TAILIEUCHUNG - The Essential Guide to Image Processing- P11

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 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. k This reconstructs the bright components of the reference image f that contains the marker m. For example as shown in Fig. the results of any prior image smoothing like the radial opening of Fig. 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 . diameter of inscribable disk is not smaller than r. In the second case only objects whose contrast . 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. k Examples of gray-level reconstruction filters are shown in Fig. . Despite their many .

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