SIFT（Scale-invariant feature transform）是一種檢測區域性特徵的演算法，該演算法通過求一幅圖中的特徵點（interest points,or corner points）及其有關scale 和 orientation 的描述子得到特徵並進行影象特徵點匹配，獲得了良好效果，詳細解析如下：

1、演算法描述
SIFT特徵不只具有尺度不變性，即使改變旋轉角度，影象亮度或拍攝視角，仍然能夠得到好的檢測效果。整個演算法分為以下幾個部分：
（1）構造尺度空間：DoG尺度空間
（2）檢測DoG尺度空間極值點
（3）去除不好的特徵點
（4）給特徵點賦值一個128維的方向引數。每個關鍵點都包含三個資訊：位置、尺度和方向。
（5）關鍵點描述子的生成：
首先將座標軸旋轉為關鍵點的方向，以確保旋轉不變性。以關鍵點為中心取8×8的視窗。
（6）最後進行特徵匹配。當兩幅影象的SIFT特徵向量（128維）生成後，採用關鍵點特徵向量的歐式聚類來作為相似性判定度量。
取影象1中的某個關鍵點，並找出其與影象2中歐式距離最近的前兩個關鍵點，在這兩個關鍵點中，如果最近的距離除以次近的距離少於某個比例閾值，則接受這一對匹配點。降低這個比例閾值，SIFT匹配點數目會減少，但更加穩定。

2、演算法實現：
（一） SIFT的Matlab程式碼實現：

% [image, descriptors, locs] = sift(imageFile)
%
% This function reads an image and returns its SIFT keypoints.
%   Input parameters:
%     imageFile: the file name for the image.
%
%   Returned:
%     image: the image array in double format
%     descriptors: a K-by
 
-128 matrix, where each row gives an invariant
%         descriptor for one of the K keypoints.  The descriptor is a vector
%         of 128 values normalized to unit length.
%     locs: K-by-4 matrix, in which each row has the 4 values for a
%         keypoint location (row, column, scale, orientation).  The
%         orientation is
 
 in the range [-PI, PI] radians.
%
% Credits: Thanks for initial version of this program to D. Alvaro and
%          J.J. Guerrero, Universidad de Zaragoza (modified by D. Lowe)

function [image, descriptors, locs] = sift(imageFile)

% Load image
image = imread(imageFile);

% If you have the Image Processing Toolbox, you can uncomment the following
%   lines to allow input of color images, which will be converted to grayscale.
% if isrgb(image)
%    image = rgb2gray(image);
% end

[rows, cols] = size(image);

% Convert into PGM imagefile, readable by "keypoints" executable
f = fopen('tmp.pgm', 'w');
if f == -1
    error('Could not create file tmp.pgm.');
end
fprintf(f, 'P5\n%d\n%d\n255\n', cols, rows);
fwrite(f, image', 'uint8');
fclose(f);

% Call keypoints executable
if isunix
    command = '!./sift ';
else
    command = '!siftWin32 ';
end
command = [command ' <tmp.pgm >tmp.key'];
eval(command);

% Open tmp.key and check its header
g = fopen('tmp.key', 'r');
if g == -1
    error('Could not open file tmp.key.');
end
[header, count] = fscanf(g, '%d %d', [1 2]);
if count ~= 2
    error('Invalid keypoint file beginning.');
end
num = header(1);
len = header(2);
if len ~= 128
    error('Keypoint descriptor length invalid (should be 128).');
end

% Creates the two output matrices (use known size for efficiency)
locs = double(zeros(num, 4));
descriptors = double(zeros(num, 128));

% Parse tmp.key
for i = 1:num
    [vector, count] = fscanf(g, '%f %f %f %f', [1 4]); %row col scale ori
    if count ~= 4
        error('Invalid keypoint file format');
    end
    locs(i, :) = vector(1, :);

    [descrip, count] = fscanf(g, '%d', [1 len]);
    if (count ~= 128)
        error('Invalid keypoint file value.');
    end
    % Normalize each input vector to unit length
    descrip = descrip / sqrt(sum(descrip.^2));
    descriptors(i, :) = descrip(1, :);
end
fclose(g);

