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C. Normalization Metrics

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Diego Herrera edited this page Jul 8, 2020 · 4 revisions

When computing correlation planes it is readily seen that the peak intensity depends on the overall intensity of the query image and the training images used on the filter. Hence, a proper normalization metric is needed to address this problem. Those metrics are used as an indicator of the peak sharpness in the correlation output. Their value is of huge importance for devising a decision algorithm in the context of biometric verification.

Peak-to-sidelobe Ratio (PSR)

As its name suggests, PSR is a measure of the ratio of the height of the peak to its width. This metric is computed by a simple formula

PSR = (peak - μ)/σ

In general, this metric is evaluated using convolution for the entire correlation plane. However, for simple applications, it is enough to select a patch in the correlation plane that contains the maximum value of the intensity, and compute mean and standard deviation over the patch. A simple code in MATLAB that performs the computation is presented next:

%% Locate vicinity of peak
% Find peak value and location
[peak, idx] = max(corplane(:));
[Y, X] = size(corplane);
[y, x] = ind2sub(size(corplane),idx);
% Size of PSE window
deltax = int16(0.4*X); deltay = int16(0.4*Y);
% Crop window
y_lim = max(y-deltay,1):min(y+deltay,Y);
x_lim = max(x-deltax,1):min(x+deltax,X);
data = corplane(...
       y_lim,...
       x_lim);

%% Compute PSE on window
pse = (peak - mean(data(:)))/std(data(:));

In the image above, the correlation plane on the left has a PSR = 167.67, while the one on the right has a PSR = 13.40. The lesson here is that

A high value of the PSR metric strongly suggest the presence of the biometric of interest in the query image, whereas a low PSR value indicates that the biometric might not be in the scene.

This fact is exploited in the classifier algorithm for verification. By thresholding the value of the metric for true matches, it is possible to decide whether the biometric of interest is present or not. If the correlation filter is designed properly, the ideal value of the threshold can be easily found by considering the ROC space. With datasets obtained via the suggested protocol, errors lower than 1% can be seen.

In the image bellow the usage of PSR metric for classifying is illustrated. The PSR metric is computed for true class and false class images, and it is clear that the true class has consistently larger values than the false class. Furthermore, the mean values for true and false class are quite different, which implies that the thresholding is expected to be very effective.

In the image above, the location of the peak for true class images is shown. The location is consistent over the dataset, as is expected from the data acquisition algorithm.

The fundamental references of the project are:

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