ALTERNATE SPACES FOR MODEL DEFORMATION: APPLICATION OF STOP AND GO ACTIVE MODELS TO MEDICAL IMAGES - Deformable Models - page 316

Table 3. Mean and Maximum Errors in Pixels per Model Point

Standard models STOP and GO

Mean error 40 14

Max error 130 55

where P Background is the probability density function for the non-desired region
and P Target is the pdf for the region of interest. Using the former equation we can
evolve the snake as follows:

∂ ∂t = sign( I ) ·

n. (12)

The last equation is a simplification of the real one, which takes into account
the curvature term. However, the effect of guiding the snake to the border where
P Background = P Target is the same as the complete equation, except for the
regularity of the final model. Figure 17 shows an example where the condition
of equiprobability fails to define the regions of interest. Figure 17a,b shows the
probability estimation of the region of interest and the background, respectively.
Figure 17c shows the mask obtained by the inequality P Background ≤

P Target .
The edges of this mask are the attraction contours. As we can see, since the
value of the probabilities is not being taken into account, the regions in which
both probabilities have small values are also being classified as desired regions.
Figure 17d shows the resulting segmentation using a region scheme. Figure 17e
displays the geometrically enhanced likelihoodmap, and, finally, Figure 17f shows
the resulting segmentation using the STOP and GO models. As we can observe,
the resulting region is much closer to the real one than the one obtained using
classic schemes.
The next experiment was performed using 100 intestinal endoscopy images.
We compare the error achieved using STOP and GO and Geodesic Region Based
models with the segmentation made by experts. Table 3 shows the resulting errors
in pixels per model point. As we can observe, the mean error for the standard
region-based technique is 40 pixels per model point. This huge difference between
automatic segmentation and expert segmentation is mainly due to the fact that all
errors in the embedded “classification” have a lot of impact on the deformation
result. As an example of this effect, the reader can check Figure 17. On the other
hand, STOP and GO models seem to overpass most of the errors and converge
more accurately to the real borders achieving a mean error of 14 pixels per model
point.