Invertible orientation scores as an application of generalized wavelet theory

R. Duits, M. Duits, M.A. Almsick, van, B.M. Haar Romenij, ter

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16 Citaten (Scopus)
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Samenvatting

Inspired by the visual system of many mammals, we consider the construction of—and reconstruction from—an orientation score of an image, via a wavelet transform corresponding to the left-regular representation of the Euclidean motion group in (R2) and oriented wavelet f ¿ (R2). Because this representation is reducible, the general wavelet reconstruction theorem does not apply. By means of reproducing kernel theory, we formulate a new and more general wavelet theory, which is applied to our specific case. As a result we can quantify the well-posedness of the reconstruction given the wavelet f and deal with the question of which oriented wavelet f is practically desirable in the sense that it both allows a stable reconstruction and a proper detection of local elongated structures. This enables image enhancement by means of left-invariant operators on orientation scores.
Originele taal-2Engels
Pagina's (van-tot)42-75
TijdschriftPattern Recognition and Image Analysis
Volume17
Nummer van het tijdschrift1
DOI's
StatusGepubliceerd - 2007

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