7.2

# The Active Shape Model fitting algorithm

We have demonstrated basic ideas for fitting a shape model to an image. The algorithm utilises ideas from the well-known Active Shape Model (ASM) approach and combines these with the methods we have developed for fitting Gaussian Process models.

In order to employ this modified ASM fitting algorithm in practical applications, a few more details need to be taken into consideration. The pose parameters (i.e. rotation and translation) need to be adjusted along with the shape. To improve the convergence of the algorithm, the algorithm is usually applied in a multi-scale setting. Furthermore, it is usually not the intensities which are modelled directly but rather the gradient changes in the images. This makes the procedure more robust.

Unfortunately, discussing all these aspects is not possible within the scope of this course. If you are interested to learn in more detail how you can apply ASMs in practical applications, we invite you to read this paper written by Tim Cootes, one of the inventors of the original method, that provides an easily accessible and practical introduction to the topic.[1]

A few remarks about the paper are in order:

• In this paper shapes are represented using a set of landmark points. As in most shape modelling papers you will find in the literature, the model is not formally defined as a Gaussian Process; instead, Principal Component Analysis (PCA) is applied directly to the discretised shapes.
• Instead of using Gaussian Process regression to find a probable shape from the matching points, the paper uses a simpler solution. It projects the solution into the space spanned by the principal components and trims the coefficient, using the fact that the coefficients are $N(0,1)$ distributed and that large coefficients correspond to unlikely shapes.
• The paper discusses a setting where rotation, translation and size are standardised.

Despite these slight differences in the mathematical setting, you should be able to understand the paper given what you have learned in this course. You should also be able to see how the theory of Gaussian Processes can be used to improve ASM fitting.