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Monomial Phase: A Matrix Representation of Local Phase
Linköpings universitet, Institutionen för medicinsk teknik, Medicinsk informatik. Linköpings universitet, Tekniska högskolan. Linköpings universitet, Centrum för medicinsk bildvetenskap och visualisering, CMIV.ORCID-id: 0000-0002-9091-4724
Linköpings universitet, Institutionen för medicinsk teknik, Medicinsk informatik. Linköpings universitet, Tekniska högskolan. Laboratory of Mathematics in Imaging, Brigham and Women’s Hospital, Harvard Medical School, Boston, MA, USA.
2014 (Engelska)Ingår i: Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data / [ed] Carl-Fredrik Westin, Anna Vilanova, Bernhard Burgeth, Springer, 2014, s. 37-73Kapitel i bok, del av antologi (Övrigt vetenskapligt)
Abstract [en]

Local phase is a powerful concept which has been successfully used in many image processing applications. For multidimensional signals the concept of phase is complex and there is no consensus on the precise meaning of phase. It is, however, accepted by all that a measure of phase implicitly carries a directional reference. We present a novel matrix representation of multidimensional phase that has a number of advantages. In contrast to previously suggested phase representations it is shown to be globally isometric for the simple signal class. The proposed phase estimation approach uses spherically separable monomial filter of orders 0, 1 and 2 which extends naturally to N dimensions. For 2-dimensional simple signals the representation has the topology of a Klein bottle. For 1-dimensional signals the new phase representation reduces to the original definition of amplitude and phase for analytic signals. Traditional phase estimation using quadrature filter pairs is based on the analytic signal concept and requires a pre-defined filter direction. The new monomial local phase representation removes this requirement by implicitly incorporating local orientation. We continue to define a phase matrix product which retains the structure of the phase matrix representation. The conjugate product gives a phase difference matrix in a manner similar to the complex conjugate product of complex numbers. Two motion estimation examples are given to demonstrate the advantages of this approach.

Ort, förlag, år, upplaga, sidor
Springer, 2014. s. 37-73
Serie
Mathematics and Visualization, ISSN 1612-3786
Nyckelord [en]
Mathematics, Computer vision, Computer graphics, Differential equations, partial, Visualization, Global differential geometryPartial Differential Equations, Differential Geometry, Computer Imaging, Vision, Pattern Recognition and Graphics, Theoretical, Mathematical and Computational Physics
Nationell ämneskategori
Datorseende och robotik (autonoma system)
Identifikatorer
URN: urn:nbn:se:liu:diva-95762DOI: 10.1007/978-3-642-54301-2_3ISBN: 978-3-642-54300-5 (tryckt)ISBN: 978-3-642-54301-2 (tryckt)OAI: oai:DiVA.org:liu-95762DiVA, id: diva2:637593
Projekt
CMIVCADICS
Forskningsfinansiär
VetenskapsrådetLinnaeus research environment CADICSNIH (National Institute of Health)Tillgänglig från: 2013-07-19 Skapad: 2013-07-19 Senast uppdaterad: 2018-01-11Bibliografiskt granskad

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Knutsson, HansWestin, Carl-Fredrik

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Knutsson, HansWestin, Carl-Fredrik
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Medicinsk informatikTekniska högskolanCentrum för medicinsk bildvetenskap och visualisering, CMIV
Datorseende och robotik (autonoma system)

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