Models
There are various models for point processes, typically based on but going beyond the classic homogeneous Poisson point process (the basic model for complete spatial randomness) to find expressive models which allow effective statistical methods.
The point pattern theory provides a major building block for generation of random object processes, allowing construction of elaborate random spatial patterns. The simplest version, the Boolean model, places a random compact object at each point of a Poisson point process. More complex versions allow interactions based in various ways on the geometry of objects. Different directions of application include: the production of models for random images either as set-union of objects, or as patterns of overlapping objects; also the generation of geometrically inspired models for the underlying point process (for example, the point pattern distribution may be biased by an exponential factor involving the area of the union of the objects; this is related to the Widom-Rowlinson model of statistical mechanics).
Read more about this topic: Stochastic Geometry
Famous quotes containing the word models:
“Today it is not the classroom nor the classics which are the repositories of models of eloquence, but the ad agencies.”
—Marshall McLuhan (1911–1980)
“Grandparents can be role models about areas that may not be significant to young children directly but that can teach them about patience and courage when we are ill, or handicapped by problems of aging. Our attitudes toward retirement, marriage, recreation, even our feelings about death and dying may make much more of an impression than we realize.”
—Eda Le Shan (20th century)
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—Samuel Butler (1835–1902)