The prior model information can range from very general such as general regularity constraints to very specific such as an exact template. A spline-based template model [7,13,14,33,35,37] is more structured than a snake, because the template is expressed as a linear combination of a set of basis functions, and its shape is determined by the coefficients of the basis functions. However, the linear combination can be arbitrary and does not usually encode a ``default'' shape as do the parametric models that are discussed later. In other words, the model is less specific than specially designed templates for a specific shape class. The choices of the spline basis can be quite broad including B-spline basis, trigonometric basis, wavelets, etc.
Staib et al. [35] have used Elliptic Fourier descriptors to represent open or closed boundary templates which are smooth and are continuously deformable with no obvious decomposition. The parameters of the deformable templates are the Fourier coefficients. A probability distribution on the Fourier coefficients is specified so that there is a flexible bias towards some particular shapes. The spread of the distribution is governed by the variability among instances of the object class. A Bayesian decision rule is then used to obtain the optimal estimate of the boundary, where the likelihood function is based on the correlation between the template and the boundary strength in the input image. Figueiredo et al. [13] used B-spline curves to describe the object boundary in MRI images. Each 2D planar curve is represented as follows:
where t is the parameterization of the curve, 
are 2D vectors called control points, and
are the B-spline basis.
A template derived using the above representation is illustrated in
Fig. 1. The observation model (likelihood) is based on the
assumption of homogeneity in MRI images (pixels inside/outside the object
follow an identical distribution).
A Minimum Description Length (MDL) criterion is used so that
the system adaptively chooses the number of degrees of freedom for
the spline model which best interprets the image data.
Figure 1: The B-spline representation of a bird template.
The ``x''s are the control points.
Wavelet basis has also been used to represent planar curves by Chuang and Kuo [7]. A wavelet-based template model has the advantage of a coarse-to-fine representation. It can also be computed efficiently using the wavelet transform.