使用c++实现sift算法

SIFT算法是一种基于图像特征点的局部特征描述算法，它可以在不同尺度和旋转下提取稳定的特征点，并对特征点进行描述。下面是一个简单的SIFT算法的实现，使用OpenCV库来处理图像。

首先，需要安装OpenCV库。可以使用以下命令在Ubuntu上安装：

sudo apt-get install libopencv-dev

接下来，我们就可以开始编写SIFT算法的实现了。以下是主要步骤：

1. 读取图像并转换为灰度图像。
2. 计算高斯金字塔。
3. 计算差分金字塔。
4. 寻找极值点。
5. 对极值点进行剔除和筛选。
6. 计算特征点的方向。
7. 计算特征点的描述符。

下面是代码实现：

#include <opencv2/opencv.hpp>
#include <iostream>
#include <vector>
#include <cmath>

using namespace cv;
using namespace std;

// 高斯函数
double Gaussian(double x, double y, double sigma) {
    double res = exp(-(x * x + y * y) / (2 * sigma * sigma));
    return res;
}

// 计算高斯核
Mat getGaussianKernel(int size, double sigma) {
    Mat kernel(size, size, CV_64FC1);
    int center = size / 2;
    double sum = 0.0;
    for (int i = 0; i < size; i++) {
        for (int j = 0; j < size; j++) {
            double x = i - center;
            double y = j - center;
            kernel.at<double>(i, j) = Gaussian(x, y, sigma);
            sum += kernel.at<double>(i, j);
        }
    }
    kernel /= sum;
    return kernel;
}

// 计算高斯金字塔
vector<vector<Mat>> getGaussianPyramid(Mat img, int octaves, int levels) {
    vector<vector<Mat>> pyramid(octaves, vector<Mat>(levels));
    double k = pow(2, 1.0 / levels);
    for (int i = 0; i < octaves; i++) {
        Mat down = img.clone();
        for (int j = 0; j < levels; j++) {
            if (i == 0 && j == 0) {
                pyramid[i][j] = down;
            } else if (j == 0) {
                pyrDown(down, pyramid[i][j]);
            } else {
                int size = pow(k, j - 1) * down.cols;
                Size s(size, size);
                pyrDown(down, down, s);
                pyrUp(down, pyramid[i][j], s);
            }
        }
        int size = down.cols / 2;
        Size s(size, size);
        pyrDown(down, down, s);
        img = down;
    }
    return pyramid;
}

// 计算差分金字塔
vector<vector<Mat>> getDifferencePyramid(vector<vector<Mat>> pyramid) {
    vector<vector<Mat>> pyramid_diff(pyramid.size(), vector<Mat>(pyramid[0].size() - 1));
    for (int i = 0; i < pyramid.size(); i++) {
        for (int j = 0; j < pyramid[i].size() - 1; j++) {
            Mat diff = pyramid[i][j + 1] - pyramid[i][j];
            pyramid_diff[i][j] = diff;
        }
    }
    return pyramid_diff;
}

// 判断是否为极值点
bool isExtremum(Mat A, Mat B, Mat C, int x, int y) {
    double value = B.at<double>(x, y);
    if (value > 0) {
        for (int i = -1; i <= 1; i++) {
            for (int j = -1; j <= 1; j++) {
                for (int k = -1; k <= 1; k++) {
                    if (i == 0 && j == 0 && k == 0) {
                        continue;
                    }
                    if (value <= A.at<double>(x + i, y + j) ||
                        value <= B.at<double>(x + i, y + j) ||
                        value <= C.at<double>(x + i, y + j)) {
                        return false;
                    }
                }
            }
        }
        return true;
    } else {
        for (int i = -1; i <= 1; i++) {
            for (int j = -1; j <= 1; j++) {
                for (int k = -1; k <= 1; k++) {
                    if (i == 0 && j == 0 && k == 0) {
                        continue;
                    }
                    if (value >= A.at<double>(x + i, y + j) ||
                        value >= B.at<double>(x + i, y + j) ||
                        value >= C.at<double>(x + i, y + j)) {
                        return false;
                    }
                }
            }
        }
        return true;
    }
}

// 找到极值点
vector<KeyPoint> findExtrema(vector<vector<Mat>> pyramid_diff) {
    vector<KeyPoint> keypoints;
    for (int i = 0; i < pyramid_diff.size(); i++) {
        for (int j = 1; j < pyramid_diff[i].size() - 1; j++) {
            Mat A = pyramid_diff[i][j - 1];
            Mat B = pyramid_diff[i][j];
            Mat C = pyramid_diff[i][j + 1];
            for (int x = 1; x < B.rows - 1; x++) {
                for (int y = 1; y < B.cols - 1; y++) {
                    if (isExtremum(A, B, C, x, y)) {
                        KeyPoint kp(y * pow(2, i), x * pow(2, i), pow(2, j), -1, 0, i);
                        keypoints.push_back(kp);
                    }
                }
            }
        }
    }
    return keypoints;
}

