FRAMELET-BASED MULTIRESOLUTION IMAGE FUSION WITH AN IMPROVED INTENSITY-HUE-SATURATION TRANSFORM

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1 FRAMELET-BASED MULTIRESOLUTION IMAGE FUSION WITH AN IMPROVED INTENSITY-HUE-SATURATION TRANSFORM M. J. Cho *, D. H. Lee, H. S. Lm Satellte Iformato Research Isttute, KARI, 45, Eoeu-dog, Yuseog-gu, Daejeo, , KOREA prme, dhlee - hslm@ar.re.r WG VII/6 Remote Sesg Data Fuso KEY WORDS: Satellte remote sesg, Pa-sharpeg, Itesty-Hue-Saturato trasform, Wavelets, Framelets, IKONOS magery. ABSTRACT: The fuso of the pachromatc (PAN) mage wth multspectral (MS) mages s a very useful tool for remote sesg applcatos that requre both hgh-spatal ad hgh-spectral resoluto. A hybrd fuso method, whch comprses of the stadard testy-huesaturato (IHS) trasform ad a wavelet trasform, was recetly troduced the lterature. The hybrd fuso method was able to elmate drawbacs of the IHS ad wavelet-based methods, whle eepg the advatages. I ths paper, we troduce a ew hybrd fuso method based o the fast IHS trasform wth a cotrol parameter alog wth the framelet trasform. The cotrol parameter s used to mmze the radace dfferece betwee the PAN mage ad the testy mage. I addto, the framelet trasform, whch s a atural geeralzato of orthoormal wavelets f redudacy s troduced to the wavelet system, s used to extract the detaled spatal formato from the dfferece mage of the PAN mage ad the testy mage. I order to verfy the performace of the proposed method, a IKONOS PAN mage wth MS mages were used. The proposed method produces more satsfactory results, both vsually ad quattatvely.. INTRODUCTION Due to the techcal lmtato, most earth observe satelltes, such as the SPOT, IKONOS, QucBrd, ad KOMPSAT-, provde a budle of multspectral (MS) mages at a lower spatal resoluto ad a pachromatc (PAN) mage at a hgher spatal resoluto, stead of MS mages at a hgh spatal resoluto. Therefore, a pa-sharpeg techque s very useful tool for remote sesg applcatos that requre both hghspatal ad hgh-spectral resoluto (Zhag,4). May mage fuso techques ad software tools have bee developed for specfc applcatos. Of the hudreds of vared mage fuso techques, the best ow methods are the testy-hue-saturato (IHS) trasform, prcpal compoet aalyss, arthmetc combatos, ad wavelet-based fuso methods. However, most of the exstg techques whch perform sutably well wth medum-resoluto mages, caot always satsfy the fuso of MS ad PAN hgh resoluto mages. Recetly, Gozález-Audícaa et al. (4) troduced a hybrd fuso method comprsed of the stadard IHS trasform ad a udecmated dscrete wavelet trasform (UDWT). The hybrd fuso method was able to elmate drawbacs of the IHS ad wavelet-based methods, whle eepg the advatages. Nevertheless, t s ot effcet eough to qucly merge massve volumes of data from hgh-resoluto satellte mages because of ts hgh computatoal complexty. To reduce the computatoal cost, a fast IHS (FIHS) trasform troduced by Tu et al.(4) s employed o a ew hybrd fuso method. Asde from ts fast computg capablty for fusg mages, ths method ca exted tradtoal three-order trasformatos to a arbtrary order. I addto, we employed a framelet trasform whch s a atural geeralzato of orthoormal wavelets f redudacy s troduced to the wavelet system. It thereby avods some of artfacts that arse whe the decmated dscrete wavelet trasform s appled to the mage fuso le the UDWT. Moreover, t ca reduce the computatoal cost to a half of that of the UDWT. More mportatly, the proposed hybrd method eables us to reduce the overall computatoal cost to a half oe aga through smplfyg the orgal mathematcal model. A detaled explaato wll be gve later the body of ths paper. O the other had, oe of dsadvatages of IHS-based methods s