OpenCV中的對極幾何

在上個教程中我們已經簡述了對極幾何的一些理論知識，本次我們來使用OpenCV中的一些函式來進行實戰，為了得到基礎矩陣我們應該在兩幅影象中找到儘量多的匹配點。我們可以使用 SIFT 描述符，FLANN 匹配器和比值檢測。

我們使用示例圖片：

先看程式碼：

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)

現在得到了一個匹配點列表，我們就可以使用它來計算基礎矩陣了。

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

· points1：從第一張圖片開始的N個點的陣列。點座標應該是浮點數(單精度或雙精度)。

· points2：與點1大小和格式相同的第二影象點的陣列。

· method：計算基本矩陣的方法。

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

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

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

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

· ransacReprojThreshold：僅用於RANSAC方法的引數，預設3。它是一個點到極線的最大距離(以畫素為單位)，超過這個點就被認為是一個離群點，不用於計算最終的基本矩陣。根據點定位、影象解析度和影象噪聲的準確性，可以將其設定為1-3左右。

· confidence：僅用於RANSAC和LMedS方法的引數，預設0.99。它指定了一個理想的置信水平(概率)，即估計矩陣是正確的。

· mask：輸出

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]

下一步我們要找到極線。我們會得到一個包含很多線的陣列。所以我們要 定義一個新的函式將這些線繪製到影象中。

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

現在我們兩幅影象中計算並繪製極線。

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

· points：輸入點。型別為CV_32FC2N×1或1×N矩陣。

· whichImage：包含點的影象(1或2)的索引。

· F：基本矩陣，可使用findFundamentalMat或stereoRectify 進行估計。

· lines：對應於另一幅影象中點的極線的輸出向量（a，b，c）表示直線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()

最終整個程式：

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()

結果：

我們可以在左側影象中看到所有Epilines都在右側影象的一點處收斂。那個匯合點就是極點。