Karthik Kannan

Feature Matching Points

Interest Point Detection

In this function, we first implement the Harris corner detection algorithm. First the image is filtered. Then at each pixel, y and y gradients are computed Ix and Iy. These are used to compute Ix2 Iy2 and Ixy. A thresholding operation is peformed and points having a sufficiently high cornerness score are selected.

Example of code

%example code
[Gx, Gy] = gradient(fspecial('Gaussian',5,1));
Ix = imfilter(image, Gx);
Iy = imfilter(image, Gy);

Gaussian_Filter = fspecial('Gaussian', feature_width, 2);
Ixx = imfilter((Ix .* Ix), Gaussian_Filter);
Ixy = imfilter(Ix .* Iy, Gaussian_Filter);
Iyy = imfilter(Iy .* Iy, Gaussian_Filter);

alpha = 0.06;
R = (Ixx.*Iyy - Ixy.^2) - alpha*((Ixx + Iyy).^2);
R = R / max(max(R));

R=R.*(R>0.025);
B=colfilt(R,[5,5],'sliding',@max);
R = R .* (R == B); 
[Y,X]=find(R);

Interest Points

Features of Interest Points

After the interest points are calculated in the previous method, each points feature descriptor is computed. 4 by 4 grid in 8 directions is constructed and each bin contains magnitude of the intensity in that angle/direction. Thus we get 128 dimensions or a vector of 1 by 128.

%example code

for i = 1: size(x,1)
    
    magnitude_mat = magnitude(y(i)-7:y(i)+8, x(i)-7:x(i)+8);
    direction_mat = direction(y(i)-7:y(i)+8, x(i)-7:x(i)+8);
    cur_feature = [];
    for xi = 1: 4 : feature_width
        
        for yi = 1: 4: feature_width
            
            points_vals = zeros(1,8);
            for xii = xi: xi+3
                
                for yii = yi: yi+3
                    
                    den = (pi/4);
                    num = (direction_mat(xii, yii) + pi);
                    pix = ceil(num / den);
                    points_vals(pix) = points_vals(pix) + magnitude_mat(xii, yii);
                    
                end
                
            end
            points_vals = points_vals / sum(points_vals);
            cur_feature = [cur_feature points_vals];
            
        end
        
    end
    features(i,:) = cur_feature;
end

Matching the features

The final step in the process is matching between feature points detected in the two images. This is done in my program by computing the Euclidean distance between every pair of feature points in the two images. The smallest distances means closest similarity amongst the different feature points in Image1 and Image2. For a given feature point in Image 1, the nearest neighbour and second nearest neighbour are identified by sorting the results of distances and getting the smallest two values. The ratio of these two distances is taken and values greater than particular treshold value are taken as pairs that are matching.

%example code


for i = 1 : size(features1, 1)
    dists = features2;
    
    %calculating distances between all features
    for j = 1 : size(dists, 1)
        dists(j, :) = (dists(j, :) - features1(i, :)).^2;
    end
    
    %sorting to help find nearest neighbor
    [sorted_distances_list, index] = sort(sum(dists, 2));
    
    %ratio of smallest and second smallest to get reliability
    rel = sorted_distances_list(2) / sorted_distances_list(1);
    confidence = (rel)^-1;
    
    if confidence < threshold
        matches(counter, 1) = i;
        matches(counter, 2) = index(1);
        confidences(counter) = confidence;
        counter = counter + 1;
    end 
end

Arrows showing the pairs matched

Results obtained for Notre Dame