Fusion of sensor data, knowledge sources and algorithms for extraction and classification of topographic objects

baltsavias, emmanuel p.

Bibliographic data

Monograph

Persistent identifier:: 856473650

Author:: Baltsavias, Emmanuel P.

Title:: Fusion of sensor data, knowledge sources and algorithms for extraction and classification of topographic objects

Sub title:: Joint ISPRS/EARSeL Workshop ; 3 - 4 June 1999, Valladolid, Spain

Scope:: III, 209 Seiten

Year of publication:: 1999

Place of publication:: Coventry

Publisher of the original:: RICS Books

Identifier (digital):: 856473650

Illustration:: Illustrationen, Diagramme, Karten

Language:: English

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

Publisher of the digital copy:: Technische Informationsbibliothek Hannover

Place of publication of the digital copy:: Hannover

Year of publication of the original:: 2016

Document type:: Monograph

Collection:: Earth sciences

Chapter

Title:: TECHNICAL SESSION 5 FUSION OF VARIABLE SPATIAL / SPECTRAL RESOLUTION IMAGES

Document type:: Monograph

Structure type:: Chapter

Chapter

Title:: FUSION OF 18 m MOMS-2P AND 30 m LANDS AT TM MULTISPECTRAL DATA BY THE GENERALIZED LAPLACIAN PYRAMID. Bruno Aiazzi, Luciano Alparone, Stefano Baronti, Ivan Pippi

Document type:: Monograph

Structure type:: Chapter

International Archives of Photogrammetry and Remote Sensing, Vol. 32, Part 7-4-3 W6, Valladolid, Spain, 3-4 June, 1999 117 2. MULTIRESOLUTION IMAGE ANALYSIS 2.1 Gaussian and Laplacian pyramids The Laplacian pyramid is derived from the Gaussian pyramid (GP) which is a multi-resolution image representation obtained through a recursive reduction (low-pass filtering and decimation) of the image data set. Let Go(m, n), m = 0,..., M — 1, and n = 0,..., N — 1, M = u x 2 h , N — v x 2 h , be a grey-scale image. The classic Burt’s GP (Burt, 1983, 1984) is defined with a decimation factor of 2 (| 2) as L r L r Gk(m,n) = reduce2[Gk-i](rn, n) = EE i=-L r j = -L r T2(i) X r 2 (j)Gk-1 (2m + i, 2n + ;') (1) for A; = m = 0, ...,M/2 k — 1, and n = 0,..., N/2 k — 1; in which k identifies the level of the pyra mid, K being the top, or root, or base-band, of size u x v. The 2D reduction low-pass filter is given as the outer product of a linear symmetric kernel, generally odd-sized, i.e. {r 2 (i), i = —L r , ■ ■ •, L r } which should have the —3 dB cut-off at one half of the bandwidth of the signal, to minimize the effects of aliasing (Crochiere, 83), although this requirement was not always strictly observed (Burt, 1983, 1984). From the GP, the enhanced LP (ELP) (Baronti, 1994; Aiazzi, 1997b) is defined, for k = 0,..., K — 1, as Lk(m,n) = Gk{rn,n) - expand2[Gk+i\(m,n) (2) in which expand2[Gk+1] denotes the (k + l)st GP level ex panded by 2 to match the size of the underlying Ac-th level: L e L e expand2[Gk+i](rn,n) — EE e 2 (i) x e 2 (j) i=-L e j — — L e (j+n) mod 2=0 (i+m) mod 2=0 X (3) for m = 0,..., M/2 k - 1, n = 0,..., N/2 k - 1, and k = 0,..., K — 1. The 2D low-pass filter for expansion is given as the outer product of a linear symmetric odd-sized kernel {e 2 (z), i = —L e , • • •, L e }, which must cut-off at one half of the bandwidth of the signal to reject the spectral images introduced by up-sampling by 2 (j' 2) (Crochiere, 1983). Summation terms are taken to be null for noninteger values of (i + m)/2 and (j + n)/2, corre sponding to interleaving zeroes. The base-band is usually added to the band-pass ELP, that is Lk (m, n) = Gk (m, n), to yield a complete multi-resolution image description. The attribute enhanced (Baronti, 1994) depends on the expan sion filter being forced to be half-band, i.e. an interpolator by 2 (Crochiere, 1983), and chosen independently of the reduction fil ter, which may be half-band as well, or not. The ELP outperforms Burt’s LP for image compression (Aiazzi, 1997b), incidentally by using different filters (Burt’s Gaussian-like kernel for reduction), thanks to its layers being almost completely uticorrelated with one another. (a) (b) Fig. 1. GP (a) and ELP (b) layers 0 to 3 of 512x512 detail from Landsat TM Band 5 portraying Elba Island and Tyrrhenian Sea, in Italy. Figure 1 shows the GP (1) and ELP (2) of a typical optic re motely sensed image. Notice the low-pass octave structure of GP layers, as well as the band-pass octave structure of ELP layers. 2.2 Generalized Laplacian pyramid When the desired scale ratio is not a power of 2, but a ratio nal number, (1) and (3) need be generalized to deal with rational factors for reduction and expansion (Kim, 1993). Reduction by an integer factor p is defined as L r L r reduce p [Gk](rn,n) = EE r P (i) x r p (j) i=-L r j=-L r x G k (pm -\-i,pn + j). (4) The reduction filter {r p (i), i = —L r , ■ ■ ■, L r } must cut-off at one p-th of bandwidth, to prevent from introduction of aliasing. Analogously, an expansion by p is defined as Le L e expand p [Gk](m,n) = EE e p (i) x e p (j) Le j = Le (j+n) mod p=0 (i+m) mod p=0 x Gl fi±E,i±»y (5) V p p J The low-pass filter for expansion {e p (i), i = -L e ,- ■ ■ ,L e } must cut-off at one p-th of bandwidth. Summation terms are taken to be null for noninteger values of (i + m)/p and (j + n)/p, corresponding to interleaved zero samples. If p/q > 1 is the desired scale ratio, (1) modifies into the cascade of an expansion by q and a reduction by p, to yield a generalized GP (GGP) (Kim 1993): Gk+i = reduce p / q [Gk] = reduce p {expand q [Gk]} (6)

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