that they destroy the spectral characterstcs of the MS data (Cho,6). Recet studes have show that the large dfferece betwee the values of the PAN ad testy mages appears to cause the large spectral dstorto of fused MS mages. Ideed, ths dfferece (PAN-I) causes the altered saturato compoet the RGB-IHS coverso model. Therefore, a FIHS trasform wth a cotrol parameter s employed to mmze the radace dfferece betwee the PAN mage ad the testy mage. I order to verfy the performace of the proposed method, a IKONOS PAN mage wth MS mages were used. The the spatal ad spectral qualty of the resultg mages were aalyzed ad compared to mages obtaed from other wellow methods. The followg chapter wll expla the theory of the framelet trasform. Readers ufamlar wth the wavelet theory are advsed to cotue to the thrd chapter, whch the * Correspodg author. 73

2 The Iteratoal Archves of the Photogrammetry, Remote Sesg ad Spatal Iformato Sceces. Vol. XXXVII. Part B7. Bejg 8 proposed method wll be explaed. The fourth chapter wll preset the expermetal results.. THE FRAMELET TRANSFORM As t s well ow, except for the Haar flterba, two-bad fte mpulse respose (FIR) orthogoal flterbas do ot allow for symmetry. I addto, mposto of orthogoalty for the two-bad FIR flterbas requres relatvely log flter support for such propertes as a hgh level of smoothess the resultg scalg fucto ad wavelets, as well as a hgh approxmato order. Symmetry ad orthogoalty ca both be obtaed f the flterbas have more tha two bads. Furthermore, due to the crtcal samplg, orthogoal flters suffer a proouced lac of shft varace, though the desrable propertes ca be acheved through the desg of tght frame flterbas, of whch orthogoal flters are a specal case. I cotrast to orthogoal flters, tght frame flters have a level of redudacy that allows for the approxmate shft varace behavor caused by the dese tme-scale plae. Besdes producg symmetry, the tght frame flterbas are shorter ad result smoother scalg ad wavelet fuctos. Before proceedg further, let me descrbe the basc cocepts of frame theory ad oversampled flterbas. A Tght Wavelet Frame A set of fuctos {, K, N } ψ ψ a square tegrable space, L ( ), s called a frame f there exst A >, B < so that, for ay fucto f L ( ), j V = Spa{ φ( t )} j, j j W = Spa{ ψ ( t )}, =, K, N wth V = V UW UW ULUW j j, j, j N, j ad the correspodg scalg fucto ad wavelets satsfy the followg multresoluto equatos: φ( t) = h ( ) φ( t ) ψ ( t) = h( ) φ( t ), =, K, N. Now, the frame boud A taes o the value. Oversampled Flterbas = N A h. = The frame codto ca be expressed terms of oversampled polyphase flters. Gve a set of N flters, we defe them terms of ther polyphase compoets:, N j A f f, ψ ( ) B f, () = j H ( z) = H ( z ) + z H ( z ), =, K, N,,, H, ( z) = h( l) z, l =,. l A ad B are ow as frame bouds, f, g : = f( x) g( x) dx, ad f : = f, f. The specal case of A = B s ow as tght frame. I a tght frame we have, for all f L ( ), whch mples N j = j f, ψ ( ) = A f Now defe the polyphase aalyss matrx as H,( z) H,( z),( ),( ) H( ) H z H z z =. M M,( ),( ) HN z HN z If we ow defe the sgal X ( z) terms of ts polyphase compoets, we the have N j j f = A f, ψ ( ) ψ ( ). = j I order to have a fast wavelet frame (or framelet) trasform, multresoluto aalyss s geerally used to derve tght wavelet frames from scalg fuctos. Now, we obta the followg spaces: T x( z) = ( X ( z) X ( z )), the equato X ( z), l =, s defed terms of the tme doma sgal, x( ), as follows: l ( ) = ( ) X z x l z. l 74

