【翻译：OpenCV-Python教程】SIFT(Scale-Invariant Feature Transform) 介绍
⚠️由于自己的拖延症，3.4.3翻到一半，OpenCV发布了4.0.1了正式版，所以接下来是按照4.0.1翻译的。
⚠️除了版本之外，其他还是照旧，Introduction to SIFT (Scale-Invariant Feature Transform)，附原文。
目标
在本章，
- 我们将会学习 SIFT 算法的概念
- 我们将学着找出 SIFT 的关键点以及描述符
理论
在前两章，我们看到了一些角点检测的算法，比如哈里斯等等。这些算法都是旋转-不变的，意思就是说，即使图像有旋转，我们也能找出相同的角点。这是明摆着的事，因为在旋转之后的图像中，角点还是角点，但如果图像放缩呢？一个角点有可能在放缩之后就不再是一个角点了。例如下面这个图，在一张小图片中的角被放大之后，从一个与之前图片同样大小的窗口中看上去就感觉是平的了。所以哈里斯角并不是放缩-不变的。
于是，在2004年，英属哥伦比亚大学的D.Lowe，在他的论文 Distinctive Image Features from Scale-Invariant Keypoints (从比例不变的关键点获取的独特的图像特征)中想出了一个新的算法，Scale Invariant Feature Transform (SIFT)(译者注：放缩不变的特征转换，缩写是“筛选”)，这个算法提取了一些关键点并且比较了他们的描述符。*(这篇论文非常简单易懂，被认为是学习 SIFT 可用的最佳教材。因此本篇的解释就仅仅是该论文的一个小小摘要)*.
在 SIFT 算法中主要涉及的步骤有4个。我们会一个一个的来看它们。
1. 放缩空间极值检测
From the image above, it is obvious that we can't use the same window to detect keypoints with different scale. It is OK with small corner. But to detect larger corners we need larger windows. For this, scale-space filtering is used. In it, Laplacian of Gaussian is found for the image with various σ values. LoG acts as a blob detector which detects blobs in various sizes due to change in σ. In short, σ acts as a scaling parameter. For eg, in the above image, gaussian kernel with low σ gives high value for small corner while gaussian kernel with high σ fits well for larger corner. So, we can find the local maxima across the scale and space which gives us a list of (x,y,σ) values which means there is a potential keypoint at (x,y) at σ scale.
But this LoG is a little costly, so SIFT algorithm uses Difference of Gaussians which is an approximation of LoG. Difference of Gaussian is obtained as the difference of Gaussian blurring of an image with two different σ, let it be σ and kσ. This process is done for different octaves of the image in Gaussian Pyramid. It is represented in below image:
image
Once this DoG are found, images are searched for local extrema over scale and space. For eg, one pixel in an image is compared with its 8 neighbours as well as 9 pixels in next scale and 9 pixels in previous scales. If it is a local extrema, it is a potential keypoint. It basically means that keypoint is best represented in that scale. It is shown in below image:
image
Regarding different parameters, the paper gives some empirical data which can be summarized as, number of octaves = 4, number of scale levels = 5, initial σ=1.6, k=2‾√ etc as optimal values.
2. 关键点定位
Once potential keypoints locations are found, they have to be refined to get more accurate results. They used Taylor series expansion of scale space to get more accurate location of extrema, and if the intensity at this extrema is less than a threshold value (0.03 as per the paper), it is rejected. This threshold is called contrastThreshold in OpenCV
DoG has higher response for edges, so edges also need to be removed. For this, a concept similar to Harris corner detector is used. They used a 2x2 Hessian matrix (H) to compute the principal curvature. We know from Harris corner detector that for edges, one eigen value is larger than the other. So here they used a simple function,
If this ratio is greater than a threshold, called edgeThreshold in OpenCV, that keypoint is discarded. It is given as 10 in paper.
So it eliminates any low-contrast keypoints and edge keypoints and what remains is strong interest points.
3. Orientation Assignment
Now an orientation is assigned to each keypoint to achieve invariance to image rotation. A neighbourhood is taken around the keypoint location depending on the scale, and the gradient magnitude and direction is calculated in that region. An orientation histogram with 36 bins covering 360 degrees is created (It is weighted by gradient magnitude and gaussian-weighted circular window with σ equal to 1.5 times the scale of keypoint). The highest peak in the histogram is taken and any peak above 80% of it is also considered to calculate the orientation. It creates keypoints with same location and scale, but different directions. It contribute to stability of matching.
4. 关键点描述
Now keypoint descriptor is created. A 16x16 neighbourhood around the keypoint is taken. It is divided into 16 sub-blocks of 4x4 size. For each sub-block, 8 bin orientation histogram is created. So a total of 128 bin values are available. It is represented as a vector to form keypoint descriptor. In addition to this, several measures are taken to achieve robustness against illumination changes, rotation etc.
5. 关键点匹配
Keypoints between two images are matched by identifying their nearest neighbours. But in some cases, the second closest-match may be very near to the first. It may happen due to noise or some other reasons. In that case, ratio of closest-distance to second-closest distance is taken. If it is greater than 0.8, they are rejected. It eliminates around 90% of false matches while discards only 5% correct matches, as per the paper.
So this is a summary of SIFT algorithm. For more details and understanding, reading the original paper is highly recommended. Remember one thing, this algorithm is patented. So this algorithm is included in the opencv contrib repo
OpenCV里的SIFT
So now let's see SIFT functionalities available in OpenCV. Let's start with keypoint detection and draw them. First we have to construct a SIFT object. We can pass different parameters to it which are optional and they are well explained in docs.
import numpy as np
import cv2 as cv
img = cv.imread('home.jpg')
gray= cv.cvtColor(img,cv.COLOR_BGR2GRAY)
sift = cv.xfeatures2d.SIFT_create()
kp = sift.detect(gray,None)
img=cv.drawKeypoints(gray,kp,img)
cv.imwrite('sift_keypoints.jpg',img)
sift.detect() function finds the keypoint in the images. You can pass a mask if you want to search only a part of image. Each keypoint is a special structure which has many attributes like its (x,y) coordinates, size of the meaningful neighbourhood, angle which specifies its orientation, response that specifies strength of keypoints etc.
OpenCV also provides cv.drawKeyPoints() function which draws the small circles on the locations of keypoints. If you pass a flag, cv.DRAW_MATCHES_FLAGS_DRAW_RICH_KEYPOINTS to it, it will draw a circle with size of keypoint and it will even show its orientation. See below example.
img=cv.drawKeypoints(gray,kp,img,flags=cv.DRAW_MATCHES_FLAGS_DRAW_RICH_KEYPOINTS)
cv.imwrite('sift_keypoints.jpg',img)
See the two results below:
image
Now to calculate the descriptor, OpenCV provides two methods.
- Since you already found keypoints, you can call sift.compute() which computes the descriptors from the keypoints we have found. Eg: kp,des = sift.compute(gray,kp)
- If you didn't find keypoints, directly find keypoints and descriptors in a single step with the function, sift.detectAndCompute().
We will see the second method:
sift = cv.xfeatures2d.SIFT_create()
kp, des = sift.detectAndCompute(gray,None)
Here kp will be a list of keypoints and des is a numpy array of shape Number_of_Keypoints×128.
So we got keypoints, descriptors etc. Now we want to see how to match keypoints in different images. That we will learn in coming chapters.