The region adjacency graph in .NET Insert Code 39 in .NET The region adjacency graph

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12.4 The region adjacency graph generate, create code 39 full ascii none in .net projects Microsoft Windows Official Website In model matching, we w barcode 39 for .NET ill make use of the region adjacency graph (RAG) as a means for identifying how the regions in a segmented image match (or do not match) faces in a three-dimensional model. A model of a polyhedron with six faces is illustrated in Fig.

12.4. The RAG for the object of Fig.

12.4 is illustrated in Fig. 12.

5; Fig. 12.6 shows another example.

. E B C A D A polyhedron has all FLAT faces. Fig. 12.4. A polyhedron with six faces. 12.4 The region adjacency graph What a mess! Do you thi nk there is a planar way to draw this graph That is, can you draw it without any lines crossing . Fig. 12.5. The RAG of the three-dimensional object in Fig. 12.4. 3 1 2 1. Fig. 12.6. The image and its RAG. Now is the problem: Giv en an observation, and the RAG derived from the observation, and given a collection of models and their corresponding graphs, which model best matches the observation We will address this matching problem later. Other graph representations are possible and often useful, for example, the constructive solid geometry (CSG) community uses a collection of primitives subjected to transformations to represent input to automatic parts manufacturing systems. The primitives are objects like spheres and cylinders.

Methods have been developed [13.8] to match scenes to models constructed from CSG representations as well as to RAG representations..

The scene graph First, let s introduce a term to help with vocabulary. When talking about models, we use the term region to represent an identi able surface/face, etc. When we are talking about the output of the segmenter, that is, what one might consider a region in the observation, we generally use the term patch.

The RAG does not contain a lot of information, only that there is a region and it is adjacent to certain other regions. We can produce a graph containing much more information by constructing an augmented RAG, which we call the scene graph. In a scene graph, nodes have properties, such as the area of the corresponding patch, the color, the albedo, etc.

An example is shown in Fig. 12.7.

Furthermore, the scene graph may be multiply traversed. In a simple RAG, the only edges between nodes are edges that correspond to the predicate ADJACENT TO, however, we can also have edges corresponding to the property JUST LARGER THAN, and thus have a mechanism for traversing the graph in order of patch size, or whatever other property seems convenient for a particular application. Generally,.

Graphs and graph-theoretic concepts 3 2 1 Patch #3 Avail: yes B. Window B. Volume Direction Normal Near Next Patch #1 Avail: yes B. Code 39 Extended for .NET Window B.

Volume Direction Normal Near Next Patch #2 Avail: yes B. Window B. Volume Direction Normal Near Next.

Fig. 12.7.

Scene graph for an image with one object segmented into three patches. Notice the use of cardinality rather than area. Why do you suppose this is Think about a range image viewed obliquely.

r r. the patch list is sorte barcode 3/9 for .NET d by cardinality (number of pixels in a patch), and each node has a pointer to a list of adjacent patches..

12.5 Using graph-matching: The subgraph isomorphism problem There are several kinds .net framework barcode code39 of problems in computer science, de ned by how long they take to run as a function of the size of the data set, represented by the variable n..

r r r Polynomial time problem VS .NET barcode code39 s. The time required may be written as a polynomial in n, e.

g. t n 3 . Exponential time problems.

The time required may be written as an exponential, e.g. t en .

Observe that as n becomes large, n k is tiny compared to k n . NP-hard problems. Here, NP says nonpolynomial, but it really means exponential.

NP-hard problems are provably exponential in complexity. That is, one can prove that there does not exist any way to compute it in polynomial time. NP-complete problems.

These are problems for which there does not exist any known algorithm to compute the answer in polynomial time. However, there is also no proof that no such algorithm exists. Any algorithm (or machine) which could convert an NP-complete problem to polynomial time would be a dramatic breakthrough, since all NP-complete problems can be shown to be isomorphic.

That is, any algorithm which could solve one NP-complete problem could be applied to any other such problems..
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