55:148 Digital Image Processing
55:247 Image Analysis and Understanding

Chapter 6, Part IV
Shape representation and description: Shape classes

Shape classes

• Representation of shape classes is considered a challenging problem of shape description.
• The shape classes are expected to represent the generic shapes of the objects belonging to the class well and emphasize shape differences between classes, while the shape variations allowed within classes should not influence the description.

• There are many ways to deal with such requirements.
• A widely used representation of in-class shape variations is determination of class-specific regions in the feature space.
• The feature space can be defined using a selection of shape features described earlier.
• Another approach to shape class definition is to use a single prototype shape and determine a planar warping transform that if applied to the prototype produces shapes from the particular class.
• The prototype shape may be derived from examples.

• If a set of landmarks can be identified on the regions belonging to specific shape classes, the landmarks can characterize the classes in a simple and powerful way.
• Landmarks are usually selected as easily recognizable border or region points.
• For planar shapes, a co-ordinate system can be defined that is invariant to similarity transforms of the plane (rotation, translation, scaling).
• If such a landmark model uses n points per 2D object, the dimensionality of the shape space is 2n.
• Clearly, only a subset of the entire shape space corresponds to each shape class and the shape class definition reduces to the definition of the shape space subsets.

• Cootes et al. determine principal components in the shape space from training sets of shapes after the shapes are iteratively aligned.
• The first few principal components characterize the most significant variations in shape.
• Thus, a small number of shape parameters represent the major shape variation characteristics associated with the shape class.
• Such a shape class representation is referred to as point distribution models and is discussed in detail in Chapter 8 in the context of image interpretation.

Last Modified: February 3, 1997