3 The Iteratoal Archves of the Photogrammetry, Remote Sesg ad Spatal Iformato Sceces. Vol. XXXVII. Part B7. Bejg 8 The overall output sgal X ˆ ( z) flterba ca be expressed as of the aalyss-sythess H ( )H( ) = I T z z (4) ˆ ( ) ( )H T ( )H( )x( = ) X z z z z z. Furthermore, to meet perfect recostructo (PR) codto X ˆ ( z ) = X ( z ), we requre that H T ( z)h( z ) = I. H ( z) H ( z),, =,, H( z) H ( z) H ( z).,( ),( ) H z H z Selesc (4), o the other had, shows that a three-bad tght frame flterba PR codtos ca be expressed terms of the Z -trasforms of the flters h, ad h. Moreover, the PR codtos ca be easly exteded to N flters dowsampled by : N- H ( z) H ( z ) = = N- = H z H z ( ) ( ) = Last, Chu et al. () show a ecessary codto for the flterba to exst. That s, the flters H ( z), =, K, N must each satsfy the followg equalty: H ( z) + H ( z) <, z =. Also, f h ( ) s compactly supported, the a soluto { h ( ) ( ) } to Eq. (4) exsts f ad oly f H ( z) + H ( z) <, z =. (5) A wavelet tght frame wth oly two symmetrc or atsymmetrc wavelets s geerally mpossble to obta wth a compactly supported symmetrc scalg fucto, φ ( t). However, Petuhov (3) states a codto that the lowpass flter h ( ) must satsfy so that ths becomes possble. Therefore, f h ( ) s symmetrc, compactly supported, ad satsfes Eq.(5), the a (at-)symmetrc soluto { h ( ) ( ) } to Eq. (4) exsts f ad oly f all the roots of Notce that the equalty reduces to the tradtoal case of a twobad orthogoal flterba..3 A Symmetrc Tght Wavelet Frame wth Two Geerators I ths secto, we troduce the costructo of a symmetrc tght wavelet frame wth two geerators based o a three-bad tght frame flterba ad provde a result ad a example (Selesc, 4). have eve multplcty. H ( z) H ( z ) H ( z) H ( z ) (6).3. Case H( z) = H( z ) : The goal s to desg a set of three flters that satsfy the PR codtos whch the lowpass flter ( ), s symmetrc ad the flters h( ) ad h ( ) are each ether symmetrc or at-symmetrc. There are two cases. Case I deotes the case h ( ) s symmetrc ad h ( ) s at-symmetrc. Case II deotes the case h ( ) ad h ( ) are both at-symmetrc. The symmetry codto for h ( ) s h ( ) = h ( N ), (7) Fgure. A three-bad PR flterba.3. PR Codtos ad Symmetry Codto: The PR codtos for the three-bad flterba, whch are llustrated Fg., ca be obtaed by settg the N the secto.. to a value of 3. That s, we have the followg two equatos: N s the legth of the flter h ( ). We dealt oly wth Case I of eve-legth flters. Solutos for Case I ca be obtaed from solutos h ( ) s a tmereversed verso of h ( ) (ad ether flter s (at-) symmetrc). ( ) ( ) = = H z H z () ( ) ( ) = = H z H z. (3) The PR codtos ca also be wrtte matrx form as 75

4 The Iteratoal Archves of the Photogrammetry, Remote Sesg ad Spatal Iformato Sceces. Vol. XXXVII. Part B7. Bejg 8 ) Fd A( z ) ad Bz ( ) from H ( z ) ad U( z) by, usg factorzato ad root selecto. 3) Fd H ( z) ad H ( ),, z by usg Eq. () ad Eq. (3), respectvely. 4) Fd H ( z ) ad H ( z) by usg H ( z ), H ( z ),, ad Eq. (8). 5) Obta (at-) symmetrc wavelets h ad h by usg Eq. (9) ad Eq. (). Fgure. The frequecy resposes of h, ad h the example To show ths, suppose that h ( ), h( ), ad h ( ) satsfy the PR codtos ad that h ( ) = h( N ). (8) The, by defg ew h ( ) = ( h( ) + h( d )), (9) ew h ( ) = ( h( ) h( d )) wth d Z, () ew ew the flters h, ad h also satsfy the PR codtos, ew ew ad h are symmetrc ad at-symmetrc as follows: ew ew h ( ) = h ( N ), ew ew h ( ) = h ( N ), N = N + d. We state ma results of the paper (Selesc, 4) wthout the proof. The flters h, ad h wth symmetres Eq. (7) ad Eq. (8) satsfy the PR codtos f ther polyphase compoets of the flters are gve by ( ) M / H ),, z = z A z B z () H (, () H (, (3) Fgure 3. The symmetrc scalg fucto, φ ( t), ad the two wavelets ψ () t ad ψ () t of the example h ( ) h ( ) h ( ) Table. Coeffcets for the example Example: To obta a lowpass flter ( ), wth a mmal legth, we used a maxmally flat lowpass eve-legth FIR flter wth the followg trasfer fucto : F m, m m+.5 + z z+ + z z+ z ( z) =. 