Proceedings, XXth congress: Proceedings, XXth congress

Altan, M. Orhan

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Multivolume work

Persistent identifier:: 1663674213

Title:: Proceedings, XXth congress

Sub title:: Istanbul, 12 - 23 July 2004

Year of publication:: 2004

Place of publication:: Istanbul

Publisher of the original:: [Verlag nicht ermittelbar]

Identifier (digital):: 1663674213

Language:: English

Additional Notes:: Erscheinungsdatum des Originals ist aus dem Copyrightjahr ermittelt.; Auch bezeichnet als XXth International Congress for Photogrammetry and Remote Sensing

Editor:: Altan, M. Orhan

Corporations:: International Society for Photogrammetry and Remote Sensing, Congress, 20., 2004, Istanbul; International Society for Photogrammetry and Remote Sensing, Commission Primary Data Acquisition

Adapter:: International Society for Photogrammetry and Remote Sensing, Congress, 20., 2004, Istanbul; International Society for Photogrammetry and Remote Sensing, Commission Primary Data Acquisition

Founder of work:: International Society for Photogrammetry and Remote Sensing, Congress, 20., 2004, Istanbul; International Society for Photogrammetry and Remote Sensing, Commission Primary Data Acquisition

Other corporate:: International Society for Photogrammetry and Remote Sensing, Congress, 20., 2004, Istanbul; International Society for Photogrammetry and Remote Sensing, Commission Primary Data Acquisition

Document type:: Multivolume work

Volume

Persistent identifier:: 166368779X

Title:: Proceedings, XXth congress

Scope:: IV, 226 Seiten

Year of publication:: 2004

Place of publication:: Istanbul

Publisher of the original:: [Verlag nicht ermittelbar]

Identifier (digital):: 166368779X

Illustration:: Illustrationen, Diagramme

Signature of the source:: ZS 312(35,B8)

Language:: English

Additional Notes:: Erscheinungsdatum des Originals ist aus dem Copyrightjahr ermittelt.

Usage licence:: Attribution 4.0 International (CC BY 4.0)

Editor:: Altan, M. Orhan

Corporations:: International Society for Photogrammetry and Remote Sensing, Congress, 20., 2004, Istanbul; International Society for Photogrammetry and Remote Sensing

Adapter:: International Society for Photogrammetry and Remote Sensing, Congress, 20., 2004, Istanbul; International Society for Photogrammetry and Remote Sensing

Founder of work:: International Society for Photogrammetry and Remote Sensing, Congress, 20., 2004, Istanbul; International Society for Photogrammetry and Remote Sensing

Other corporate:: International Society for Photogrammetry and Remote Sensing, Congress, 20., 2004, Istanbul; International Society for Photogrammetry and Remote Sensing

Publisher of the digital copy:: Technische Informationsbibliothek Hannover

Place of publication of the digital copy:: Hannover

Year of publication of the original:: 2019

Document type:: Volume

Collection:: Earth sciences

Chapter

Title:: THE CURVELET TRANSFORM FOR IMAGE FUSION Myungjin Choi, Rae Young Kim, Moon-Gyu Kim

Document type:: Multivolume work

Structure type:: Chapter

bul 2004 Ticients > Radon (7) 1ofa |- Radon ind / is 12° ie all such | dyadic =Qg we a nice ve dilate lucing a ;, make ransport (8) jares at a dO 4 (9) h sent any 1e form near the ridgelet 0=0 rted near of local tting the International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B-YF. Istanbul 2004 scale s vary defines the multiscale ridgelet dictionary D (ye ois2 sS QeQ,. a» 0, be RO c[0,27)) by Q^ Yabo T OI WV, po that is, a whole pyramid of local ridgelets at various lengths and locations. This is, of course, a massively overcomplete representation system and no formula like (9) is available for this multiscale ridgelet pyramid, because it is highly overcomplete. 2.3 Discrete Ridgelet Transfrom(DRT) A basic strategy for calculating the continuous ridgelet transform is first to compute the Radon transform Rf (0,1) and second to apply a one-dimensional wavelet transform to the slices Af (0. -).. A fundamental fact about the Radon transform is the projection- slice formula(Deans, 1983) : f («cos 0, w sin 0) = [ron (10) This says that the Radon transform can be obtained by applying the one-dimensional inverse Fourier transform to the two- dimensional Fourier transform restricted to radial lines through the origin. This of course suggests that approximate Radon transforms for digital data can be based on discrete fast Fourier transforms. In outline, one simply does the following, 1. 2D-FFT Compute the two-dimensional Fast Fourier Transform (FFT) of 1. 2. Cartesian to polar conversion Using an interpolation scheme, substitute the sampled values of the Fourier transform obtained on the square lattice with sampled values of f on a polar lattice: that is, on a lattice where the points fall on lines through the origin. 3. 1D-IFFT Compute the one-dimensional Inverse Fast Fourier Transform (IFFT) on each line; i.e., for each value of the angular parameter. The use of this strategy in connection with ridgelet transform has been discussed in the articles( Deans, 1983 ; Donoho, 1998). 3. DIGITAL CURLET TRANSFORM The idea of curvelets (Candes er al, 1999;Starck et al, 2002;Starck et al, 2003) is to represent a curve as a super- position of functions of various lengths and widths obeying the scaling law width = length” . This can be done by first decomposing the image into subbands, i.e., separating the object into a series of disjoint scales. Each scale is then analysed by means of a local ridgelet transform. 61 a 1 wo Radon Transform Ridgelet[Transform 2 e < Frequency Figure 1. Ridgelet transform flowgraph. Each of the 27 radial lines in the Fourier domain is processed separately. The 1-D inverse FFT is calculated along each radial line followed by a I-D nonorthogonal wavelet transform. In practice, the 1-D wavelet coefficients are directly calculated in the Fourier space. Curvelets are based on multiscale ridgelets combined with a spatial bandpass filtering operation to isolate different scales. This spatial bandpass filter nearly kills all multiscale ridgelets which are not in the frequency range of the filter. In other words, a curvelet is a multiscale ridgelet which lives in a prescribed frequency band. The bandpass is set so that the curvelet length and width at fine scales are related by a scaling law width = length” and so the anisotropy increases with decreasing scale like a power law. There is very special relationship between the depth of the multiscale pyramid and the index of the dyadic subbands; the side length of the localizing windows is doubled at every other dyadic subband, hence maintaining the fundamental property of the curvelet 15 transform which says that elements of length about 2^ serve for the analysis and synthesis of the / th subband [2,27]. While multiscale ridgelets have arbitrary dyadic length and arbitrary dyadic widths, curvelets have a scaling obeying width = length” . Loosely speaking, the curvelet dictionary is a subset of the multiscale ridgelet dictionary, but which allows reconstruction. The discrete curvelet transform of a continuum function f (31,x?) makes use of a dyadic sequence of scales, and a bank of filters (P f, A, f, A, f,L) with the property that the passband filter ^ is concentrated near the frequencies 2s+2 ]. €.2. 2s [2.2

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