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Topic 5A Edge detectors in .NET Creator bar code 39 in .NET Topic 5A Edge detectors




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Topic 5A Edge detectors using .net framework todraw code 39 full ascii for asp.net web,windows application Microsoft .NET official Website Examination of ANSI/AIM Code 39 for .NET the literature in biological imaging systems, all the way back to the pioneering work of Hubel and Wiesel in the 1960s [5.13] suggests that biological systems analyze images by making local measurements which quantify orientation, scale, and motion.

Keeping this in mind, suppose we wish to ask a question like is there an edge at orientation at this point How might we construct a kernel that is speci cally sensitive to edges at that orientation A straightforward approach [5.37] is to construct a weighted sum of the two Gaussian rst derivative kernels, G x and G y , using a weighting something like G = G x cos + G y sin ..

Could you calc ulate the orientation selectivity What is the smallest angular difference you could detect with a 3 3 kernel determined in this way . (5.38). Unfortunately, unless quite large kernels are used, the kernels obtained in this way have rather poor orientation selectivity. In the event that we wish to differentiate across scale, the problem is even worse, since a scale space representation is normally computed rather coarsely, to minimize computation time. Perona [5.

31] provides an approach to solving these problems.. 5A.3. Inferring line segments from edge points After we have chosen the very best operators to estimate derivatives, have chosen the best thresholds, and selected the best estimates of edge position, we still have nothing for a set of pixels, some of whom have been marked as probably part of an edge. If those points are adjacent, one could walk from one pixel to the next, eventually circumnavigating a region, and there are representations such as the chain code which make this process easy. However, the points are unlikely to be connected the way we would like them to be.

Some points may be missing due to blur, noise, or partial occlusion. There are many ways to approach this problem, including relaxation labeling, and parametric transforms, both of which will be discussed in detail later in this book. In addition, there are combination methods, such as the work of Deng and Iyengar [5.

11] which combines relaxation and Bayes methods as well as other methods [5.29] which we do not have space to discuss..

5A.4. Space/frequenc y representations Wavelets are very important, but a thorough examination of this area is beyond the scope of this book. Therefore we present only a rather super cial description here, and provide some pointers to literature. For example, Castleman [4.

6] has a readable chapter on wavelets.. 5A.4.1.

Why wavelets Consider the image illustrated in Fig. 5.17.

Clearly, the spatial frequencies appear to be different, depending on where one looks in the image. The Fourier transform has no mechanism for capturing this intuitive need to represent both frequency and location. The Fourier transform of this image will be a two-dimensional array of numbers, representing the amount of energy in the entire image at each spatial frequency.

Clearly, since the Fourier transform is invertible, it captures all this spatial and frequency information, but there is no obvious way to answer the question: at each position, what are the local spatial frequencies . Linear operators and kernels Fig. 5.17. An image in which spatial frequencies vary dramatically. The wavelet ap .NET barcode 3 of 9 proach is to add a degree of freedom to the representation. Since the Fourier transform is complete and invertible, all we really need to characterize the image is a single two-dimensional array.

Instead however, following the space/frequency philosophy as described in section 5.8, we use a three-(or higher) dimensional data structure. In this sense, the space/frequency representation is redundant (or overcomplete ), and requires signi cantly more storage than the Fourier transform.

. 5A.4.2.

The basic wave .NET barcode 3 of 9 let and wavelet transform We de ne a basic5 wavelet (x, y) as any function of the two spatial variables x and y, which meets a certain criterion that we need not concern ourselves with here. Basically, we desire a function which is symmetric about the origin and has almost nite support.

By almost nite support, we mean that the magnitude of this function drops off to zero rapidly (in a particular way de ned by the admissibility criterion) as it goes away from its center. A one-dimensional example basic wavelet is 2 x2 (x) = (1 x 2 ) exp 2 3 (5.39).

graphed in Fig . 5.18.

From one such wavelet, one may then generate a (potentially in nite) set of similar functions by translation and scaling of the original. That is, we de ne a translated, scaled version of by (again, in one dimension). a,b (x). 1 = a.
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