eigenfigure

An eigenfigure is a concept in the field of computer vision and image processing, particularly within the domain of shape analysis and recognition. It is a mathematical representation of a shape that captures its essential characteristics in a compact form. Eigenfigures are derived from a set of training shapes and are used to describe the variability within a class of shapes. This is achieved by performing a principal component analysis (PCA) on the shapes, which identifies the most significant modes of variation.

The term "eigenfigure" is often used in the context of active shape models (ASMs) and active appearance models (AAMs), which are popular techniques for shape and appearance modeling in images. In these models, eigenfigures represent the average shape and the principal modes of variation, allowing for the generation of new shapes that are similar to those in the training set. This is particularly useful in applications such as medical imaging, where the accurate modeling of anatomical structures is crucial.

Eigenfigures are computed by aligning a set of training shapes to a common coordinate system and then applying PCA to the resulting shape vectors. The eigenvectors of the covariance matrix represent the principal modes of variation, while the eigenvalues indicate the amount of variation captured by each mode. By combining the average shape with a linear combination of the eigenvectors, new shapes can be generated that are constrained to lie within the space spanned by the training shapes.

In summary, an eigenfigure is a powerful tool for shape analysis and recognition, providing a compact and efficient representation of shape variability. Its applications span various fields, including medical imaging, computer graphics, and pattern recognition.