Segmentation in .NET Development barcode 39 in .NET Segmentation

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Segmentation using vs .net toassign code 39 full ascii in web,windows application OneCode metric function) is the negative of the distance transform. This is the key point to understanding level sets. You are modifying EVERY point, outside and inside the contour..

(x, y) =. DT (x, y) DT (x, y). if (x, y) is outside the contour if (x, y) is inside the contour. (8.3). It is important bar code 39 for .NET to note that for points on the contour, the metric function is equal to zero. The set of points where (x, y) = C is called the C-level set of , and we are particularly interested in the zero-level set.

Now we will modify the metric function . For every point (x, y) we compute a new value of (x, y). There are several ways we could modify those points, and we will mention some of them below, but remember, the contour of interest is still the set of points where the (modi ed) metric function takes on a value of zero.

We initialized it to be the distance transform, but from here on, you should no longer think of it as a distance transform (although it will retain some of those characteristics). Instead, just think of it as another brightness, a function of x and y. What is the gradient of the metric function You knew how to compute the gradient when it was brightness.

It is no different. Thinking about a level set as an isophote, you knew that the gradient is normal to the isophote, so, given the gradient vector, how did you get the normal Do you remember how to calculate the gradient G(x, y) = (x, y), (x, y) x y. (8.4). then the normal .net vs 2010 bar code 39 is just the normalized (naturally) version of the gradient. n(x, y) = G(x, y) .

. G(x, y). (8.5). So we can relat e the normal to the contour to the gradient of the metric function. We can also relate [9.46] the movement of the contour in the normal direction to a function (which is called the speed function), describing how rapidly the metric changes, producing a differential form for the change in : (x, y) = s( ).

(x, y). , t (8.6). where s is a pr VS .NET USS Code 39 oblem-dependent speed function, with curvature and image edginess as parameters, similar to that de ned in Eq. (8.

2). We could modify the metric function in a variety of ways. For example, we could use a form which looks like a gradient descent.

Now precisely w hat is the difference between equations (8.7) and (8.8) .

(x, y) =. (x, y) s(x, y). (x, y). . . (8.7). Or a form which looks like a differential equation (x, y) t (x, y). = s(x, y). (x, y). ,. (8.8). 8.6 Segmentation of surfaces To be consisten t with the literature (and so it will t on one line), we are using the subscript notation for partial derivatives here.. where s involve visual .net Code 3/9 s something about the brightness variations in the image and also involves the curvature (in 2D) of the isophote at x, y. Of course, if you insist on using the 2D curvature of the zero level set, you need to relate that to the function , which fortunately is not too hard.

Since the normal vector has already been worked out, and the curvature can be related to changes in normal direction, it is possible to show that: =. xx 2 x 2 3/2 y (8.9). Fig. 8.16.

A co VS .NET Code 39 Extended ntour with a very sharp crease in it. A unit step in the normal direction near the crease moves the new contour inside the old.

. where the funct ional notation has been dropped. Over the course of the algorithm, the metric function evolves following a rule like Eq. (8.

7). As it evolves, it will have zero values at different points, and those points will de ne the evolution of the contour. One interesting detail which one must consider when implementing an algorithm like this is the possibility that the contour might cross itself.

For example, consider the contour segment illustrated in Fig. 8.16.

The current contour contains a sharp concavity. Some typical normal vectors are illustrated. A unit step in the direction of the normal at the lowest point would place the new contour point inside the contour.

One approach to dealing with this is a simple heuristic which states that points which were labeled inside can never again be considered as outside. The idea of using level sets for adaptive contours was rst proposed by Sethian [9.66, 9.

67]. Malladi et al. [9.

46] extended this by observing that there are advantages to considering only a set of points near the current contour. Taubin and Ronfard [9.84] use the concept of a level set implicitly in tting piecewise-linear curves.

Kimmel et al. [9.40] demonstrate that level sets may be used for other things, such as nding the shortest path on a surface.

Not all algorithms which use a deformable contour philosophy follow the strategies described in section 8.5. For example, Lai and Chin [8.

33] describe a variation which treats the contour points as a sequence of random variables, which may therefore be described by a Markov process, and optimized using MAP strategies. Space does not permit a discussion of those algorithms here, but the reader may nd adequate direction in the sources cited in the bibliography at the end of this chapter..

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