P. F. M. Nacken. Image Analysis Methods Based on Hierarchies of Graphs and Multi-Scale Mathematical Morphology. PhD thesis, University of Amsterdam, Amsterdam, The Netherlands, 1994. Home/Search Document Details and Download
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Generalized Pattern Spectra Sensitive to Spatial Information - Wilkinson (2002) (Correct)
....size classes, often without prior segmentation of the image. The simplest way to do this is through the use of pattern spectra which show how the number of foreground pixels in the image changes as a function of the size parameter [5] Here, size is usually defined in terms of the width of objects [7, 10], though area may be used as well [12] This information can be used in e.g. soil analysis [11] A drawback of the classical definition of pattern spectra is that spatial information, i.e. information about the position of components removed by each filter, is not included in a pattern spectrum. ....
....also information on the distribution of these details. A subset of these methods ensure rotation, translation and scale invariance of the spatial pattern spectrum. Besides defining spatial pattern spectra, it is shown that an algorithm based on Nacken s approach to chamfer based granulometries [10] can be adapted to spatial pattern spectra in the case of binary images. 2 Theory 2.1 Granulometries Let binary images X and Y be defined as a subset of the image domain M Z or R (usually n = 2) Grey scale images are a mapping from M to Z or R. Definition 1 A binary granulometry is a ....
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P. F. M. Nacken. Image Analysis Methods Based on Hierarchies of Graphs and Multi-Scale Mathematical Morphology. PhD thesis, University of Amsterdam, Amsterdam, The Netherlands, 1994.
Finding Connected Components with Dual Irregular Pyramids - Macho, Kropatsch (1995) (Correct)
....2a) we see only one edge connecting f 1 and f 2 (v 3 ,v 4 ) in 2b) there are two edges connecting these faces ( v 3 ; v 5 ) and (v 4 ; v 5 ) The edges in the face graph correspond to borders of the regions which are represented by the vertices in the neighbourhood graph (chapter 6.3.1. in [9]) Using this information it is possible to reconstruct this border between two regions in the pyramid. 4 Building the pyramids The process to build dual pyramids consists of two independent operations [4] Selecting the decimation parameters (surviving vertices and their receptive fields) by ....
....s4 s1 s3 s4 s1 s3 s4 n1 n4 s2 s2 s2 s3 n2 n3 s5 s5 n5 s5 Figure 3: Visualisation of the two processes in the dual graph contraction 6 Searching for connected components 6. 1 Our image House Figure 4 shows an example of an image of size 16 Theta 16 pixels, similar to one used in [9], page 100. In the upper left corner we see the original image, from left to right and top to bottom the receptive fields of the vertices of the neighbourhood graph in 5 levels of searching for connected components are visualized in false colors. Figure 4: Steps to find connected components in ....
Peter Nacken. Image Analysis Methods Based on Hierarchies of Graphs and Multi-Scale Mathematical Morphology. PhD-thesis, University of Amsterdam, 1994
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