Abstract
This work presents a novel approach for curve tracing and user-steered boundary tracking in image segmentation, named Bandeirantes. The proposed approach was devised using Image Foresting Transform with unexplored and dynamic connectivity functions, which incorporate the internal energy of the paths, at any curvature scale, resulting in better segmentation of smooth-shaped objects and leading to a better curve tracing algorithm. We analyze its theoretical properties and discuss its relations with other popular methods, such as riverbed, live wire and G-wire. We compare the methods in a curve tracing task of an automatic grading system. The results show that the new method can significantly increase the system accuracy.
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Notes
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The Bandeirantes were 17th-century Portuguese settlers in Brazil and fortune hunters from the São Paulo region. They led expeditions called bandeiras which penetrated the interior of Brazil far south and west of the Tordesillas Line of 1494. As they ventured into unmapped regions in search of profit and adventure, they expanded the effective borders of the Brazilian colony.
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Consider the moment when the first pixel u not in \({{{\mathcal {O}}}}^1\) leaves the priority queue. Note that \(\tau ^{P}_u\) is optimum in \(G^2\), because otherwise, since f is monotone, an optimum path \(\langle a_0, \ldots , a_m = u \rangle \) to u in \(G^2\) would have a cost \(f(\langle a_0, \ldots , a_i \rangle ) < f(\tau ^{P}_u)\) for all \(i \le m\). So some ancestor of u in \(\langle a_0, \ldots , a_m = u \rangle \) not in \({{{\mathcal {O}}}}^1\) must be removed from \({{{\mathcal {Q}}}}\) prior to u, leading to a contradiction.
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Acknowledgements
Thanks to CNPq (308985/2015-0, 486083/2013-6, FINEP 1266/13), FAPESP (2011/50761-2,2014/12236-1), CAPES, and NAP eScience - PRP - USP for funding, and Alexandre Morimitsu and Fabio Albuquerque Dela Antonio for helping to build the dataset.
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Condori, M.A.T., Mansilla, L.A.C., Miranda, P.A.V. (2017). Bandeirantes: A Graph-Based Approach for Curve Tracing and Boundary Tracking. In: Angulo, J., Velasco-Forero, S., Meyer, F. (eds) Mathematical Morphology and Its Applications to Signal and Image Processing. ISMM 2017. Lecture Notes in Computer Science(), vol 10225. Springer, Cham. https://doi.org/10.1007/978-3-319-57240-6_8
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