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# AKAZE local features matching

## Introduction

In this tutorial we will learn how to use [AKAZE] local features to detect and match keypoints on two images.

We will find keypoints on a pair of images with given homography matrix, match them and count the number of inliers (i. e. matches that fit in the given homography).

You can find expanded version of this example here: https://github.com/pablofdezalc/test_kaze_akaze_opencv

[AKAZE] | Fast Explicit Diffusion for Accelerated Features in Nonlinear Scale Spaces. Pablo F. Alcantarilla, Jesús Nuevo and Adrien Bartoli. In British Machine Vision Conference (BMVC), Bristol, UK, September 2013.

## Data

We are going to use images 1 and 3 from Graffity sequence of Oxford dataset.

Homography is given by a 3 by 3 matrix:

    7.6285898e-01  -2.9922929e-01   2.2567123e+02
    3.3443473e-01   1.0143901e+00  -7.6999973e+01
    3.4663091e-04  -1.4364524e-05   1.0000000e+00

You can find the images (graf1.png, graf3.png) and homography (H1to3p.xml) in opencv/samples/cpp.

### Source Code

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    #include <opencv2/features2d.hpp>
    #include <opencv2/imgcodecs.hpp>
    #include <opencv2/opencv.hpp>
    #include <vector>
    #include <iostream>

    using namespace std;
    using namespace cv;

    const float inlier_threshold = 2.5f; // Distance threshold to identify inliers
    const float nn_match_ratio = 0.8f;   // Nearest neighbor matching ratio

    int main(void)
    {
        Mat img1 = imread("../data/graf1.png", IMREAD_GRAYSCALE);
        Mat img2 = imread("../data/graf3.png", IMREAD_GRAYSCALE);

        Mat homography;
        FileStorage fs("../data/H1to3p.xml", FileStorage::READ);
        fs.getFirstTopLevelNode() >> homography;

        vector<KeyPoint> kpts1, kpts2;
        Mat desc1, desc2;

        Ptr<AKAZE> akaze = AKAZE::create();
        akaze->detectAndCompute(img1, noArray(), kpts1, desc1);
        akaze->detectAndCompute(img2, noArray(), kpts2, desc2);

        BFMatcher matcher(NORM_HAMMING);
        vector< vector<DMatch> > nn_matches;
        matcher.knnMatch(desc1, desc2, nn_matches, 2);

        vector<KeyPoint> matched1, matched2, inliers1, inliers2;
        vector<DMatch> good_matches;
        for(size_t i = 0; i < nn_matches.size(); i++) {
            DMatch first = nn_matches[i][0];
            float dist1 = nn_matches[i][0].distance;
            float dist2 = nn_matches[i][1].distance;

            if(dist1 < nn_match_ratio * dist2) {
                matched1.push_back(kpts1[first.queryIdx]);
                matched2.push_back(kpts2[first.trainIdx]);
            }
        }

        for(unsigned i = 0; i < matched1.size(); i++) {
            Mat col = Mat::ones(3, 1, CV_64F);
            col.at<double>(0) = matched1[i].pt.x;
            col.at<double>(1) = matched1[i].pt.y;

            col = homography * col;
            col /= col.at<double>(2);
            double dist = sqrt( pow(col.at<double>(0) - matched2[i].pt.x, 2) +
                                pow(col.at<double>(1) - matched2[i].pt.y, 2));

            if(dist < inlier_threshold) {
                int new_i = static_cast<int>(inliers1.size());
                inliers1.push_back(matched1[i]);
                inliers2.push_back(matched2[i]);
                good_matches.push_back(DMatch(new_i, new_i, 0));
            }
        }

        Mat res;
        drawMatches(img1, inliers1, img2, inliers2, good_matches, res);
        imwrite("res.png", res);

        double inlier_ratio = inliers1.size() * 1.0 / matched1.size();
        cout << "A-KAZE Matching Results" << endl;
        cout << "*******************************" << endl;
        cout << "# Keypoints 1:                        \t" << kpts1.size() << endl;
        cout << "# Keypoints 2:                        \t" << kpts2.size() << endl;
        cout << "# Matches:                            \t" << matched1.size() << endl;
        cout << "# Inliers:                            \t" << inliers1.size() << endl;
        cout << "# Inliers Ratio:                      \t" << inlier_ratio << endl;
        cout << endl;

        return 0;
    }

### Explanation

1. Load images and homography

>     Mat img1 = imread("graf1.png", IMREAD_GRAYSCALE);
>     Mat img2 = imread("graf3.png", IMREAD_GRAYSCALE);

>     Mat homography;
>     FileStorage fs("H1to3p.xml", FileStorage::READ);
>     fs.getFirstTopLevelNode() >> homography;

> We are loading grayscale images here. Homography is stored in the xml created with FileStorage.

1. Detect keypoints and compute descriptors using AKAZE

>     vector<KeyPoint> kpts1, kpts2;
>     Mat desc1, desc2;

>     AKAZE akaze;
>     akaze(img1, noArray(), kpts1, desc1);
>     akaze(img2, noArray(), kpts2, desc2);

> We create AKAZE object and use it’s operator() functionality. Since we don’t need the mask parameter, noArray() is used.

1. Use brute-force matcher to find 2-nn matches

>     BFMatcher matcher(NORM_HAMMING);
>     vector< vector<DMatch> > nn_matches;
>     matcher.knnMatch(desc1, desc2, nn_matches, 2);

> We use Hamming distance, because AKAZE uses binary descriptor by default.

1. Use 2-nn matches to find correct keypoint matches

>     for(size_t i = 0; i < nn_matches.size(); i++) {
>         DMatch first = nn_matches[i][0];
>         float dist1 = nn_matches[i][0].distance;
>         float dist2 = nn_matches[i][1].distance;

>         if(dist1 < nn_match_ratio * dist2) {
>             matched1.push_back(kpts1[first.queryIdx]);
>             matched2.push_back(kpts2[first.trainIdx]);
>         }
>     }

> If the closest match is ratio closer than the second closest one, then the match is correct.

1. Check if our matches fit in the homography model

>     for(int i = 0; i < matched1.size(); i++) {
>         Mat col = Mat::ones(3, 1, CV_64F);
>         col.at<double>(0) = matched1[i].pt.x;
>         col.at<double>(1) = matched1[i].pt.y;

>         col = homography * col;
>         col /= col.at<double>(2);
>         float dist = sqrt( pow(col.at<double>(0) - matched2[i].pt.x, 2) +
>                            pow(col.at<double>(1) - matched2[i].pt.y, 2));

>         if(dist < inlier_threshold) {
>             int new_i = inliers1.size();
>             inliers1.push_back(matched1[i]);
>             inliers2.push_back(matched2[i]);
>             good_matches.push_back(DMatch(new_i, new_i, 0));
>         }
>     }

> If the distance from first keypoint’s projection to the second keypoint is less than threshold, then it it fits in the homography.

> We create a new set of matches for the inliers, because it is required by the drawing function.

1. Output results

>     Mat res;
>     drawMatches(img1, inliers1, img2, inliers2, good_matches, res);
>     imwrite("res.png", res);
>     ...

> Here we save the resulting image and print some statistics.

### Results

## Found matches

## A-KAZE Matching Results

> ::code-block:: none
>   Keypoints 1: 2943 Keypoints 2: 3511 Matches: 447 Inliers: 308 Inlier Ratio: 0.689038

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