使用方法：
1.尋找影象中的sift特徵：

[image,descrips,locs] = sift('scene.pgm');
showkeys(image,locs);

scene.pgm

book.pgm

2、對兩幅圖中的sift特徵進行匹配

match(‘scene.pgm’,’book.pgm’);
由於scene和book兩幅圖中有相同的一本書，但是方向和尺度都不同，從匹配結果可以看出去sift特徵匹配檢測效果非常好滴！

（二）SIFT的Python實現：

import cv2
import numpy as np
import pdb
pdb.set_trace()#turn on the pdb prompt

#read image
img = cv2.imread('E:\OpenCV\Picture\sky.jpg',cv2.IMREAD_COLOR)
gray = cv2.cvtColor(img,cv2.COLOR_BGR2GRAY)
cv2.imshow('origin',img);

#SIFT
detector = cv2.SIFT() #呼叫SIFT特徵描述子
keypoints = detector.detect(gray,None)#檢測興趣點
img = cv2.drawKeypoints(gray,keypoints)#畫出興趣點
#img = cv2.drawKeypoints(gray,keypoints,flags = cv2.DRAW_MATCHES_FLAGS_DRAW_RICH_KEYPOINTS)
cv2.imshow('test',img);
cv2.waitKey(0)
cv2.destroyAllWindows()

測試：

實驗結果：

（三）SIFT的OpenCV實現

#include <opencv2/opencv.hpp>
#include <opencv2/core/core.hpp>
#include <opencv2/imgproc/imgproc.hpp>
#include <opencv2/highgui/highgui.hpp>
#include <iostream>
#include <opencv2/features2d/features2d.hpp>
#include <opencv2/legacy/legacy.hpp>
#include <opencv2/nonfree/nonfree.hpp>
#include <vector>
using namespace std;
using namespace cv;
int main(void)
{
       cout << "當前使用的OpenCV版本：" << CV_VERSION << endl;
       Mat image = imread("scene.pgm");
       Mat image2 = imread("book.pgm");
       if (image.empty())
       {
              fprintf(stderr, "Cannot load image %s \n", "scene.pgm");
              return -1;
       }
       if (image2.empty())
       {
              fprintf(stderr, "Cannot load image %s \n", "book.pgm");
              return -1;
       }
       //顯示影象
       imshow("image before", image);
       waitKey(10);
       imshow("image2 before", image2);
       waitKey(10);
       //sift特徵點檢測
       SiftFeatureDetector siftdtc;
       vector<KeyPoint> kp1, kp2;
       siftdtc.detect(image, kp1);
       Mat outimg1;
       drawKeypoints(image, kp1, outimg1);
       imshow("image1 keypoints", outimg1);
       siftdtc.detect(image2, kp2);
       Mat outimg2;
       drawKeypoints(image2, kp2, outimg2);
       imshow("image2 keypoints", outimg2);
       //生成描述子
       SiftDescriptorExtractor ext;
       Mat descp1, descp2;
       BruteForceMatcher<L2<float>> matcher;
       vector<DMatch> matches;
       Mat img_matches;
       ext.compute(image, kp1, descp1);
       ext.compute(image2, kp2, descp2);
       imshow("desc", descp1);
       waitKey(10);
       //cout << endl << descp1 << endl;
       matcher.match(descp1, descp2, matches);

       drawMatches(image, kp1, image2, kp2, matches, img_matches);
       imshow("matches", img_matches);
       waitKey(10);
       //namedWindow("My Image");
       //imshow("My Image",image);
       //waitKey(0);
       //Mat result,image2,image3;
       //result = image;
       //image2 = result;
       //result.copyTo(image3);
       //flip(image, result, 1);//正數水平翻轉，0表示垂直翻轉，負數表示既有水平也有垂直翻轉
       //namedWindow("Output window");
       //imshow("Output window", result);
       //namedWindow("1");
       //imshow("1", image2);
       //namedWindow("2");
       //imshow("2", image3);
       waitKey(0);
       return 0;
}