An instance of the analytical form-based shape model is that of Widrow
[42], where parameterized templates called ``rubber masks''
were used to describe 2D irregular shapes.
The parameters described the sizes and the relationships between subparts of a shape.
Lakshmanan et al. [24] have used a parametric template model to
locate the airport runway boundary in radar images. The a
priori knowledge that the runway boundary consists of two straight
parallel edges is used to derive a global shape model for the runway,
parameterized by three parameters:
the slope of the two edges, k, and the intercept of each edge, 
and 
.
The runway edge detection problem is formulated as a Bayesian
estimation using a physics-based model of the radar imaging process
based on the assumption that the runway boundary divides the image into
three relatively homogeneous regions.
The set of parameter values which
maximizes the Bayesian a posteriori density determines the runway boundary.
In this application, the global deformable model helps in the runway detection because the model is able to integrate the local intensity homogeneity and gradient information and adjusts itself to the desired position. The use of the prior structural information contributes to its robustness to image noise. A typical edge detector does not work well here because the image is textured due to the noisy nature of the millimeter wave images.
Yuille et al. [45] have used deformable templates to extract facial features. They designed parametric models for eye and mouth templates using circles and parabolic curves. The parameters which control the shape of a template are the center and the radius of the circle, and the characteristic parameters of the parabola. Regularization constraints are imposed on the parameters in terms of the size of facial features such as the mouth and the eyes, as well as the interactions between them, e.g., the center of the mouth template should be close to the line which is at equal distances to the centers of the two eye templates. The image (external) energy term is defined in terms of edges, peaks, and valleys in the input intensity image based on the features for the eyes and mouth so that different parts of the template interact with different image features such as intensity peaks and valleys. This method gives reasonable detection and tracking results of the eyes and mouths in real images.
For all the techniques discussed above, a good initialization of the contour is required for meaningful solutions. The approximate translation, orientation and scale of the object to be segmented are supposed to be known. Furthermore, the initial contour implicitly biases the converged configuration. The applicability of the parametric deformable model is limited because the shapes under investigation have to be well-defined so that they can be represented by a set of curves with, preferably, a small number of parameters.