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Sample Article:		Region-Growing

Task: Given a collection of data D = {d1, d2, ...}, partition it meaningfully
	(where "meaningfulness" is measured by some criterion scheme F)

Basic Approach: 
	1) Initially, consider the discrete partition; that is,
	   P ← { {d1}, {d2}, ...}
	2) Pick the two members of partition P which are the closest in meaning
	   (according to F), and merge them (replace them by their union).
	3) Repeat step (2) as long as the total meaningfulness of P doesn't decrease

Considerations:
	1) What form might F assume?
	   One possible scheme is the following: We are given a vector-valued
	   function F': {subsets of D} → {real vectors with m components}. F' is
	   supposed to indicate the texture, the local characteristics, of any
	   given region (any subset of D). We are also given some constraints F''
	   of the form 
	      "regions whose F'-values differ in this way must never merge..."
	      "regions whose F'-values differ only in this way should merge..."
	   After each merging, the F'-value of the new region must be computed.
	2) What algorithm should be used to efficiently find the best two regions?
	   An empirical and aesthetic solution is the following: Whenever possible,
	   we prefer to let one of the two regions be the one that was last merged
	   (the result of the last merge), and let the other region be
	    "geographically" close to this first one (where "geographic distance"
	   is some elementary relationship F''' easily computed associatively
	   -- from a given region, it should be simple to find F'''-nearby regions).
	   This particular consideration is what gives the method its name.

Limitations
	1) The whole scheme collapses if the data D represent slow, continuous
	   changes; then the F-values for two neighboring regions may differ
	   greatly, while they are the same along their boundary.
	2) The derivation of F', F'' which are good enough to work for a whole
	   space of possible D's. This is ad hoc and nontrivial.
	3) The existence of F''', which makes step (1) in the algorithm quick,
	   is not always certain. Else we must search through DxD in some other way.
	4) Often, regions overlap conceptually, but this method does not allow that.

Advantages
	1) When F', F'', F''' are available, this provides a framework for 
	   incorporating all that knowledge.
	2) When borders are fuzzy, this is an effective isolation technique.
	3) A Bayseian analysis can be performed on a system using this strategy;
	   for a reference, see Yakimovsky and Feldman, 3IJCAI,...

Typical Applications:
	1) Scene Analysis
	   D is a digitized photograph,
	   P is a collection of objects; one region ≡ one object in the scene.
	   F' refers to graininess, brightness, color, etc.
	   F'' depends on the semantics of what the picture might contain;
	      for example, in the domain "seascapes", a "sky-blue" region
	      must never merge into a "sea-green" region;
	      in the domain of "mosques in the desert", this constraint is reversed.
	   F''' is physical proximity in the photograph
	   A reference for this is Yakamovsky...

Ideas for possible new applications:
	1) Speech understanding
	   D is digitized recordings of speech (perhaps broken into several bands).
	   P is a set of words; one region ≡ one word
	   F' is volume, pitch, derivatives of these quantities, etc.
	   F'' depends on the allowed grammar, common ways of slurring, etc.
	   F''' is temporal proximity in the recording
	2) Detection: Organizing Records by a key not explicitly supplied
	   D is a set of transcripts of students at Stanford (without their majors)
	   P is a file of transcripts organized by major department
	   F' considers the departments in which courses were taken
	   F'' considers distributional requirements, major requirements
	   F''' might include a set of pointers from courses to students who took
	     	them; when growing the CS "region", see who took CS courses.
	3) Even stranger examples...
	   
Pointers
	More Details about this concept can be found in these publications:...
	If this is the right situation but the wrong strategy, see these articles:
		Concept-formation, Inductive-inference, ...
	If region-growing seems right, but you are worried about speed, see...
	If no semantic constraints F'' exist, see the article on Blind Search...
	If...