// 计算特征点的方向
void computeOrientation(Mat img, KeyPoint& kp, int bins, double sigma) {
    double angleStep = 2 * M_PI / bins;
    Mat kernel = getGaussianKernel(1 + 2 * ceil(2.5 * sigma), sigma);
    vector<double> hist(bins);
    double maxVal = 0;
    int maxIndex = -1;
    for (int i = 0; i < bins; i++) {
        hist[i] = 0;
        for (int x = -1; x <= 1; x++) {
            for (int y = -1; y <= 1; y++) {
                int px = round(kp.pt.y) + x;
                int py = round(kp.pt.x) + y;
                if (px >= 0 && px < img.rows && py >= 0 && py < img.cols) {
                    double dx = img.at<double>(px, py + 1) - img.at<double>(px, py - 1);
                    double dy = img.at<double>(px - 1, py) - img.at<double>(px + 1, py);
                    double mag = sqrt(dx * dx + dy * dy);
                    double angle = atan2(dy, dx);
                    if (angle < 0) {
                        angle += 2 * M_PI;
                    }
                    int binIndex = floor(angle / angleStep);
                    hist[binIndex] += mag * kernel.at<double>(y + 1, x + 1);
                }
            }
        }
        if (hist[i] > maxVal) {
            maxVal = hist[i];
            maxIndex = i;
        }
    }
    double left = hist[(maxIndex - 1 + bins) % bins];
    double right = hist[(maxIndex + 1) % bins];
    double peak = maxVal / (left + right + maxVal);
    kp.angle = maxIndex * angleStep;
    kp.size /= 2.0;
}

// 计算特征点的描述符
Mat computeDescriptor(Mat img, KeyPoint kp, int bins, double sigma) {
    Mat descriptor(bins, bins, CV_64FC1);
    double angleStep = 2 * M_PI / bins;
    Mat kernel = getGaussianKernel(1 + 2 * ceil(2.5 * sigma), sigma);
    double dx[bins], dy[bins];
    for (int i = 0; i < bins; i++) {
        dx[i] = cos(i * angleStep);
        dy[i] = sin(i * angleStep);
    }
    for (int i = -bins / 2; i < bins / 2; i++) {
        for (int j = -bins / 2; j < bins / 2; j++) {
            double hist[bins];
            for (int k = 0; k < bins; k++) {
                hist[k] = 0;
            }
            for (int x = -2; x <= 1; x++) {
                for (int y = -2; y <= 1; y++) {
                    int px = round(kp.pt.y + i * kp.size / bins) + x;
                    int py = round(kp.pt.x + j * kp.size / bins) + y;
                    if (px >= 0 && px < img.rows && py >= 0 && py < img.cols) {
                        double dx_p = img.at<double>(px, py + 1) - img.at<double>(px, py - 1);
                        double dy_p = img.at<double>(px - 1, py) - img.at<double>(px + 1, py);
                        double mag = sqrt(dx_p * dx_p + dy_p * dy_p);
                        double angle = atan2(dy_p, dx_p);
                        if (angle < 0) {
                            angle += 2 * M_PI;
                        }
                        int binIndex = floor(angle / angleStep);
                        double weight = kernel.at<double>(y + 2, x + 2) * mag;
                        hist[binIndex] += weight;
                    }
                }
            }
            for (int k = 0; k < bins; k++) {
                descriptor.at<double>(i + bins / 2, j + bins / 2) += hist[k] * dx[k];
                descriptor.at<double>(i + bins / 2, j + bins / 2) += hist[k] * dy[k];
            }
        }
    }
    normalize(descriptor, descriptor, 1, 0, NORM_L2);
    return descriptor;
}

// 主函数
int main(int argc, char** argv) {
    Mat img = imread(argv[1], IMREAD_GRAYSCALE);
    if (img.empty()) {
        cout << "Can't read image" << endl;
        return -1;
    }
    img.convertTo(img, CV_64FC1);
    vector<vector<Mat>> pyramid = getGaussianPyramid(img, 4, 5);
    vector<vector<Mat>> pyramid_diff = getDifferencePyramid(pyramid);
    vector<KeyPoint> keypoints = findExtrema(pyramid_diff);
    for (int i = 0; i < keypoints.size(); i++) {
        computeOrientation(pyramid[keypoints[i].octave][keypoints[i].level], keypoints[i], 8, 1.5);
        Mat descriptor = computeDescriptor(pyramid[keypoints[i].octave][keypoints[i].level], keypoints[i], 4, 1.5);
        keypoints[i].response = descriptor.at<double>(1, 1);
    }
    Mat result;
    drawKeypoints(img, keypoints, result);
    imshow("SIFT keypoints", result);
    waitKey(0);
    return 0;
}

注意，此代码仅供参考，可能需要根据具体情况进行修改和优化。