编写matlab实现SIFT

由于SIFT算法是一种较为复杂的图像特征提取算法，需要用到多种图像处理和计算方法，因此编写SIFT算法的MATLAB代码相对较为困难，需要具备较高的编程和计算机视觉知识。以下是一些可能的步骤和代码片段，但并不是完整的SIFT算法实现。

1. 读取图像

可以使用MATLAB的imread函数读取待处理的图像，并将其转换为灰度图像。

img = imread('img.jpg');
grayImg = rgb2gray(img);

2. 构建高斯金字塔

可以使用MATLAB的imresize函数进行图像缩放，然后使用fspecial函数生成高斯滤波器，最后使用imfilter函数进行卷积操作。

sigma = 1.6;
numOctaves = 4;
numScales = 5;
k = 2^(1/numScales);
scaleSpace = cell(numOctaves, numScales+3);

for i = 1:numOctaves
    for j = 1:numScales+3
        if i == 1 && j == 1
            scaleSpace{i,j} = grayImg;
        elseif j == 1
            scaleSpace{i,j} = imresize(scaleSpace{i-1,end-2}, 0.5);
        else
            sigmaPrev = sigma * k^(j-2);
            sigmaCurr = sigma * k^(j-1);
            h = fspecial('gaussian', [ceil(6 * sigmaCurr), ceil(6 * sigmaCurr)], sigmaCurr);
            scaleSpace{i,j} = imfilter(scaleSpace{i,j-1}, h, 'replicate');
        end
    end
end

3. 构建DoG金字塔

可以使用MATLAB的diff函数计算高斯金字塔相邻两层的差分图像，即DoG金字塔。

dogPyramid = cell(numOctaves, numScales+2);

for i = 1:numOctaves
    for j = 1:numScales+2
        dogPyramid{i,j} = scaleSpace{i,j+1} - scaleSpace{i,j};
    end
end

4. 寻找关键点

可以使用MATLAB的imregionalmax函数寻找DoG金字塔中的局部极值点，并使用一些条件对这些点进行筛选，得到稳定的关键点。

threshold = 0.01;
edgeThreshold = 10;
keypoints = cell(numOctaves, 1);

for i = 1:numOctaves
    [height, width] = size(dogPyramid{i,1});
    [X, Y] = meshgrid(1:width, 1:height);
    for j = 2:numScales+1
        % Find local maxima
        isMaxima = imregionalmax(dogPyramid{i,j});
        [x, y] = find(isMaxima);
        % Discard points near image edges
        keep = (x > edgeThreshold) & (y > edgeThreshold) & (x < height - edgeThreshold) & (y < width - edgeThreshold);
        x = x(keep);
        y = y(keep);
        % Discard points with low contrast
        idx = sub2ind([height, width], x, y);
        contrast = abs(dogPyramid{i,j}(idx));
        keep = contrast > threshold;
        x = x(keep);
        y = y(keep);
        % Discard points with low ratio of principal curvatures
        H = hessian3D(dogPyramid{i,j}, 1);
        curvatureRatio = (H(:,1) .* H(:,3) - H(:,2).^2) ./ (H(:,1) + H(:,3)).^2;
        keep = curvatureRatio < 12.1;
        x = x(keep);
        y = y(keep);
        % Add points to the list
        octaveIdx = repmat(i, size(x));
        scaleIdx = repmat(j-1, size(x));
        keypoints{i} = [keypoints{i}; x, y, scaleIdx, octaveIdx, contrast];
    end
end

5. 计算关键点的SIFT描述子

可以使用MATLAB的vl_sift函数计算关键点的SIFT描述子，得到一个128维的向量。

numKeypoints = size(keypoints, 1);
descriptors = zeros(numKeypoints, 128);

for i = 1:numKeypoints
    x = keypoints(i,1);
    y = keypoints(i,2);
    scale = keypoints(i,3);
    octave = keypoints(i,4);
    patchSize = 2^(octave-1) * 15;
    patch = imcrop(scaleSpace{octave,scale+1}, [y-patchSize/2, x-patchSize/2, patchSize-1, patchSize-1]);
    [frames, descriptors(i,:)] = vl_sift(single(patch));
    keypoints(i,1:2) = keypoints(i,1:2) + frames(1:2,:);
end