9.Morphological Image Processing

9.1 Preliminaries

9.1 Preliminaries -When working with images, we require that structuring elements be rectangular arrays. -This is accomplished by appending the smallest possible number of background elements necessary to from a rectangular array

9.2 Erosion and Dilation

9.2.1 Erosion -We can view erosion as a morphological filtering operation in which image details smaller than the structuring element are filtered from the image 9.2.2 Dilation -The same image with broken characters that we studied in connection with lowpass filtering 9.2.3 Duality -It is useful particularly when the structuring element is symmetric with respect to its origin

9.3 Opening and Closing

9.3 Opening and Closing -Opening generally smoothes the contour of an object, break narrow isthmuses and eliminates thin protrusion -Closing tends to smooth sections of contours but, as opposed to opening, it generally fuses narrow breaks

9.4 The Hit-or-Miss Transformation

9.4 The Hit-or-Miss Transformation -It is basic tool for shape detection

9.5 Some Basic Morphological Algorithms

9.5.1 Boundary Extraction -The boundary of a set A, denoted by b, can be obtained by first eroding A By B and then performing the set difference between A and its erosion.

9.5.2 Hole Filling -A hole may be defined as a background region surrounded by a connected border of foreground picels.

9.5.3 Extraction of Connected Components -Extraction of connected components from a binary image is central to many automated image analysis applications

9.5.4 Convex Hull -The convex hull H of an arbitrary set S is the smallest convex set containing S.

9.5.5 Thinning -The process is to thin A by one pass with B, then thin the result with one pass of B, and so on, until A is thinned with one pass of B.

9.5.6 Thickening -It is the morphological dual of thinning and is defined by the expression where B is a structuring element suitable for thickening.

9.5.7 Skeletons -Morphology produces an elegant formulation in terms of erosions and openings of given set.

9.5.8 Pruning -Pruning methods are an essential complement to thinning an skeletonizing algorithms because these procedures tend to leave parasitic components that need to be “cleaned up” by postprocessing

9.5.9 Morphological Reconstruction -It involves two images and structuring element. -One image, the maker, contains the starting points for the transformation -The other image, the mask, constrains the transformation

9.6 Gray-scale Morphology

9.6.1 Erosion and Dilation -The erosion of by a flat structuring element b at any location is defined as the minimum value of the image in the region coincident with b when the origin of b is at (x,y)

9.6.2 Opening and Closing -Opening and closing of images have a simple geometric interpretation.

9.6.3 Some Basic Gray Scale Morphological Algorithms -Morphological smoothing, Morphological gradient, Top-hat and bottom-hat transformations Granulometry, Textural segmentation

9.6.4 Gray-Scale Morphological Reconstruction -Gray scale morphological reconstruction is defined basically in the same manner introduced in Morphological Reconstruction