1 June 1992 Generalized skeleton representation and adaptive rectangular decomposition of binary images
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This report presents a technique of decomposing an arbitrary binary image into the union of rectangles so that the number of rectangles becomes as small as possible. This decomposition is referred as adaptive rectangular decomposition. Decomposing a binary image into objects with a same basic shape but with different sizes is familiar as morphological skeleton decomposition. To implement adaptive rectangular decomposition, we generalize the discrete version of morphological skeleton decomposition by replacing a sequences of disks {nB}, n equals 0,1, (DOT)(DOT)(DOT) with a structuring element sequence {Bn}, where Bn equals Bn-1 (direct sum) Gn-1 and Gn is called a generator. A good selection of each generator in a generator sequence {Gn} makes a compact representation of a given binary image. In adaptive rectangular decomposition, we restrict each generator Gn by one of only two objects; the vertical 2-pixel line V and the horizontal 2-pixel line H. The adaptive rectangular decomposition algorithm selects the best sequence {Gn} using dynamic programming (DP) technique. In some experiments, we compared adaptive rectangular decomposition with other types of decomposition in the viewpoint of the time cost of morphological operations by decomposed structuring elements (decomposed binary images). Experimental results show that the time cost of the operations by the structuring elements represented by adaptive rectangular decompositions is smaller than the case of other types of decompositions.
© (1992) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Kenji Shoji "Generalized skeleton representation and adaptive rectangular decomposition of binary images", Proc. SPIE 1769, Image Algebra and Morphological Image Processing III, (1 June 1992); doi: 10.1117/12.60660; https://doi.org/10.1117/12.60660

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