4 4 = A( zaz ) ( ) = Uz, ( ) B( zbz ) ( ) =.5.5 Uz ( ), U( z) U( z ) = H ( z) H ( z ), ad M = N /.,,.3.3 Flter Desg: Frst, obta a lowpass flter ( ), whch has a eve-legth ad whch satsfes the symmetry codto of Eq. (6). The desg procedure s as follows: ) Kowg H ( z ) ad, thus H ( ), z, use spectral factorzato to fd U( z ) from H ( z) H ( z ).,, Ufortuately, although the settg of H ( z): = F m, ( z ) gves a H ( ) z that does ot satsfy Eq. (6), we ca use a lear combato of varous Fm, ( z) values to obta a H ( z) flter that does satsfy Eq. (6). For example, f we use a settg of ( ) H ( z) = z αf ( z) + ( α ) F ( z), (4) 4, 3, the, for specal values of α, H ( ) z satsfes Eq. (6). 76

5 The Iteratoal Archves of the Photogrammetry, Remote Sesg ad Spatal Iformato Sceces. Vol. XXXVII. Part B7. Bejg 8 Fgure shows the flters for α =.7. Fgure 3 shows the resultg scalg fucto ad wavelets. Table I lsts the coeffcets of the flters h ad h..3.5 Two-Dmesoal Exteso: The D exteso ca be obtaed by alteratg betwee rows ad colums, as s usually doe for typcal dscrete wavelet trasforms. The correspodg flter ba, whch s llustrated Fg.4, s terated o the lowpass brach (the frst brach). 3. THE PROPOSED FUSION METHOD To apply ay of the methods of mage fuso descrbed ths paper, the MS mage ad the PAN mage must be accurately supermposed. Thus, both mages must be co-regstered, ad the MS mage resampled to mae ts pxel sze the same as the PAN mage. I order to acheve ths, a robust regstrato techque ad a b-cubc terpolator were used. Ir ew r PAN = I = I + W, (6) s the low-frequecy verso of the wavelettrasformed testy mage ad = W PAN s the sum of hghfrequecy versos of the wavelet-trasformed PAN mage. 3.3 The Proposed Hybrd Method Assume that, wthout the loss of geeralty, the hybrd method s based o the FIHS fuso method stead of o the tradtoal IHS method. Ths s because Eq. (5) holds. The hybrd method ca be smplfed wth the followg procedure: R + (PAN-I) = F(R) R + (I ew I) F(G) = G + (I ew I) = G + W(PAN-I) = F(B) B + (I ew I) B + W(PAN-I) = W, (7) = W (PAN I) s the sum of the hgh-frequecy versos of the wavelet-trasformed dfferece mage of the PAN mage ad the I mage. Fgure 4. A oversampled flterba for a -D mage 3. FIHS Fuso Method The FIHS fuso for each pxel ca be formulated by the followg procedure (Tu et al., ): F(R) R + (PAN I) F(G) = G + (PAN I), (5) F(B) B + (PAN I) F(X) s the fused mage of the X bad, for X = R, G, ad B, respectvely. 3. The Hybrd Method proposed by Gozález-Audícaa et al. A multresoluto wavelet decomposto s used to execute the detaled extracto phase, ad the IHS procedure s followed to ject the spatal detal of the PAN mage to the MS mage. I other words, stead of usg the PAN mage Eq. (5), the results of the PAN mage ad the testy mage fused by the substtutve wavelet method s used. The fuso results of the PAN mage ad the testy mage are expressed as follows: As a result, we easly obtaed fused mages wth the fast scheme of the hybrd method: We smply added to each MS mage the detaled formato extracted from the dfferece mage of the PAN mage ad the testy mage. Therefore, the proposed hybrd method s much smpler ad faster tha the hybrd method. 3.4 IKONOS Pa-sharpeg Techque Whe IHS-le fuso methods are used wth IKONOS magery, there s a sgfcat color dstorto, due prmarly to the extesve rage of wavelegths a IKONOS PAN mage. Ths dfferece obvously duce the color dstorto problem IHS fuso as a result of the msmatch; that s, the PAN mage ad the testy mage are spectrally dssmlar. To mmze the radace dffereces betwee the I mage ad the PAN mage, Tu et al. (4) troduced the ear-frared (NIR) bad wth spectral adjustmet appled to the I mage, cosderg that R + a G + b B + NIR I=, (8) 3 a ad b are weghtg parameters defed to tae to accout that the spectral respose of the PAN mage does ot cover that of the blue ad gree bad. The value of these parameters was estmated expermetally after the fuso of 9 IKONOS mages, coverg dfferet areas. Accordg to the expermetal results obtaed by Tu et al. (4), the best 77

