EEPW论坛

OpenCV-Python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_7POINTfor a 7-point algorithm. N=7

·cv2.FM_8POINTfor an 8-point algorithm. N≥8

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

·cv2.FM_LMEDSfor 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。