Homography estimation（旋转估计)

以下内容节选自https://bitesofcode.wordpress.com/2017/09/12/augmented-reality-with-python-and-opencv-part-1/comment-page-1/#comment-61

对于上图中，怎么估计\(\begin{bmatrix}h_{11} & h_{12} & h_{13} \\ h_{21} & h_{22} & h_{23} \\ h_{31} & h_{32} & h_{33} \end{bmatrix}\)?
我们可以使用Random Aample Consebsus(RANSAC)

RANSAC算法过程如下：

1. 均匀随机选择点集合中的一部分点；
2. Fit a model to subset
3. find all remaining points that are "close" to the model and reject the rest as outliers
4. do this many times and choose the best model

举个例子，假设我们有一下点集，我们想用使用RANSAC来用一条直线拟合：

算法过程如下：

1. sample (randomly) the number of points required to fit the model
2. solve for model params using samples
3. Score by the fraction of inliers within a present threshold 't' of the model
4. repeat 1-3 until the best model is found with high confidence

运行这个算法的结果图如下，显示了第一次迭代的前三个步骤， 之后的是Score步骤：

对于我们homograpy estimation，

在Opencv中

# assuming matches stores the matches found and 
# returned by bf.match(des_model, des_frame)
# differenciate between source points and destination points
src_pts = np.float32([kp_model[m.queryIdx].pt for m in matches]).reshape(-1, 1, 2)
dst_pts = np.float32([kp_frame[m.trainIdx].pt for m in matches]).reshape(-1, 1, 2)
# compute Homography
M, mask = cv2.findHomography(src_pts, dst_pts, cv2.RANSAC, 5.0)

以上代码中5.0是阈值距离来决定一个匹配是否跟预估的Homography 一致，在预估了homography之后，我们可以投影四个角点：

# Draw a rectangle that marks the found model in the frame
h, w = model.shape
pts = np.float32([[0, 0], [0, h - 1], [w - 1, h - 1], [w - 1, 0]]).reshape(-1, 1, 2)
# project corners into frame
dst = cv2.perspectiveTransform(pts, M)  
# connect them with lines
img2 = cv2.polylines(img_rgb, [np.int32(dst)], True, 255, 3, cv2.LINE_AA) 
cv2.imshow('frame', cap)
cv2.waitKey(0)

结果如下：