OpenCVPython系列之对极几何实践

OpenCV中的对极几何

在上个教程中我们已经简述了对极几何的一些理论知识，本次我们来使用OpenCV中的一些函数来进行实战，为了得到基础矩阵我们应该在两幅图像中找到尽量多的匹配点。我们可以使用 SIFT 描述符，FLANN 匹配器和比值检测。

我们使用示例图片：

先看代码：

import numpy as np
import cv2 as cv
from matplotlib import pyplot as plt
 
 
img1 = cv.imread('myleft.jpg', 0)  # queryimage # left image
img2 = cv.imread('myright.jpg', 0)  # trainimage # right image
sift = cv.xfeatures2d.SIFT_create()
# find the keypoints and descriptors with SIFT
kp1, des1 = sift.detectAndCompute(img1, None)
kp2, des2 = sift.detectAndCompute(img2, None)
# FLANN parameters
FLANN_INDEX_KDTREE = 1
index_params = dict(algorithm=FLANN_INDEX_KDTREE, trees=5)
search_params = dict(checks=50)
flann = cv.FlannBasedMatcher(index_params, search_params)
matches = flann.knnMatch(des1, des2, k=2)
good = []
pts1 = []
pts2 = []
# ratio test as per Lowe's paper
for i, (m, n) in enumerate(matches):
    if m.distance < 0.8*n.distance:
        good.append(m)
        pts2.append(kp2[m.trainIdx].pt)
        pts1.append(kp1[m.queryIdx].pt)

现在得到了一个匹配点列表，我们就可以使用它来计算基础矩阵了。

retval, mask=cv.findFundamentalMat(points1, points2, method, ransacReprojThreshold, confidence, mask)

· points1：从第一张图片开始的N个点的数组。点坐标应该是浮点数(单精度或双精度)。

· points2：与点1大小和格式相同的第二图像点的数组。

· method：计算基本矩阵的方法。

· cv2.FM_7POINT for a 7-point algorithm. N=7

· cv2.FM_8POINT for an 8-point algorithm. N≥8

· cv2.FM_RANSAC （默认） for the RANSAC algorithm. N≥8

· cv2.FM_LMEDS for the LMedS algorithm. N≥8

· ransacReprojThreshold：仅用于RANSAC方法的参数，默认3。它是一个点到极线的最大距离(以像素为单位)，超过这个点就被认为是一个离群点，不用于计算最终的基本矩阵。根据点定位、图像分辨率和图像噪声的准确性，可以将其设置为1-3左右。

· confidence：仅用于RANSAC和LMedS方法的参数，默认0.99。它指定了一个理想的置信水平(概率)，即估计矩阵是正确的。

· mask：输出

pts1 = np.int32(pts1)

pts2 = np.int32(pts2)

F, mask = cv.findFundamentalMat(pts1, pts2, cv.FM_LMEDS)

# We select only inlier points

pts1 = pts1[mask.ravel() == 1]

pts2 = pts2[mask.ravel() == 1]

下一步我们要找到极线。我们会得到一个包含很多线的数组。所以我们要 定义一个新的函数将这些线绘制到图像中。

def drawlines(img1, img2, lines, pts1, pts2):
    ''' img1 - image on which we draw the epilines for the points in img2
        lines - corresponding epilines '''
    r, c = img1.shape
    img1 = cv.cvtColor(img1, cv.COLOR_GRAY2BGR)
    img2 = cv.cvtColor(img2, cv.COLOR_GRAY2BGR)
    for r, pt1, pt2 in zip(lines, pts1, pts2):
        color = tuple(np.random.randint(0, 255, 3).tolist())
        x0, y0 = map(int, [0, -r[2]/r[1]])
        x1, y1 = map(int, [c, -(r[2]+r[0]*c)/r[1]])
        img1 = cv.line(img1, (x0, y0), (x1, y1), color, 1)
        img1 = cv.circle(img1, tuple(pt1), 5, color, -1)
        img2 = cv.circle(img2, tuple(pt2), 5, color, -1)
    return img1, img2

现在我们两幅图像中计算并绘制极线。

lines = cv.computeCorrespondEpilines(points, whichImage, F, lines)

