期刊
JOURNAL OF MATHEMATICAL IMAGING AND VISION
卷 21, 期 1, 页码 5-26出版社
SPRINGER
DOI: 10.1023/B:JMIV.0000026554.79537.35
关键词
Poisson kernel; scale-space; local phase; analytic signal; Riesz transform; monogenic signal
In this paper we address the topics of scale-space and phase-based image processing in a unifying framework. In contrast to the common opinion, the Gaussian kernel is not the unique choice for a linear scale-space. Instead, we chose the Poisson kernel since it is closely related to the monogenic signal, a 2D generalization of the analytic signal, where the Riesz transform replaces the Hilbert transform. The Riesz transform itself yields the flux of the Poisson scale-space and the combination of flux and scale-space, the monogenic scale-space, provides the local features phase-vector and attenuation in scale-space. Under certain assumptions, the latter two again form a monogenic scale-space which gives deeper insight to low-level image processing. In particular, we discuss edge detection by a new approach to phase congruency and its relation to amplitude based methods, reconstruction from local amplitude and local phase, and the evaluation of the local frequency.
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