6 The Iteratoal Archves of the Photogrammetry, Remote Sesg ad Spatal Iformato Sceces. Vol. XXXVII. Part B7. Bejg 8 weghtg parameters of a ad b for G ad B bads are.75 ad.5, respectvely. However, sce the above two weghtg parameters are totally depeds o the IKONOS magery, these parameters caot be appled to other satellte mage fuso. Therefore, a cotrol parameter, β, wll addtoally be suggested ths paper. Ths wll be selected whe the mea value of the dfferece betwee the PAN mage ad the β I mage s a mmum, so as to mmze the radace dfferece betwee two mages. The proposed hybrd method for IKONOS mage fuso s as follows: R + W(PAN-β I ) = F( R) G + W(PAN- I ) ( ) β F G. (9) = = F( B) B + W(PAN-β I ) F( NIR) = NIR + W(PAN-β I ) = I sum, we employed the FIHS method order to reduce the computatoal cost of the orgal hybrd method alog wth the smplfcato of the mathematcal model, ad suggested the cotrol parameter ad the framelet trasform order to ehace the overall performace of the fused mages. 4. EXPERIMENTAL STUDY AND ANALYSIS To verfy the performace of the proposed method, a IKONOS PAN mage ad MS mages of the Korea cty of Daejeo, whch were acqured o 9 March, were used. The IKONOS magery cotas a m PAN mage ad four-bad 4 m MS mages. The data for ths expermet comprsed a PAN mage ad four R, G, B, ad NIR MS mages. bas (%) (deal value: ) CC (deal value: ) SD (%) (deal value: ) scc R G B NIR R G B NIR R G B NIR R G B eihs esw- Wavelet s eswi- Trous efswi- Framelets NIR ERGAS SAM(deg.) Q Table. Comparso of IKONOS Fuso Results I order to assess the qualty of the fused MS mages, referece MS mages wth the same spatal resoluto as the PAN mage were eeded. However, sce such MS mages were uavalable, spatally degraded PAN ad MS mages, whch were geerated by a lowpass flterg ad sub-samplg procedure, were cosdered (Wald et al., 997). 4. The Qualty Idces for Quattatve Aalyss The spectral ad spatal qualty dces for quattatve aalyss have bee used (Rach et al.,; Alparoe et al., 4): amely, the bas; the stadard devato (SD); the correlato coeffcet (CC); the relatve global dmesoal sythess error, whch s ow as the erreur relatve globale admesoelle de sythése (ERGAS); the spectral agle mapper (SAM); the global qualty dex, Q4; ad the spatal correlato dex proposed by Zhou et al. (scc). Note that the bas, SD, CC, ERGAS, SAM ad Q4 are appled at degraded scale, but scc s appled oly at full scale wthout ay degradato. 4. Quattatve Aalyss Table shows the results of a comparatve aalyss of the IKONOS mage fuso wth the seve qualty dces. The comparso preseted Table shows that the exteded IHS method (eihs) has lower CC ad Q4 values but greater bas, SD, ERGAS, SAM values tha the exteded substtutve wavelet method (esw-wavelets). Therefore, the spectral qualty of the mages fused by the esw-wavelets method s greater tha that of the mages fused by the eihs method. However, sce the scc values of the eihs method are greater tha those of the esw-wavelets, the spatal qualty of the mages fused by the eihs method s greater tha that of the mages fused by the esw-wavelets. O the other had, the hybrd method betwee the eihs ad esw methods (eswi-trous) has lower bas, SD, ERGAS, ad SAM values but greater CC, scc ad Q4 values tha both the eihs ad the esw methods. Cosequetly, the spatal ad spectral qualty of the mages fused by the eswi-trous