Image matching in .NET Paint ANSI/AIM Code 39 in .NET Image matching

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Image matching use .net vs 2010 barcode code39 creator tobuild 3 of 9 barcode for .net GS1 supported barcodes 13A.3. Image indexing Up to this point, we have considered the process of image matching as searching a data base of models for the model which best matches the observation. We have not addressed the process of search itself. One could, of course, simply try all models, but that could be prohibitively time-consuming, particularly in instances which involve large data bases of models.

In applications like automatic target recognition, where matching requires both high speed and large data bases [13.45], better methods are required. The alternate paradigm, indexing (sometimes called image hashing ) is analyzed in [9.

6]. In an indexing scheme, a set of parameters are extracted from the image. Obviously, such parameters need to be invariant to as many image transformations as possible and also need to be robust [13.

1]. This resulting parameter vector is then used as indices into a lookup table containing references to models. The lookup process returns a list of candidate models consistent with this particular parameter vector.

To see how this works, consider the following algorithm. Begin by looking at local areas around the boundary and attempting to match each local area with a data base of feature descriptors such as lines, circular arcs, and minima and maxima of curvature. Assuming a successful segmentation of an unoccluded object, we start with an edge image, where the edges are not required to be connected.

About some point [x0 , y0 ] on the edge, we sample the edge in that neighborhood using a sampling scheme3 which is invariant to zoom. Form all possible combinations of that point with two other nearby points and generate an invariant parameter vector similar to that described in [9.37].

That parameter vector is then used to index a data base of local shapes. For each entry selected, a feature instance is extracted and after all the triples have been considered, the feature instance with the highest number of votes is selected. Now, the boundary is represented by a sequence of feature instances, and the indexing method may be repeated, using a look-up table of object models which are indexed by geometry and occurrence of feature instances.

Numerous other approaches to indexing exist [13.5, 13.32]; an excellent review is included in [13.

48]. The space requirements for some indexing schemes are analyzed in [13.25].

As data bases get larger, one must consider the image indexing problem in the context of the entire digital library. The reader is directed to an entire special issue of IEEE Transactions on Pattern Analysis and Machine Intelligence (August, 1996) which addresses this..

13A.4. Matching geometric invaria nts We start with simply nding a set of numbers which are invariant. The approach will be to nd ve points in the 3D model and calculate from them some properties which uniquely characterize them in an invariant way. Then, we will nd ve points in the image and determine which model they best match.

Choose a set of ve feature points {X 1 , X 2 , X 3 , X 4 , X 5 } from the 3D model, at least four of which are noncoplanar. Since ve points cannot be linearly independent, we can write one of them as a linear combination of the others. We choose to represent point X 5 in this way,.

To avoid cluttering this d Code 3/9 for .NET escription of the indexing paradigm with lots of details, we ask the reader to tolerate the omission of some details. They are in the cited paper.

. Topic 13A Matching using homogeneous coordina .net framework ANSI/AIM Code 39 tes (section 9.1) X 5 = a X 1 + bX 2 + cX 3 + d X 4 .

(13.20). We make use of the observa tion that the determinant of a matrix of points is invariant to rigid body motions,4 and write the determinant which is constructed from any four of the ve points, using as a subscript, the index of the point we omitted. For example, M1 = . X 2 X 3 X 4 X 5 . (13.21).

From the linear dependence bar code 39 for .NET of X 5 in Eq. (13.

20), we substitute for X 5 in each case, deriving M1 = a. X 2 X 3 X 4 X 1 + b X 2 X 3 X 4 X 2 + c X 2 X 3 X 4 X 3 + d X 2 X 3 X 4 X 4 . (13.22).

This can be simpli ed by o bserving that the determinant of a matrix which has two identical columns is zero: M1 = a. X 2 X 3 X 4 X 1 . (13.23).

But this can be simpli ed Code 39 Full ASCII for .NET even more by observing that if you interchange two columns, you ip the sign of the determinant. M1 = ( a).

X 1 X 3 X 4 X 2 = a. X 1 X 3 X 2 X 4 = ( a). X 1 X 2 X 3 X 4 . So M1 = a M5 . Similarl visual .

net 39 barcode y M2 = bM5 M3 = cM5 M4 = d M5 . From this, we can write an expression for the coef cients: a= M1 M5 b= M2 M5 c= M3 M5 d= M4 . M5 (13.

27) (13.26) (13.25) (13.

24). In 2D, the same ve points project to a set of 3-vectors (again, using homogeneous coordinates), and x5 = ax1 + bx2 + cx3 + d x4 . (13.28).

We construct 3 3 matrice barcode code39 for .NET s by leaving out two indices, and denoting by subscript the indices left out: m 12 = . x3 x4 x5 .. (13.29). In fact, absolute invarian Visual Studio .NET barcode 39 ts of linear forms are always ratios of powers of determinants [13.19].

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