Biomedical Engineering Reference
In-Depth Information
Prior information: Curves Smoothness
Deformable Model
Represented by Parametric curves
Represented by vectors of textures
Represented by vectors of pixel coordinates
Active Contour
Model
Active Shape
Model
Active Appearance
Model
Additional prior information: class of shape
Additional prior information: texture within the shape
Fig. 2.8 Three main classes of deformable model
constraints to match the borders of the targeted object in a given image. The word
'active' stems primarily from the nature of the curves in adapting themselves to fit
the targeted object. There are three main classes of deformable model: active con-
tour model, active shape model and active appearance model. Each of the classes
differs mainly in the aspect of the incorporated prior information and curves repre-
sentations as illustrated in Fig. 2.8 .
Deformable models assemble the mathematical knowledge from physics in
limiting the shape flexibility over the space, geometry in shape representation,
and optimization theory in model-object fitting [ 95 ]. These mathematical foun-
dations work together by playing their roles to establish the deformable model.
For instance, the geometric representation with certain degree of freedoms is to
cover broader shape changes; the principle in physics, in accordance to forces
and constraints, controls the changes of shape to permit only meaningful geomet-
ric flexibility; optimization theory adjusts the shape to fulfil the objective func-
tion constituted by external energy and internal energy; the external energy is
associated with the deformation of model to fit the targeted object due to external
potential energy, whereas, the internal energy constrain the smoothness of the con-
structed model in terms of internal elasticity forces.
2.7.1 Active Contour Model
Kass et al. [ 12 ] proposed active contour model or known as 'snake' as a potential
solution to segmentation problem [ 96 ]. From the perspective of geometry, it is an
embedded parametric curve represented as v ( s ) = ( x ( s ) , y ( s )) T on image plane
( x , y ) ∈ R 2 , where x( s ) and y( s ) denote coordinates functions, and s ∈[ 0,1 ] denotes
the parametric domain. A snake in this context illustrates an elastic contour that
fits to some preferred features in image. The shape function of the contour that
 
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