Abstract
Bit-quads are \(2\times 2\) binary patterns which are counted within a binary image and can be used to compute attributes. Based on previous works which proposed an efficient algorithm to count bit-quads in component trees, in this paper, we discuss how we can count these patterns in tree of shapes by presenting two approaches. In the first one, we show how counting quads in component trees can be used to count them in tree of shapes by using the depth of the node as the value of pixels in a larger and interpolated image representation (used in an algorithm for constructing tree of shapes). In the second approach, we propose a novel algorithm which uses this larger image representation, but, the resulting quad counts are for the input image. In this way, our approach gives exactly the counts for the original image. We also provide experimental results showing that our algorithm is much faster than the non-incremental naive approach.
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Acknowledgements
This study was financed in part by the CNPq - Conselho Nacional de Desenvolvimento Científico e Tecnológico (Proc. 141422/2018-1 and 428720/2018-8); CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (Finance Code 001); FAPESP - Fundação de Amparo a Pesquisa do Estado de São Paulo (Proc. 2015/01587-0 and 2018/15652-7).
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da Silva, D.J., Alves, W.A.L., Morimitsu, A., Gobber, C.F., Hashimoto, R.F. (2019). Incremental Bit-Quads Count in Tree of Shapes. In: Burgeth, B., Kleefeld, A., Naegel, B., Passat, N., Perret, B. (eds) Mathematical Morphology and Its Applications to Signal and Image Processing. ISMM 2019. Lecture Notes in Computer Science(), vol 11564. Springer, Cham. https://doi.org/10.1007/978-3-030-20867-7_13
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