similarityMatrix

R2026b

Compute self-similarity matrix for a set of image features based on bag of words representation

Since R2026b

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Syntax

simMatrix = similarityMatrix(bag,features)
simMatrix = similarityMatrix(bag,features,StrongestResults=Value)

Description

simMatrix = similarityMatrix(bag,features) returns a self-similarity matrix simMatrix for the ORB or SIFT features specified by features using the distributed bag of words (DBoW) representation specified by the bagOfFeaturesDBoW object, bag.

example

simMatrix = similarityMatrix(bag,features,StrongestResults=Value) additionally specifies the number of top similarity scores to retain in the output similarity matrix using the StrongestResults name-value argument. In each column of the output similarity matrix, the function retains only the similarity scores for the specified number of top‑ranking image features, and sets all the remaining scores to 0. The default value of StrongestResults is 10.

Examples

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Open Live Script

This example shows how to create a bag of words vocabulary using SIFT features extracted from images and compute self similarity matrix for all the images. It also shows how to use the computed similarity matrix to visualize images that are most similar to a given query image.

Load a set stop-sign images as an image datastore.

folder=fullfile(toolboxdir("vision"),"visiondata","stopSignImages");
imds=imageDatastore(folder);

Compute the scale-invariant feature transform (SIFT) features for all the images in the datastore.

siftFeatures = cell(numel(imds.Files),1);
for i = 1:numel(siftFeatures)
    img = rgb2gray(readimage(imds,i));
    siftFeatures{i} = extractFeatures(img,detectSIFTFeatures(img));
end

Create a bag of features object for the images using the bagofFeaturesDBoW object. To use SIFT image features while constructing the bag of features vocabulary, specify the FeatureType name-value argument as "SIFT".

bag = bagOfFeaturesDBoW(imds,FeatureType="SIFT");

Compute the similarity matrix for all the image features using the similarityMatrix object function. The function returns a sparse matrix that stores similarity scores for only the top visually similar images for each image feature, as specified by the StrongestResults name‑value argument. By default, each column has 10 nonzero similarity scores, and all other entries are zeros. Diagonal entries are 1 because each image is compared with itself, and all other similarity scores fall between 0 and 1, with higher values indicating stronger visual similarity.

You can adjust how many similar images are retained by specifying the StrongestResults name‑value argument.

simMatrix = similarityMatrix(bag,siftFeatures,StrongestResults=10)
simMatrix = 41×41

    1.0000    0.0675    0.0762    0.0600    0.0711         0         0    0.0605         0         0         0         0    0.0382         0         0         0         0         0         0         0         0    0.0594    0.0544         0         0    0.0534         0         0         0         0         0    0.0894    0.0856    0.0536    0.0915    0.0716         0    0.0570         0         0    0.0857
         0    1.0000    0.0891         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0    0.0497         0         0         0         0    0.0598         0         0         0         0         0         0         0         0         0         0
         0    0.0891    1.0000         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0    0.0488         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0
         0         0         0    1.0000    0.0804         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0    0.0612    0.0545         0         0         0         0         0         0         0         0         0         0    0.0549         0         0         0    0.0583         0         0         0
         0         0         0    0.0804    1.0000         0         0         0         0         0    0.0118         0    0.0363         0         0         0         0         0         0         0         0    0.0745    0.0604         0         0    0.0483         0         0         0         0         0         0         0    0.0617         0    0.0737    0.0427    0.0601    0.0286         0         0
    0.0885         0         0         0    0.0668    1.0000         0         0         0         0         0         0         0         0    0.1062    0.0947    0.1018    0.1001    0.1050         0    0.0882         0    0.0515         0         0         0         0         0         0         0         0    0.0986    0.0908         0         0         0         0    0.0537         0    0.1006    0.0906
         0         0         0         0         0         0    1.0000    0.1024    0.0791    0.0172    0.0203    0.0513         0         0         0         0         0         0         0    0.0401         0         0         0         0         0    0.0494    0.0238    0.0063         0    0.0689    0.0619         0         0         0         0         0         0         0         0         0         0
         0         0         0         0         0         0    0.1024    1.0000    0.1072    0.0106    0.0144    0.0355         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0
         0         0         0         0         0         0    0.0791    0.1072    1.0000         0    0.0124    0.0429    0.0357         0         0         0         0         0         0         0         0         0         0         0         0    0.0514         0         0    0.0714    0.0709    0.0631         0         0         0         0         0         0         0         0         0         0
         0         0         0         0         0         0         0         0         0    1.0000    0.0889    0.0633         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0    0.0075         0         0         0         0         0         0         0         0         0         0         0         0         0
         0         0         0         0         0         0         0         0         0    0.0889    1.0000    0.0760         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0
         0         0         0         0         0         0         0         0         0    0.0633    0.0760    1.0000         0    0.0260         0         0         0         0         0         0         0         0         0         0         0         0         0    0.0073         0         0         0         0         0         0         0         0         0         0         0         0         0
         0         0         0         0         0         0         0         0         0         0         0         0    1.0000    0.0698         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0    0.0558         0    0.0350         0         0
         0         0         0         0         0         0         0         0         0    0.0119         0         0    0.0698    1.0000         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0    0.0478         0    0.0566         0         0
         0    0.0699    0.0789         0         0    0.1062    0.0699    0.0674    0.0813         0         0         0         0         0    1.0000    0.1187    0.1276    0.1160    0.1314    0.0385    0.0947         0         0    0.0904    0.0675         0    0.0238         0    0.0781    0.0815    0.0640    0.0969    0.0935         0    0.1016         0         0         0         0    0.1275    0.0966
      ⋮

