Abstract
Representing object shape in two or three dimensions has typically involved the description of the object boundary. This paper proposes a means for characterizing object structure and shape that avoids the need to find an explicit boundary. Rather, it operates directly from the imageintensity distribution in the object and its background, using operators that do indeed respond to “boundariness.” It produces a sort of medial-axis description that recognizes that both axis location and object width must be defined according to a tolerance proportional to the object width. This generalized axis is called themultiscale medial axis because it is defined as a curve or set of curves in scale space. It has all of the advantages of the traditional medial axis: representation of protrusions and indentations in the object, decomposition of object-curvature and object-width properties, identification of visually opposite points of the object, incorporation of size constancy and orientation independence, and association of boundary-shape properties with medial locations. It also has significant new advantages: it does not require a predetermination of exactly what locations are included in the object, it provides gross descriptions that are stable against image detail, and it can be used to identify subobjects and regions of boundary detail and to characterize their shape properties.
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This research was partially supported by National Institute of Health grant P01 CA47982, National Aeronautics and Space Administration contract NAS5-30428, U.S. Air Force Office of Scientific Research grant 91-00-58, National Library of Medicine grant LM05508-01, National Library of Medicine/National Cancer Institute medical informatics research training grant 5 T15 LM07071, and a sabbatical grant from the Netherlands Organization for Scientific Research. It was reported orally at the NATO Advanced Research Workshop on Shape in Picture: The Mathematical Description of Shape in Greylevel Images, Driebergen, The Netherlands, in 1992.
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Pizer, S.M., Burbeck, C.A., Coggins, J.M. et al. Object shape before boundary shape: Scale-space medial axes. J Math Imaging Vis 4, 303–313 (1994). https://doi.org/10.1007/BF01254105
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DOI: https://doi.org/10.1007/BF01254105