Image Processing Techniques in Emission Tomography - Correction Techniques in Emission Tomography - page 135

TABLE 7.1: Similarity measures and their field of application.

Measure Monomodal Multimodal

SSD x -

NCC x -

MI x x

NGF x x

where n is the normalized gradient

( rI(x)

p krI(x)k 2 + 2 ; rI(x) 6= 0
0

n(I;i) := (7.20)

otherwise :

0

2R is an edge parameter.

For NGF it is assumed that the gradients of the template and reference image
match when the images are perfectly aligned. Edges with a low gradient are
treated as noise. This is controlled by the edge parameter in Equation (7.20)
which keeps the normalized gradient relatively low in such cases. This prevents
low gradients in the images from dominating the registration results. As NGF
does not operate directly on the image intensities, it is suitable for monomodal
and multimodal registration (see [26] for details).
The four different similarity measures presented here are summarized and
categorized according to their suitability for monomodality and multimodality
in Table 7.1.

Other approaches
Besides the similarity measures discussed above, other approaches exist. An
extension of MI called conditional mutual information (cMI) is proposed
in [40], where a spatial component of the joint intensity pair is incorporated
into MI. Another information-theoretic measure called cross-cumulative resid-
ual entropy (CCRE), which is a measure of entropy using cumulative distribu-
tions, was proposed in [67]. In contrast to fixed similarity measures, a learning
similarity criterion, derived from max-margin structured output learning, was
published in [35].

7.4.2 Validation
For evaluating newly developed methods, validation is essential. A compar-
ison with existing methods as well as a quantitative and objective validation
is required. Algorithms can be validated and quantified according to

1. Precision/Accuracy

2. Robustness