DIA实验——匹配几何校验

匹配几何校验

一、 任务描述

1. 给定一对图像，利用提取好的SIFT特征文件，根据距离阈值准则（跨图像的局部SIFT特征距离小于0.4），得到图像间的初始局部特征匹配关系；
2. 基于上述初步匹配结果，实现spatial coding方法，进行匹配校验，确定几何不一致的匹配；
3. 将几何一致的匹配和不一致的匹配在图像上画出来，分别用蓝色和红色进行区分。

二、 实验步骤

1. 寻找匹配对：寻找并提取第1张图与第2张图的SIFT描述子匹配对的(x,y)座标点集，分别放进维数为（2*对应点数）的矩阵Map1，Map2中。
2. 生成空间映射：根据Map1，Map2每个点相对其他点座标的左右上下位置关系，以及k种（本实验中取k=4）旋转角度，生成由0、1构成的维数为（对应点数对应点数k）的空间编码矩阵GX1，GY1，GX2，GY2中。
3. 计算不一致性矩阵：将空间编码矩阵GX1与GX2，GY1与GY2进行逻辑异或操作得到不一致性矩阵Vx，Vy。
4. 计算不一致性总和Sx，Sy: 矩阵Vx，Vy各行元素求和，再对k个方向各行元素和求总和，得到Sx，Sy，维数为（匹配点数*1）
5. 检查Sx，Sy，识别错误匹配项：首先基于Vx，计算Sx，找到对应的i*, 然后从Vx和Vy中把对应的第i行、第i列全部删掉（或者mask掉，本实验中以置零方式进行mask），随后立即更新红蓝连线；然后基于更新后的Vy，计算Sy，找到对应的j*, 然后从Vx和Vy中把对应的第j行、第j列全部删掉（或者mask掉，本实验中以置零方式进行mask），随后立即更新红蓝连线。 对更新后的Vx和Vy重复上面两步，直到收敛（本实验取不一致性总和的阈值为（0.8*匹配对数）取整）。

三、 实验效果

四、 实验代码

其中本实验对图像特征描述子的读取通过已准备好的“.sift”文件直接读进matlab中，也可以自己在matlab中读取“.jpg”图片后转为SIFT格式的描述子数据，matlab代码如下：

%% Set path and parameters
clear;
close all;
clc;

src_1 = './test images/37967br1.jpg';  
src_2 = './test images/791.jpg';

% src_1 = './test images/4.jpg';  
% src_2 = './test images/Apollo-266.jpg';

% src_1 = './test images/771.jpg';  
% src_2 = './test images/305.jpg';

% src_1 = './test images/Apollo-49.jpg';
% src_2 = './test images/Apollo-266.jpg';

ext = '.sift'; % extension name of SIFT file
siftDim = 128;
maxAxis = 400;


%%  Load image
im_1 = imread(src_1);
if max(size(im_1)) > maxAxis
    im_1 = imresize(im_1, maxAxis / max(size(im_1)));
end

im_2 = imread(src_2);
if max(size(im_2)) > maxAxis
    im_2 = imresize(im_2, maxAxis / max(size(im_2)));
end


%%  Load SIFT feature from file
featPath_1 = [src_1, ext];
featPath_2 = [src_2, ext];

fid_1 = fopen(featPath_1, 'rb');
featNum_1 = fread(fid_1, 1, 'int32');
SiftFeat_1 = zeros(siftDim, featNum_1);
paraFeat_1 = zeros(4, featNum_1);
for i = 1 : featNum_1
    SiftFeat_1(:, i) = fread(fid_1, siftDim, 'uchar');
    paraFeat_1(:, i) = fread(fid_1, 4, 'float32');
end
fclose(fid_1);

fid_2 = fopen(featPath_2, 'rb');
featNum_2 = fread(fid_2, 1, 'int32');
SiftFeat_2 = zeros(siftDim, featNum_2);
paraFeat_2 = zeros(4, featNum_2);
for i = 1 : featNum_2
    SiftFeat_2(:, i) = fread(fid_2, siftDim, 'uchar');
    paraFeat_2(:, i) = fread(fid_2, 4, 'float32');
end
fclose(fid_1);


%%Normalization
SiftFeat_1 = SiftFeat_1 ./ repmat(sqrt(sum(SiftFeat_1.^2)), size(SiftFeat_1, 1), 1);
SiftFeat_2 = SiftFeat_2 ./ repmat(sqrt(sum(SiftFeat_2.^2)), size(SiftFeat_2, 1), 1);


%% Check match based on distances between SIFT descriptors across images
normVal = mean(sqrt(sum(SiftFeat_1.^2)));
matchInd = zeros(featNum_1, 1);
matchDis = zeros(featNum_1, 1);
validDis = [];
gridDisVec = [];
ic = 0;
for i = 1 : featNum_1                                           %以第一张图描述子数量为基准进行匹配
    tmpFeat = repmat(SiftFeat_1(:, i), 1, featNum_2);   % repmat(A,m,n)，将矩阵 A 复制 m×n 块，即128*featNum_2
    d = sqrt(sum((tmpFeat - SiftFeat_2).^2)) / normVal; % L2 distance，图1第i个描述子与图2所有描述子的距离向量
    matchDis(i) = min(d);
    [v, ind] = sort(d);
    if v(1) < 0.4            % 最小距离小于0.4，则认为构成一对匹配
        matchInd(i) = ind(1);
        ic = ic + 1;
        validDis(ic, 1 : 3) = [v(1), v(2), v(1) / v(2)];
        tmp = (SiftFeat_1(:, i) - SiftFeat_2(:, ind(1))).^2;
        tmp2 = reshape(tmp(:), 8, 16);
        gridDisVec(ic, 1 : 16) = sqrt(sum(tmp2));       % 第ic个匹配描述子的L2距离
    end
end
figure; stem(matchDis); ylim([0, 1.2]);                    %绘制茎状图
figure; stem(matchDis(matchInd > 0)); ylim([0, 1.2]);

