Euclidian distance showing different result for different formula

d = (query_feature' - train_feature').^2; % Eucledian distance
d_1 = sqrt(sum((query_feature' - train_feature') .^ 2))

The method with d is giving some error in retrieval, but when using d_1 it always give 100% accurate retrival (all retrieved images are similar as query image)

What can be wrong? Any suggestions appreciated.

[Image Analyst]

Not sure what is wrong. Can you attach your data?

d is a list of the squared differences, while d_1 is the root mean square - a single number and a different thing. Not sure what you're expecting. The only way d or d_1 would be zero (meaning no differences and 100% accuracy) would be if query_feature exaclty equaled train_feature. Is that the case?

[new_user]

db = 'CBIR';

[fn, pn] = uigetfile(db);

im = fullfile(pn, fn);

outputFlder = fullfile('Test'); %returns full path of last arugument

rootFolder = fullfile(outputFlder); %variable storing path

images_query = imageDatastore(rootFolder, 'IncludeSubfolders',true, 'LabelSource','foldernames'); %%'ReadFcn', @readCBIR

%R = imread("99 (5).jpeg"); % Read image

R = imread(im); % Read image

Input_Layer_Size_q = net.Layers(1).InputSize(1:2); % (1:2 = 1st 2 elemnts of input size), input layer size stored in this variable (Input_layer_size)

Resized_Test_image_q = augmentedImageDatastore(Input_Layer_Size_q, R, 'ColorPreprocessing','gray2rgb'); %% For defining test image replace "Testing _image with test folder

%Extract feature

train_feature = activations(net, Resized_Training_image, 'Animal Feature Learner', 'OutputAs', 'Rows');

query_feature = activations(net, Resized_Test_image_q, 'Animal Feature Learner', 'OutputAs', 'Rows');

%Equation 2

a = query_feature; % transposing

b = transpose(1-a);

%Equation 3

c = zeros(Number_of_Classes,Number_of_Training_images);

d = (query_feature' - train_feature').^2; % Eucledian distance

% d = sqrt(sum((query_feature' - train_feature') .^ 2)); % other method eucledian: giving all images from same category maybe something is wrong

for e = 1 : Number_of_Training_images

f = b.*d(:,e);

c(:, e) = f;

end

c = sqrt(sum(c))';

% Fetch top 25 similar images

g = sort(c);

[~, n] = sort(c);

n = n(1:50);

files = cell(1, 50);

for h =1:50

files{h} = Training_image.Files{n(h)};

end

%Display query image

figure;

imshow(R);

title('query')

% Display retrived images

figure;

montage(files);

title("retrived")

Answer 1

[John D'Errico]

What you write in d is simply not Euclidean distance What can be wrong? Your belief that it is so? What you write in d1 IS a Euclidean distance computation, so that it works should be no surprise.

[new_user]

but giving all the time 100% retrival accuracy using pretrained CNN is ok?

I mean I am using pretrained CNN to extract features and then measuing the similarity between them using d & d_1. So, the result for d_1 are 100% always.

Answer 2

[Meg Noah]

Some code - look at the sizes of the arrays to see why:

nsamples = 25;
ncomponents = 4;
s = RandStream('dsfmt19937','Seed',1123581321);
query_feature = rand(s,nsamples,ncomponents);
train_feature = rand(s,1,ncomponents);

% relative vector between query vectors and training vector
d = (query_feature' - train_feature').^2; 

% Three ways to compute Eucledian distance between query vectors and a
% training vector
d_1 = sqrt(sum((query_feature' - train_feature') .^ 2))';
d_2 = sqrt(sum(bsxfun(@minus, query_feature, train_feature).^2,2));
d_3 = vecnorm((query_feature'-train_feature'),2)';

[new_user]

running d_2 is showing error. Matrix size mismatch

[Meg Noah]

The code snippet above creates the distances as vectors - arrays that are nsamples in rows and with one column. What matrix deimension is your code expecting?