Structured Point Distribution Models: Model Intermittently Present Features

Point distribution models have been successful in describing the shape constraints on two dimensional objects for shape description and image search. It is often the case that a class of objects to be modelled contains certain features which may be wholly present or absent in different instances. Moustaches on faces are a common example. Here we describe a method of coding the presence or absence of a feature within the PDM framework. We show that the method captures the intermittent nature of the feature as one of the modes of variation, and demonstrate that, where features are intermittently present, greater model specificity is achieved. 1 Intermittently Present Features There are classes of images that exhibit features which are only found in some instances and not others. Examples include face images which may or may not show moustaches and/or glasses and histological sections, in which structures may appear in a proportion of contiguous slices in a stack. The particular example that led to the approach described here is the study of electron microscope images of nerve capillaries. There are several concentric layers of structures in capillary cross-sections (figure 1). The central region is the lumen: the space through which blood cells pass; this is surrounded by a layer of endothelial cells, and then the basement membrane. In disease condition, such as diabetic neuropathy, changes occur in the normal structure of the capillaries, including constriction of the lumen. In some cases the lumen can become so constricted as to be unidentifiable (figure 1(b)). Finding the boundaries between these structures is important in quantifying disease status and we have approached this task using Active Shape Models and Genetic Search for the Basement Membrane / Endothelial Cell (BMEC) boundary [6]. The lumen boundary is potentially easier to locate due to the clearer contrast, but in modelling it we need to take account of the fact that it is often missing. To use Active Shape Model search we need to build Point Distribution Models (PDMs) of all the structures in the capillaries, including the lumen, when it is present. We have considered three possibilities for dealing with the intermittent presence of the lumen: Separate models for capillaries with and without a visible