一、原理

【计算机视觉】基础矩阵、外极线寻找最佳匹配

二、代码

功能：计算图像对的特征匹配，并估计基础矩阵。使用外极线作为第二个输入，通过在外极线上对每个特征点寻找最佳的匹配来找到更多的匹配。

from PIL import Image
from numpy import *
from pylab import *
import numpy as np

from PCV.geometry import camera
from PCV.geometry import homography
from PCV.geometry import sfm
from PCV.localdescriptors import sift
from imp import reload

camera = reload(camera)
homography = reload(homography)
sfm = reload(sfm)
sift = reload(sift)

# Read features
im1 = array(Image.open('images4/1.jpg'))
sift.process_image('images4/1.jpg', 'im1.sift')

im2 = array(Image.open('images4/2.jpg'))
sift.process_image('images4/2.jpg', 'im2.sift')

l1, d1 = sift.read_features_from_file('im1.sift')
l2, d2 = sift.read_features_from_file('im2.sift')

matches = sift.match_twosided(d1, d2)
ndx = matches.nonzero()[0]

x1 = homography.make_homog(l1[ndx, :2].T)
ndx2 = [int(matches[i]) for i in ndx]
x2 = homography.make_homog(l2[ndx2, :2].T)

d1n = d1[ndx]
d2n = d2[ndx2]
x1n = x1.copy()
x2n = x2.copy()

figure(figsize=(16,16))
sift.plot_matches(im1, im2, l1, l2, matches, True)
show()

#def F_from_ransac(x1, x2, model, maxiter=5000, match_threshold=1e-6):
def F_from_ransac(x1, x2, model, maxiter=5000, match_threshold=1e-6):
    """ Robust estimation of a fundamental matrix F from point
    correspondences using RANSAC (ransac.py from
    http://www.scipy.org/Cookbook/RANSAC).

    input: x1, x2 (3*n arrays) points in hom. coordinates. """

    from PCV.tools import ransac
    data = np.vstack((x1, x2))
    d = 10 # 20 is the original
    # compute F and return with inlier index
    F, ransac_data = ransac.ransac(data.T, model,
                                   8, maxiter, match_threshold, d, return_all=True)
    return F, ransac_data['inliers']


# find F through RANSA43C
model = sfm.RansacModel()
F, inliers = F_from_ransac(x1n, x2n, model, maxiter=5000, match_threshold=1e-3)
print (F)


P1 = array([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0]])
P2 = sfm.compute_P_from_fundamental(F)#Computes the second camera matrix 


print (P2)
print (F)


# triangulate inliers and remove points not in front of both cameras
X = sfm.triangulate(x1n[:, inliers], x2n[:, inliers], P1, P2)



# plot the projection of X
cam1 = camera.Camera(P1)
cam2 = camera.Camera(P2)
x1p = cam1.project(X)
x2p = cam2.project(X)


figure(figsize=(16, 16))
imj = sift.appendimages(im1, im2)
imj = vstack((imj, imj))

imshow(imj)

cols1 = im1.shape[1]
rows1 = im1.shape[0]
for i in range(len(x1p[0])):
    if (0<= x1p[0][i]<cols1) and (0<= x2p[0][i]<cols1) and (0<=x1p[1][i]<rows1) and (0<=x2p[1][i]<rows1):
        plot([x1p[0][i], x2p[0][i]+cols1],[x1p[1][i], x2p[1][i]],'c')
axis('off')
show()


d1p = d1n[inliers]
d2p = d2n[inliers]


# Read features
im3 = array(Image.open('images4/3.jpg'))
sift.process_image('images4/3.jpg', 'im3.sift')
l3, d3 = sift.read_features_from_file('im3.sift')

matches13 = sift.match_twosided(d1p, d3)


ndx_13 = matches13.nonzero()[0]
x1_13 = homography.make_homog(x1p[:, ndx_13])
ndx2_13 = [int(matches13[i]) for i in ndx_13]
x3_13 = homography.make_homog(l3[ndx2_13, :2].T)

figure(figsize=(16, 16))
imj = sift.appendimages(im1, im3)
imj = vstack((imj, imj))#vstack函数功能：垂直（按照行顺序）地把数组给堆叠起来

imshow(imj)

cols1 = im1.shape[1]
rows1 = im1.shape[0]
for i in range(len(x1_13[0])):
    if (0<= x1_13[0][i]<cols1) and (0<= x3_13[0][i]<cols1) and (0<=x1_13[1][i]<rows1) and (0<=x3_13[1][i]<rows1):
        plot([x1_13[0][i], x3_13[0][i]+cols1],[x1_13[1][i], x3_13[1][i]],'c')
axis('off')
show()

P3 = sfm.compute_P(x3_13, X[:, ndx_13])

print (P3)

print (P1)
print (P2)
print (P3)