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

Chapter 6, Part I
Shape representation and description: Region identification

Shape representation and description

• Defining the shape of an object can prove to be very difficult. Shape is usually represented verbally or in figures.
• There is no generally accepted methodology of shape description. Further, it is not known what in shape is important.

• Current approaches have both positive and negative attributes; computer graphics or mathematics use effective shape representations which are unusable in shape recognition and vice versa.
• In spite of this, it is possible to find features common to most shape description approaches.

• Common shape description methods can be characterized from different points of view
• Input representation form: Object description can be based on boundaries or on more complex knowledge of whole regions
• Object reconstruction ability: That is, whether an object's shape can or cannot be reconstructed from the description.
• Incomplete shape recognition ability: That is, to what extent an object's shape can be recognized from the description if objects are occluded and only partial shape information is available.
• Local/global description character: Global descriptors can only be used if complete object data are available for analysis. Local descriptors describe local object properties using partial information about the objects. Thus, local descriptors can be used for description of occluded objects.
• Mathematical and heuristic techniques: A typical mathematical technique is shape description based on the Fourier transform. A representative heuristic method may be elongatedness.
• Statistical or syntactic object description.
• A robustness of description to translation, rotation, and scale transformations: Shape description properties in different resolutions.

• Sensitivity to scale is even more serious if a shape description is derived, because shape may change substantially with image resolution.
• Therefore, shape has been studied in multiple resolutions which again causes difficulties with matching corresponding shape representations from different resolutions.
• Moreover, the conventional shape descriptions change discontinuously.
• A scale-space approach aims to obtain continuous shape descriptions if the resolution changes continuously.

• In many tasks, it is important to represent classes of shapes properly, e.g. shape classes of apples, oranges, pears, bananas, etc.
• The shape classes should represent the generic shapes of the objects belonging to the same classes well. Obviously, shape classes should emphasize shape differences among classes while the influence of shape variations within classes should not be reflected in the class description.

• Despite the fact that we are dealing with two-dimensional shape and its description, our world is three-dimensional and the same objects, if seen from different angles (or changing position/orientation in space), may form very different 2D projections.
• The ideal case would be to have a universal shape descriptor capable of overcoming these changes -- to design projection-invariant descriptors.

• Consider an object with planar faces and imagine how many very different 2D shapes may result from a given face if the position and 3D orientation of this simple object changes with respect to an observer. In some special cases, like circles which transform to ellipses, or planar polygons, projectively invariant features (invariants} can be found.

• Object occlusion is another hard problem in shape recognition. However, the situation is easier here (if pure occlusion is considered, not combined with orientation variations yielding changes in 2D projections as discussed above), since visible parts of objects may be used for description.
• Here, the shape descriptor choice must be based on its ability to describe local object properties -- if the descriptor only gives a global object description, such a description is useless if only a part of an object is visible. If a local descriptor is applied, this information may be used to compare the visible part of the object to all objects which may appear in the image. Clearly, if object occlusion occurs, the local or global character of the shape descriptor must be considered first.

Region identification

• Region identification is necessary for region description. One of the many methods for region identification is to label each region (or each boundary) with a unique (integer) number; such identification is called labeling or coloring, also connected component labeling.
• Goal of segmentation was to achieve complete segmentation, now, the regions must be labeled.

• Label collision is a very common occurrence -- examples of image shapes experiencing this are U-shaped objects, mirrored E objects, etc.
• The equivalence table is a list of all label pairs present in an image; all equivalent labels are replaced by a unique label in the second step.
• The algorithm is basically the same in 4-connectivity and 8-connectivity, the only difference being in the neighborhood mask shape.

Last Modified: February 4, 1997