Abstract
This chapter presents the tree of shapes of an image, a mix of the component trees of upper and lower level sets. Its existence under fairly weak assumptions and its completeness are proven. Ignoring the small details of the image, we show the essentially finite nature of the tree. Finally, we illustrate these theoretical results with a direct application to gray level quantization.
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© 2010 Springer-Verlag Berlin Heidelberg
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Caselles, V., Monasse, P. (2010). The Tree of Shapes of an Image. In: Geometric Description of Images as Topographic Maps. Lecture Notes in Mathematics(), vol 1984. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04611-7_2
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DOI: https://doi.org/10.1007/978-3-642-04611-7_2
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-04610-0
Online ISBN: 978-3-642-04611-7
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