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The Essential Guide to Image Processing- P11

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The Essential Guide to Image Processing- P11:We are in the middle of an exciting period of time in the field of image processing. Indeed, scarcely a week passes where we do not hear an announcement of some new technological breakthrough in the areas of digital computation and telecommunication. | 304 CHAPTER 13 Morphological Filtering Image marker a 10 iters b 40 iters c Reconstruction opening d FIGURE 13.4 a Original binary image 192 x 228 pixels and a square marker within the largest component. The next three images show iterations of the conditional dilation of the marker with a 3 x 3-pixel square structuring element b 10 iterations c 40 iterations d reconstruction opening reached after 128 iterations. Replacing the binary with gray-level images the set dilation with function dilation and A with A yields the gray-level reconstruction opening of a gray-level image f from a marker image m Pb m f lim gk gk 8b gk-1 A f go m - f. 13.30 k This reconstructs the bright components of the reference image f that contains the marker m. For example as shown in Fig. 13.2 the results of any prior image smoothing like the radial opening of Fig. 13.2 b can be treated as a marker which is subsequently reconstructed under the original image as reference to recover exactly those bright image components whose parts have remained after the first operation. There is a large variety of reconstruction openings depending on the choice of the marker. Two useful cases are i size -based markers chosen as the Minkowski erosion m f rB of the reference image f by a disk of radius r and ii contrast -based markers chosen as the difference m x f x h of a constant h 0 from the image. In the first case the reconstruction opening retains only objects whose horizontal size i.e. diameter of inscribable disk is not smaller than r. In the second case only objects whose contrast i.e. height difference from neighbors exceeds h will leave a remnant after the reconstruction. In both cases the marker is a function of the reference signal. Reconstruction of the dark image components hit by some marker is accomplished by the dual filter the reconstruction closing Pb m f Jim gk gk SB gk-1 vf go m f. 13.31 k Examples of gray-level reconstruction filters are shown in Fig. 13.5. Despite their many .

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