Statistical Image Modeling and Processing Using Wavelet-Domain Hidden Markov Models - Nonlinear Signal and Image Processing: Theory, Methods and Applications - page 359

TABLE 10.3
Segmentation Results of the Five Contexts Regarding P a ,
P b , and P c
Context-1

Context-2 Context-3 Context-4 Context-5

P a

0.9365 0.9728 0.9260 0.9186 0.8327

P b

0.2098 0.3567 0.3716 0.3000 0.1173

P c

0.6389 0.5189 0.7071 0.7222 0.7237

boundaries that coincide with the true ones, showing boundary specificity ,
and P c the percentage of true boundaries that can be detected, showing
boundary sensitivity .Weconduct segmentation experiments on 10 mosaics,
as shown in Figure 10.11. For each context, we perform pixel-level segmen-
tation on the 10 mosaics using the supervised context-based segmentation
algorithm. 7 P a , P b , and P c , which are averaged over 10 trials, are shown in
Table 10.3.
A good segmentation requires high P a , P b , and P c . Even though P a is usu-
ally most important, high P b and P c provide more desirable segmentation
results with high accuracy of boundary localization and detection. On the
other hand, boundary localization and detection in textured regions are usu-
ally regarded as difficult issues due to abundant edges and structures around
textured boundaries. 41 , 42 From Table 10.3, it is found that none of the five con-
text models can work well singly in terms of the three criteria. For example,
Context-2 has the best P a but the worst P c . This fact experimentally verifies
that the context models used in References 7 and 33 are good choices in terms
of P a . Context-5 is the strongest in P c but the weakest in P a . Context-3 gives
the highest P b , but P a and P c suffer. These observations are almost completely
consistent in each trial. Intuitively speaking, interscale context models, e.g.,
Context-1 and Context-2, favor P a by encouraging the formation of large, uni-
formly classified regions across scales of the pyramid. The intrascale context
model Context-5 helps P c by being sensitive to boundaries within a scale. As
a hybrid inter- and intrascale context model, Context-3 provides the best P b
by appropriately balancing both interscale and intrascale dependencies into
the SMAP Bayesian estimation. Thus, a natural idea is to integrate multiple
context models to achieve high P a , P b , and P c simultaneously.
Generally speaking, given y y ( n ) |

the collection of mul-
tiscale random fields of an image Y ,acontext model V is used to simplify
the characterization of the joint statistics of y with local contextual model-
ing. Thus, given different context models, we can have different statistical
characterizations of y . Accordingly, we may have different Bayesian segmen-
tation results. For example, the quadtree pyramid 32 and the interscale context
models 7 , 33 emphasize the homogeneity of the labeling across scales, and the
segmentation results tend to be composed of large, uniformly classified re-
gions. However, those contexts cannot provide high accuracy of boundary

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