Many shapes have natural systematic variations, or the parts may come from families where they vary in some standard way. The rigid part recognition approach of the first system is not usually suitable for recognising these new parts. Accordingly, we introduce a technique based on identifying the systematic modes of variation (the Point Distribution Model), which is based on Principal Component Analysis. We also see an example that extends the variations from a few points to a complete image (the Eigenface method).
Because many shapes have natural variation, or the parts may come from parametric families, we introduce the Point Distribution Model (PDM) approach to learning and representing the main modes of variation in a set of shapes.
By using PCA to analyze the systematic variation in the positions of key points on the shapes, we can build up a parametric structural model of the family of shapes. On top of this, we can add a multi-variate Gaussian model of allowable parameters for the shapes.
In order to apply the PDM method, we need to have the parts and corresponding points in a standard position. We introduce some heuristic methods suitable for the example parts used here.
Once we have a model for the class of shapes, then we use the model to recognize new instances of the part. This video shows how to both learn a model and ruse the model to recognize
We illustrate the PDM approach by using it to recognize a set of Tee shapes.
We discuss the strengths and weaknesses of the PDM method
We can apply the same PCA modeling approach to other types of problems, in this case to whole images of faces in the famous Eigenface method