Retrieve the indices of the images most similar to a selected query image. In this example, you extract the nonzero similarity entries for the 15th image, sort them in descending order of similarity score, and return the corresponding image indices.

queryImageIdx = 15;
idx = find(simMatrix(:,queryImageIdx));
[~,order] = sort(simMatrix(idx,queryImageIdx),"descend");
sortedIdx = idx(order)'
sortedIdx = 1×10

    15    19    17    40    16    18     6    35    32    41

Visualize the query image and its 10 most similar images in the order of decreasing similarity scores. This helps you qualitatively inspect how well the similarity matrix captures visual similarity among the image features.

figure
tl = tiledlayout(3,4,TileSpacing="compact",Padding="compact");
title(tl,"Query Image and 10 Most Similar images in Descending Order")
nexttile
ax = gca;
imshow(readimage(imds,queryImageIdx))
hold on
rectangle(Position=[ax.XLim(1) ax.YLim(1) diff(ax.XLim) diff(ax.YLim)],Edgecolor="r",LineWidth=2)
title("Query Image")

for k = 1:numel(sortedIdx)
nexttile
    imshow(readimage(imds,sortedIdx(k)))
    title(sprintf("Similar Image %d", k))
end

Figure contains 11 axes objects. Hidden axes object 1 with title Query Image contains 2 objects of type image, rectangle. Hidden axes object 2 with title Similar Image 1 contains an object of type image. Hidden axes object 3 with title Similar Image 2 contains an object of type image. Hidden axes object 4 with title Similar Image 3 contains an object of type image. Hidden axes object 5 with title Similar Image 4 contains an object of type image. Hidden axes object 6 with title Similar Image 5 contains an object of type image. Hidden axes object 7 with title Similar Image 6 contains an object of type image. Hidden axes object 8 with title Similar Image 7 contains an object of type image. Hidden axes object 9 with title Similar Image 8 contains an object of type image. Hidden axes object 10 with title Similar Image 9 contains an object of type image. Hidden axes object 11 with title Similar Image 10 contains an object of type image.

Input Arguments

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Distributed bag of visual words (DBoW) representation for the set image features, specified as a bagOfFeaturesDBoW object.

ORB or SIFT feature descriptors, specified as a cell array of M binaryFeatures objects or M feature vectors, respectively.

Output Arguments

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Self-similarity matrix for M input image features, returned as an M x M matrix, where each element represents the similarity score between two image feature vectors. Each entry at row i and column j quantifies how similar the i‑th and j‑th image features are. Diagonal entries are 1 because they compare each image with itself, while all other similarity scores lie between 0 and 1, with higher values indicating greater visual similarity.

Version History

Introduced in R2026b

See Also

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