Spectral Imaging: Methods, Design, and Applications - Biomedical Optical Imaging Technologies: Design and Applications - page 150

4.5.3.2 Similarity Mapping

In cases such as histological stains used with tissue section, the measured spectra
may be a result of a complex interaction of the stains with the sample so that
isolation of unique components that can be used as reference spectra is not doable,
and therefore, the linear decomposition method that was described above cannot be
used.
Still, the complex mixtures may be systematically found in the sample, and for
such cases, algorithms that compare the spectra that are selected from within the
image itself can be used. The similarity mapping algorithm is an example to these
types of the algorithms. It is based on selecting information from the sample itself
or from similar samples. The spectra can be defined by averaging the spectra in a
region of the image that was defined by the user based on prior knowledge. The
spectra from these regions are saved in a library as I i ./ where i is the index of
each of these spectra.
The similarity mapping algorithm simply tests the degree of similarity of each
spectrum in the image with each one of the reference spectra. Different criteria can
be used depending on the specific application and spectral features.
More commonly, a least-square algorithm is used. For every tested spectrum
I./,then-dimensional distance for each reference is calculated by

r X I i ./ I./ 2 :

D i D (4.15)

The most similar reference spectrum i is the one that has the smallest distance
D i . The spectra can also be normalized to have one unit area (or peak intensity), so
that only spectral shape differences are tested. Another similarity mapping algorithm
is based on calculating the M -dimensional angle between each reference spectrum
and the tested spectrum (M being the number of points in the spectrum). Each
reference spectrum i is defined as a vector I i D .I i;1 ;I i;2 ;:::;I i;n / and the angle

˛ i between the reference spectrum and the tested spectrum I is calculated by

0
@

1
A :

P I i ./ I./

D cos 1

I i I
j I i j j I j

D cos 1 q P I i ./ 2 q P I./ 2

˛ i (4.16)

Here too, the reference spectrum that gives the smallest angle is the more similar
one.

4.5.3.3 Spectral Un-mixing in Bright-Field Measurements

This algorithm is similar to the linear decomposition algorithm described before
for fluorescence measurements but is specific for bright-field (transmission)

microscopy. The method is somewhat more complex because the relevant