method s greater tha those of the mages fused by both the eihs ad the esw methods. That s to say, the hybrd fuso method was able to elmate drawbacs of the IHS ad wavelet-based methods, whle eepg the advatages. I addto, Table shows that the proposed fast hybrd method (efswi-framelets) has lower bas, SD, ERGAS, ad SAM values but greater CC, scc ad Q4 values tha the eswi-trous method. Therefore, the spatal ad spectral qualty of the mages fused by the efswi-framelets method s greater tha those of the mages fused by the esw-trous method. Ths s why the cotrol parameter ad the framelet trasform are suggested ths paper. 4.3 Vsual Aalyss Fgure 5 shows the results of full-scale vsual fuso. For Fg. 5 (b), alasg artfacts duced durg the terpolato process are apparetly vsble. Such mparmets dsappear mages fused by the eihs method ad are easly explaed by Eq. (5), 78

7 The Iteratoal Archves of the Photogrammetry, Remote Sesg ad Spatal Iformato Sceces. Vol. XXXVII. Part B7. Bejg 8 whch the alasg patters, preset MS mages, ad hece also the testy mage, are cacelled whe the testy mage s subtracted from each of the spectral bads. Smlarly, the alasg artfacts also dsappear mages fused by the eswi-trous ad the efswi-framelets methods. However, the alasg artfacts stll appear mages fused by the esw- Wavelets method. Cosequetly, the eihs, the eswi-trous ad the efswi-framelets methods are more acceptable for vsual aalyss. ACKNOWLEDGMENT We would le to tha Prof. Paolo Gamba for supplyg the quattatve evaluato programs whch are provded by the IEEE GRSS DFTC, L. Alparoe. REFERENCE Alparoe, L., Baro, S., Garzell, A., ad Nec, F.,4. A Global Qualty Measuremet of Pa-Sharpeed Multspectral Imagery. IEEE GRSL. (4), pp (a) (c) (e) (b) (d) (f) Cho, M.,6. A New Itesty-Hue-Saturato Fuso Approach to Image Fuso Wth a Tradeoff Parameter. IEEE TGRS, 44(6), pp Chu, C. K., ad He, W.,. Compactly supported tght frames assocated wth refable fuctos. ACHA, 8, pp Gozález-Audícaa, M., Saleta, J. L., Catala, R. G., ad Garca, R., 4. Fuso of Multspectral ad Pachromatc mages Usg Improved IHS ad PAC mergers Based o Wavelet Decomposto. IEEE TGRS, 4(6), pp Petuhov, A.,3. Symmetrc framelets. Costructve Approxmato. 9(), pp Rach, T. ad Wald, L.,. Fuso of Hgh Spatal ad Spectral Resoluto mages: The ARSIS cocept ad Its Implemetato. PE&RS. 66, pp Selesc, I. W.,4. Symmetrc wavelet tght frames wth two geerators. ACHA, 7, pp.-5. Tu, T. M., Su, S. C., Shy, H. C., ad Huag, P. S.,. A ew loo at HIS-le mage fuso methods. Iformato Fuso. (3), pp Tu, T. M., Huag, P. S., Hug, C. L., ad Chag. C.P.,4. A Fast Itesty-Hue-Saturato Fuso Techque Wth Spectral Adjustmet for IKONOS Imagery. IEEE GRSL, (4), pp Fgure 5. The results of full-scale vsual fuso: (a) the PAN mage; (b) the resampled orgal MS mage; (c) fused by the eihs; (d) fused by esw-wavelets; (e) fused by eswi-trous; (f) fused by the efswi-framelets. Wald, L., Rach, T., ad Magol, M.,997. Fuso of Satellte mages of dfferet spatal resoluto: Assessg the qualty of resultg mages. PE&RS, 63(6), pp Zhag, Y.,4. Uderstadg Image Fuso. PE&RS, 7(6), pp CONCLUSION We preset the ew hybrd fuso method based o the FIHS trasform wth a cotrol parameter alog wth the framelet trasform, ad valdate ths ew approach by mergg a IKONOS PAN mage wth MS mages. To aalyze the spatal ad spectral qualty of the resultg mages, we used the seve qualty dces, amely the bas, CC, SD, ERGAS, SAM, Q4, ad scc, ad compared the results wth the qualty of mages fused by other methods of mage fuso. I sum, the proposed method produces more satsfactory results, both vsually ad quattatvely. 79

8 The Iteratoal Archves of the Photogrammetry, Remote Sesg ad Spatal Iformato Sceces. Vol. XXXVII. Part B7. Bejg 8 8