%% 实现spatial coding方法，进行匹配校验准备
Map1 = [];
Map2 = [];
m= 1;
for i = 1 : featNum_1
    if matchInd(i) > 0
        Map1 = [Map1, paraFeat_1(1:2, i)];
        Map2 = [Map2, paraFeat_2(1:2, matchInd(i))];
    end
end
%         xys = paraFeat_1(:, i);
%         xys2 = paraFeat_2(:, matchInd(i));
r = 4;    
GX1(ic, ic, r) = 0;
GY1(ic, ic, r) = 0;
GX2(ic, ic, r) = 0;
GY2(ic, ic, r) = 0;
for k = 1:r
    %将其分解为r个独立的子区域，旋转k个单位的座标集
    theta = (k-1)*pi/(2*r);
    G1(1:2, 1:ic, k) = [cos(theta), -sin(theta); sin(theta), cos(theta)]*Map1;
    G2(1:2, 1:ic, k) = [cos(theta), -sin(theta); sin(theta), cos(theta)]*Map2;
    %获取空间编码01矩阵
    for i = 1:ic
        for j = 1:ic
            if G1(1, i, k) >= G1(1, j, k) 
                GX1(j, i, k) = 1;
            end
            if G1(2, i, k) >= G1(2, j, k) 
                GY1(i, j, k) = 1;
            end
            if G2(1, i, k) >= G2(1, j, k) 
                GX2(j, i, k) = 1;
            end
            if G2(2, i, k) >= G2(2, j, k) 
                GY2(i, j, k) = 1;
            end
        end
    end
end
Vx = xor(GX1, GX2);
Vy = xor(GY1, GY2);

%% Show the local matching results on RGB image
[row, col, cn] = size(im_1);
[r2, c2, n2] = size(im_2);
imgBig = 255 * ones(max(row, r2), col + c2, 3);
imgBig(1 : row, 1 : col, :) = im_1;
imgBig(1 : r2, col + 1 : end, :) = im_2;
% np = 40;
% thr = linspace(0,2*pi,np) ;
% Xp = cos(thr);
% Yp = sin(thr);
paraFeat_2(1, :) = paraFeat_2(1, :) + col;      %为了让两幅图画面并排，使右侧图x座标右移col个单位
figure(3); imshow(uint8(imgBig)); axis on;
hold on;
matchCount = 0;
for i = 1 : featNum_1
    if matchInd(i) > 0
        matchCount = matchCount + 1;
        xys = paraFeat_1(:, i);
        xys2 = paraFeat_2(:, matchInd(i));
        figure(3);
%         hold on;
%         plot(xys(1) + Xp * xys(3) * 6, xys(2) + Yp * xys(3) * 6, 'r');                      %图1匹配描述子红圈
%         plot(xys2(1) + Xp * xys2(3) * 6, xys2(2) + Yp * xys2(3) * 6, 'r');              %图2匹配描述子红圈
        hold on; plot([xys(1), xys2(1)], [xys(2), xys2(2)], '-b', 'LineWidth', 0.8);    
    end
end

%% 几何匹配校验
Map2(1, :) = Map2(1, :) + col;      %为了让两幅图画面并排，使右侧图x座标右移col个单位
threshold = floor(ic*0.8);
for i = 1:ic
    Sx = sum(sum(Vx, 2), 3);    %矩阵各行元素求和，再对k个方向各行元素和求总和
    [Cx, Ix] = max(Sx(:, :), [], 1); %求出第k个方向的列最大值
    if Cx>threshold
        Vx(Ix, :, :) = 0;       %把最不匹配的描述子mask
        Vx(:, Ix, :) = 0;
        Vy(Ix, :, :) = 0;       %把最不匹配的描述子mask
        Vy(:, Ix, :) = 0;
        hold on;plot([Map1(1, Ix), Map2(1, Ix)], [Map1(2, Ix), Map2(2, Ix)], '-r', 'LineWidth', 0.8);    %不匹配的描述点对连线
    end
    Sy = sum(sum(Vy, 2), 3);    %矩阵对各行元素求和
    [Cy, Iy] = max(Sy(:, :), [], 1);
    if Cy>threshold
        Vx(Iy, :, :) = 0;       %把最不匹配的描述子mask
        Vx(:, Iy, :) = 0;
        Vy(Iy, :, :) = 0;       %把最不匹配的描述子mask
        Vy(:, Iy, :) = 0;
        hold on;plot([Map1(1, Iy), Map2(1, Iy)], [Map1(2, Iy), Map2(2, Iy)], '-r', 'LineWidth', 0.8);    %不匹配的描述点对连线
    end
end
figure(3);
title(sprintf('Total local matches : %d (%d-%d)', length(find(matchInd)), featNum_1 ,featNum_2));
hold off;

五、参考文献

代码及资料
Wengang Zhou, Yijuan Lu, Houqiang Li, Y. Song, and Qi Tian, “Spatial coding for large scale partial-duplicate web image search,” ACM International Conference on Multimedia (MM), pp.131-140, 2010.