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(vi v ) (vi v )T . in .NET Creation code 128 barcode in .NET (vi v ) (vi v )T .

(vi v ) (vi v )T . use visual studio .net code-128 development todeploy code 128 code set c on .net QR Code Symbol Versions (7.41). Statistical shape properties Global properties VS .NET Code 128 Code Set A The deformable curve models discussed above employ physical or biomechanical shape constraints, such as smoothness and elasticity. The models discussed in this section, in the literature known as active shape models [32] or active appearance models [33], are constructed by learning the shape or appearance of one speci c object type from a representative set of examples.

This way, the number of degrees of freedom of the model is signi cantly reduced, but the model retains the necessary exibility to cope with the normal shape variability between different instances of this object type. A shape model is built by examining the statistics of the coordinates of corresponding points in a training set of shapes. Each shape is described by n labeled points and corresponding points in different shape instances have the same label.

The model and image template are rst aligned using the eigenfaces method (see p. 174) to correct for differences in pose. This way, m contours {vi , i = 1, 2, .

. . , m} in the same reference frame are obtained.

Each contour can be written as a column vector of coordinates (xik , yik ), that is, vi = [xi1 yi1 xi2 yi2 xin yin ]T . The shape variations vi v , where v is the mean shape and de ned as v= 1 m. This matrix can a lso be written as S=Q QT, (7.42). where Q = [r1 r2 Code 128C for .NET r2n ] is the 2n 2n unitary matrix of eigenvectors rk of S, and is the diagonal matrix of corresponding eigenvalues k (with 1 2 ). The new axes rk in feature space correspond to the new modes of variation, which are mutually uncorrelated and are characteristic for the shape diversity in the training set.

k is the standard deviation along rk of all the shapes in the learning set. The shape model can then be written as. v=v+ ck r k . (7.43). vi ,. (7.40). Each eigenvector Code 128C for .NET rk has a corresponding eigenvalue k , which is the variance of parameter ck in the set of training shapes. Because 1 2 , the foremost modes of variation explain most of the variability in the training set.

By constraining the model to include only the most important modes of variation that explain most of the variability in the training set, the number of degrees of freedom of the model can be signi cantly reduced without affecting much of its descriptive power. Any contour instance v can then be written as v = v + . can be represente d in a 2n-dimensional feature space whose axes correspond to the 2n labeled points along the contour. The variations on different labels are not necessarily uncorrelated. To work in an uncorrelated feature space, the theory of principal component analysis (PCA) can be applied as follows.

The shape. [32] T. F. Cootes Visual Studio .

NET Code128 , C. J. Taylor, D.

H. Cooper, and J. Graham.

Active shape models: Their training and application. Computer Vision and Image Understanding, 61(1): 38 59, 1995. [33] T.

F. Cootes, G. J.

Edwards, and C. J. Taylor.

Active appearance models. IEEE Transactions on Medical Imaging, 23(6): 681 685, 2001..

ck r k . (7.44). By varying the co ef cients ck , the shape of a model instance can be modi ed. If the parameters ck have a normal distribution, the internal energy is (see Eqs. (7.

29) and (7.19)) Eint = 1 2. k=1. ck 2 . k (7.45). 7: Medical image analysis The external ener barcode code 128 for .NET gy can for example be de ned heuristically as in Eq. (7.

35):. Eext = I (v). 2 ds. (7.46). An alternative is , for example, to maximize the similarity with a statistical model of the image intensities perpendicular to each characteristic contour point. Finally the goal is to nd the parameters ck by minimizing the weighted sum of the external and internal energies, i.e.

, Eext + Eint . Figure 7.18 shows an example.

A drawback of the method is that a training phase is needed for each new object type. This usually involves a manual delineation of a suf cient number of representative shapes and the identi cation of corresponding points in the training set. This can be tedious and time consuming but needs to be done carefully, as differences in point coordinates resulting from inconsistencies in the labeling cannot be discriminated from true shape variability.

The matching procedure further assumes that the initialization is suf ciently accurate for convergence to the correct optimum. The initial pose can be speci ed interactively or obtained through a separate procedure, such as the eigenfaces approach, discussed on p. 174.

. Local properties Visual Studio .NET ANSI/AIM Code 128 As stated before, this strategy assumes that the model can be represented as a trajectory or path of contiguous pixels and that the objective function can be expressed in terms of local properties along the path. While before these properties had a physical or biomechanical meaning, in this section the local geometric and photometric properties are obtained by learning the local shape and appearance from a training set.

Figure 7.19(a) shows an example of a thoracic radiograph in which a radiologist delineated the lung boundary by indicating a set of characteristic points, which are connected by straight lines. Repeating this procedure for a representative set of images yields a training set of contours, characterized by the local photometry around each point and by the direction between neighbors.

The local photometry around each labeled point can be modeled studying a small window around this point and applying the theory of eigenfaces (see Figure 7.14). After applying PCA this yields the following local external energy for each labeled point li (see Eqs.

(7.19) and (7.45)).

k=1 2. Eext (li ) =.
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