· points：输入点。类型为CV_32FC2N×1或1×N矩阵。

· whichImage：包含点的图像(1或2)的索引。

· F：基本矩阵，可使用findFundamentalMat或stereoRectify 进行估计。

· lines：对应于另一幅图像中点的极线的输出向量（a，b，c）表示直线ax+by+c=0。

# Find epilines corresponding to points in right image (second image) and
# drawing its lines on left image
lines1 = cv.computeCorrespondEpilines(pts2.reshape(-1, 1, 2), 2, F)
lines1 = lines1.reshape(-1, 3)
img5, img6 = drawlines(img1, img2, lines1, pts1, pts2)
# Find epilines corresponding to points in left image (first image) and
# drawing its lines on right image
lines2 = cv.computeCorrespondEpilines(pts1.reshape(-1, 1, 2), 1, F)
lines2 = lines2.reshape(-1, 3)
img3, img4 = drawlines(img2, img1, lines2, pts2, pts1)
plt.subplot(121), plt.imshow(img5)
plt.subplot(122), plt.imshow(img3)
plt.show()

最终整个程序：

import numpy as np
import cv2 as cv
from matplotlib import pyplot as plt
 
 
def drawlines(img1, img2, lines, pts1, pts2):
    ''' img1 - image on which we draw the epilines for the points in img2
        lines - corresponding epilines '''
    r, c = img1.shape
    img1 = cv.cvtColor(img1, cv.COLOR_GRAY2BGR)
    img2 = cv.cvtColor(img2, cv.COLOR_GRAY2BGR)
    for r, pt1, pt2 in zip(lines, pts1, pts2):
        color = tuple(np.random.randint(0, 255, 3).tolist())
        x0, y0 = map(int, [0, -r[2]/r[1]])
        x1, y1 = map(int, [c, -(r[2]+r[0]*c)/r[1]])
        img1 = cv.line(img1, (x0, y0), (x1, y1), color, 1)
        img1 = cv.circle(img1, tuple(pt1), 5, color, -1)
        img2 = cv.circle(img2, tuple(pt2), 5, color, -1)
    return img1, img2
 
 
img1 = cv.imread('myleft.jpg', 0)  # queryimage # left image
img2 = cv.imread('myright.jpg', 0)  # trainimage # right image
sift = cv.xfeatures2d.SIFT_create()
# find the keypoints and descriptors with SIFT
kp1, des1 = sift.detectAndCompute(img1, None)
kp2, des2 = sift.detectAndCompute(img2, None)
# FLANN parameters
FLANN_INDEX_KDTREE = 1
index_params = dict(algorithm=FLANN_INDEX_KDTREE, trees=5)
search_params = dict(checks=50)
flann = cv.FlannBasedMatcher(index_params, search_params)
matches = flann.knnMatch(des1, des2, k=2)
good = []
pts1 = []
pts2 = []
# ratio test as per Lowe's paper
for i, (m, n) in enumerate(matches):
    if m.distance < 0.8*n.distance:
        good.append(m)
        pts2.append(kp2[m.trainIdx].pt)
        pts1.append(kp1[m.queryIdx].pt)
 
pts1 = np.int32(pts1)
pts2 = np.int32(pts2)
F, mask = cv.findFundamentalMat(pts1, pts2, cv.FM_LMEDS)
# We select only inlier points
pts1 = pts1[mask.ravel() == 1]
pts2 = pts2[mask.ravel() == 1]
 
# Find epilines corresponding to points in right image (second image) and
# drawing its lines on left image
lines1 = cv.computeCorrespondEpilines(pts2.reshape(-1, 1, 2), 2, F)
lines1 = lines1.reshape(-1, 3)
img5, img6 = drawlines(img1, img2, lines1, pts1, pts2)
# Find epilines corresponding to points in left image (first image) and
# drawing its lines on right image
lines2 = cv.computeCorrespondEpilines(pts1.reshape(-1, 1, 2), 1, F)
lines2 = lines2.reshape(-1, 3)
img3, img4 = drawlines(img2, img1, lines2, pts2, pts1)
plt.subplot(121), plt.imshow(img5)
plt.subplot(122), plt.imshow(img3)
plt.show()

结果：

我们可以在左侧图像中看到所有Epilines都在右侧图像的一点处收敛。那个汇合点就是极点。