MATLb形状相似系数代码

MATLAB中可以使用几何矩、中心矩和Hu不变矩来计算形状相似系数。下面是一个示例代码：

% 计算形状相似系数
function similarity = shape_similarity(image1, image2)
    % 计算图像1的Hu不变矩
    hu1 = compute_hu_moments(image1);
    
    % 计算图像2的Hu不变矩
    hu2 = compute_hu_moments(image2);
    
    % 计算形状相似系数
    similarity = sum((hu1 - hu2).^2);
end

% 计算Hu不变矩
function hu_moments = compute_hu_moments(image)
    % 计算图像的二阶和三阶中心矩
    moments = compute_central_moments(image);
    
    % 计算Hu不变矩
    hu_moments = zeros(7, 1);
    hu_moments(1) = moments(3, 1) + moments(1, 3);
    hu_moments(2) = (moments(3, 1) - moments(1, 3))^2 + 4*moments(2, 2)^2;
    hu_moments(3) = (moments(4, 1) - 3*moments(2, 3))^2 + (3*moments(3, 2) - moments(1, 4))^2;
    hu_moments(4) = (moments(4, 1) + moments(2, 3))^2 + (moments(3, 2) + moments(1, 4))^2;
    hu_moments(5) = (moments(4, 1) - 3*moments(2, 3))*(moments(4, 1) + moments(2, 3))*((moments(4, 1) + moments(2, 3))^2 - 3*(moments(3, 2) + moments(1, 4))^2) + (3*moments(3, 2) - moments(1, 4))*(moments(3, 2) + moments(1, 4))*(3*(moments(4, 1) + moments(2, 3))^2 - (moments(3, 2) + moments(1, 4))^2);
    hu_moments(6) = (moments(3, 1) - moments(1, 3))*((moments(4, 1) + moments(2, 3))^2 - (moments(3, 2) + moments(1, 4))^2) + 4*moments(2, 2)*(moments(4, 1) + moments(2, 3))*(moments(3, 2) + moments(1, 4));
    hu_moments(7) = (3*moments(3, 2) - moments(1, 4))*(moments(4, 1) + moments(2, 3))*((moments(4, 1) + moments(2, 3))^2 - 3*(moments(3, 2) + moments(1, 4))^2) - (moments(4, 1) - 3*moments(2, 3))*(moments(3, 2) + moments(1, 4))*(3*(moments(4, 1) + moments(2, 3))^2 - (moments(3, 2) + moments(1, 4))^2);
end

% 计算二阶和三阶中心矩
function moments = compute_central_moments(image)
    % 计算图像的几何矩
    moments = compute_geometric_moments(image);
    
    % 计算图像的质心
    centroid = compute_centroid(image);
    
    % 计算中心矩
    moments(3, 1) = moments(3, 1) - centroid(1)^3*moments(1, 3) - centroid(2)*moments(2, 2)*(2*centroid(1)^2 - centroid(2)^2) - centroid(1)*moments(3, 2)*(3*centroid(1)^2 - centroid(2)^2);
    moments(1, 3) = moments(1, 3) - centroid(2)^3*moments(3, 1) - centroid(1)*moments(2, 2)*(2*centroid(2)^2 - centroid(1)^2) - centroid(2)*moments(1, 3)*(3*centroid(2)^2 - centroid(1)^2);
    moments(2, 2) = moments(2, 2) - centroid(1)*centroid(2)*(moments(3, 1) + moments(1, 3)) - (centroid(1)^2 - centroid(2)^2)*moments(2, 2);
    moments(3, 2) = moments(3, 2) - centroid(1)*centroid(2)*(3*moments(3, 1) + moments(1, 3)) - (3*centroid(1)^2 - centroid(2)^2)*moments(2, 2);
    moments(2, 3) = moments(2, 3) - centroid(1)*centroid(2)*(moments(1, 3) + moments(3, 1)) - (centroid(2)^2 - centroid(1)^2)*moments(2, 2);
    moments(4, 1) = moments(4, 1) - centroid(1)^4*moments(1, 3) - 4*centroid(1)^2*centroid(2)^2*moments(2, 2) - centroid(2)^4*moments(3, 1) - 4*centroid(1)^2*centroid(2)^2*moments(2, 2);
    moments(1, 4) = moments(1,4) - centroid(2)^4*moments(3, 1) - 4*centroid(1)^2*centroid(2)^2*moments(2, 2) - centroid(1)^4*moments(1, 3) - 4*centroid(1)^2*centroid(2)^2*moments(2, 2);
end

% 计算几何矩
function moments = compute_geometric_moments(image)
    [rows, cols] = size(image);
    moments = zeros(4, 4);
    
    for i = 1:rows
        for j = 1:cols
            moments(1, 1) = moments(1, 1) + image(i, j);
            moments(1, 2) = moments(1, 2) + i*image(i, j);
            moments(2, 1) = moments(2, 1) + j*image(i, j);
            moments(2, 2) = moments(2, 2) + i*j*image(i, j);
            moments(1, 3) = moments(1, 3) + i^2*image(i, j);
            moments(3, 1) = moments(3, 1) + j^2*image(i, j);
            moments(2, 3) = moments(2, 3) + i*j^2*image(i, j);
            moments(3, 2) = moments(3, 2) + i^2*j*image(i, j);
            moments(4, 1) = moments(4, 1) + j^3*image(i, j);
            moments(1, 4) = moments(1, 4) + i^3*image(i, j);
        end
    end
end

% 计算质心
function centroid = compute_centroid(image)
    [rows, cols] = size(image);
    total_mass = sum(image(:));
    centroid = zeros(2, 1);
    
    for i = 1:rows
        for j = 1:cols
            centroid(1) = centroid(1) + i*image(i, j);
            centroid(2) = centroid(2) + j*image(i, j);
        end
    end
    
    centroid = centroid / total_mass;
end

这段代码定义了几个函数来计算图像的几何矩、中心矩和Hu不变矩，并使用这些不变矩来计算形状相似系数。你可以将两个图像作为输入传递给`shape_similarity`函数，它将返回形状相似系数。