road1gray = cv2.cvtColor(road1, cv2.COLOR_RGB2GRAY)
road2gray = cv2.cvtColor(road2, cv2.COLOR_RGB2GRAY)
sift = cv2.xfeatures2d.SIFT_create()
keypoints1, des1 = sift.detectAndCompute(road1gray,None)
keypoints2, des2 = sift.detectAndCompute(road2gray,None)
road1 = cv2.drawKeypoints(road1gray, keypoints1, road1)
#cv2.imwrite('sift_keypoints_road1.png', road1)
road2 = cv2.drawKeypoints(road2gray, keypoints2, road2)
#cv2.imwrite('sift_keypoints_road2.png', road2)
In [132]:
#find and plot matches
matcher = cv2.BFMatcher()
matches = matcher.knnMatch(des1, des2, k=2)
#perform ratio test to remove ambigous points as suggested in OpenCV guide
good = []
for m, n in matches:
if m.distance < .75*n.distance:
good.append([m])
#draw the matches
matchImg = cv2.drawMatchesKnn(road1, keypoints1, road2, keypoints2, good, None, flags=2)
plt.imshow(matchImg)
Out[132]:
In [133]:
# estimate fundamental matrix using function from part B, slightly modified for keypoints
def computeF(matches, keypoints1, keypoints2):
xl = [keypoints1[match[0].queryIdx] for match in matches]
xr = [keypoints2[match[0].trainIdx] for match in matches]
A = []
for i in xrange(len(xl)):
x = xl[i].pt
x_prime = xr[i].pt
A.append([x[0]*x_prime[0], x[1]*x_prime[0], x_prime[0],
x[0]*x_prime[1], x[1]*x_prime[1], x_prime[1], x[0], x[1], 1])
A = np.array(A)
_, _, V = linalg.svd(A)
F = V[-1,:].reshape((3,3))
U, s, V = linalg.svd(F)
sigma = np.diag(s)
sigma[2,2] = 0
return np.matmul(U, np.matmul(sigma, V))
#translated plotMatches.m, lifted from problem 2
def plotLine(img, line, color):
a = line[0]
b = line[1]
c = line[2]
cols, rows, _ = img.shape
flag = 0
cp = np.zeros((2,2))
p1 = -(b+c)/a
p2 = -(a+c)/b
p3 = -(b * cols + c)/a
p4 = -(a * rows + c)/b
# Keep track of number of intersections and corresponding edge
if flag <= 1 and p1 >= 1 and p1 <= rows:
cp[flag,:] = [p1,0];
flag = flag + 1;
if flag <= 1 and p2 >= 1 and p2 <= cols:
cp[flag,:] = [0,p2];
flag = flag + 1;
if (flag <= 1 and p3 >= 1 and p3 <= rows):
cp[flag,:] = [p3,cols];
flag = flag + 1;
if (flag <= 1 and p4 >= 1 and p4 <= cols):
cp[flag,:] = [rows,p4];
flag = flag + 1
ax.plot([cp[0,0], cp[1,0]], [cp[0,1], cp[1,1]], color=color)
plt.draw()
F = computeF(good, keypoints1, keypoints2)
print(F)
In [134]:
# grab 5 random points, and plot their epipolar lines for the right image
import random
points = random.sample(keypoints1, 5)
lines = []
for i in range(5):
#generate epipolar lines for the points.
lines.append(np.matmul([points[i].pt[0], points[i].pt[1], 1], F))
plt.imshow(road2)
ax = plt.gca()
for line in lines:
plotLine(road2, line, "g")
In [135]:
#grab 5 random points and plot their epipolar lines for the left image.
random.sample(keypoints2, 5)
lines = []
for i in range(5):
#Generate lines for the 5 points
lines.append(np.matmul(F, [points[i].pt[0], points[i].pt[1], 1]))
plt.imshow(road1)
ax = plt.gca()
for line in lines:
plotLine(road1, line, "g")
In [136]:
# Perform RANSAC method
N = 100000
s = 8
currF = None
maxInliers = 0
for n in xrange(N):
sampledMatches = random.sample(good, s)
FToTest = computeF(sampledMatches, keypoints1, keypoints2)
numIn = 0
for match in good:
p = keypoints1[match[0].queryIdx].pt
q = keypoints2[match[0].trainIdx].pt
if (abs(np.matmul([p[0], p[1], 1], np.matmul(FToTest, [q[0], q[1], 1])))) < .01:
numIn += 1
if numIn > maxInliers:
maxInliers = numIn
currF = FToTest
print(currF)
print(maxInliers)
In [137]:
inlierSet = []
#calculate the final set of inliers
for match in good:
p = keypoints1[match[0].queryIdx].pt
q = keypoints2[match[0].trainIdx].pt
if abs(np.matmul([p[0], p[1], 1], np.matmul(currF, [q[0], q[1], 1]))) < .01:
inlierSet.append(match[0])
xl = [keypoints1[match.queryIdx] for match in inlierSet]
xr = [keypoints2[match.trainIdx] for match in inlierSet]
#recalculate fundamental matrix with all inliers.
A = []
for i in xrange(len(xl)):
x = xl[i].pt
x_prime = xr[i].pt
A.append([x[0]*x_prime[0], x[1]*x_prime[0], x_prime[0],
x[0]*x_prime[1], x[1]*x_prime[1], x_prime[1], x[0], x[1], 1])
A = np.array(A)
_, _, V = linalg.svd(A)
F = V[-1,:].reshape((3,3))
U, s, V = linalg.svd(F)
sigma = np.diag(s)
sigma[2,2] = 0
F = np.matmul(U, np.matmul(sigma, V))
#plot the inliers
drawInliers = map(lambda x: [x], inlierSet)
matchImg = cv2.drawMatchesKnn(road1, keypoints1, road2, keypoints2, drawInliers, None, flags=2)
plt.imshow(matchImg)
Out[137]:
In [138]:
# grab 5 random points, and plot their epipolar lines for the right image
points = random.sample(keypoints1, 5)
lines = []
for i in range(5):
lines.append(np.matmul([points[i].pt[0], points[i].pt[1], 1], F))
plt.imshow(road2)
ax = plt.gca()
for line in lines:
plotLine(road2, line, "y")
In [139]:
#grab 5 random points and plot their epipolar lines for the left image.
random.sample(keypoints2, 5)
lines = []
for i in range(5):
lines.append(np.matmul(F, [points[i].pt[0], points[i].pt[1], 1]))
plt.imshow(road1)
ax = plt.gca()
for line in lines:
plotLine(road1, line, "y")
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