Cadastral Triangulation: A Block Adjustment Approach for Joining Numerous Cadastral Blocks

Transcription

1 Nordc Journal of Surveyng and Real Estate Research Specal Seres Vol. 4, 2009 Nordc Journal of Surveyng and Real Estate Research, Specal Seres, Vol. 4 (2009) Receved November 25, 2008 Accepted after revson February 23, 2009 Cadastral Trangulaton: A Block Adustment Approach for Jnng Numerous Cadastral Blocks Mchael Klebanov, Yerach Doytsher Mappng and Geo-Informaton Engneerng Technon - Israel Insttute of Technology Technon Cty, Hafa 32000, Israel klebanov@map.gov.l, doytsher@technon.ac.l Abstract. In the last decade or so, there has been a very clear transton n many countres throughout the world from a graphcal cadastre and/or relatvely non-accurate dgtal cadastre toward an accurate coordnate based legal cadastre. Amng at defnng accurately the turnng pnts poston of the cadastral sub-dvson based on current data wthout the need to re-measure the cadastral enttes, motvates the development of new algorthms and approaches sutable to performng the task. Implementaton on a natonwde level requres to frst develop advanced mathematcal algorthms and methods to process separate parcellatons (cadastral blocks or mutaton plans), and then addtonal algorthms and methods to combne the numerous separate parcellatons nto a cadastral contnuty mantanng rgd topologcal compatblty. Practcal experence, especally from the Israel vewpnt, ndcates that mplementaton of advanced computatonal technques for processng separate cadastral blocks, s only a partal soluton of the problem. An optmal nng of the separate cadastral blocks nto a homogeneous seamless cadastral space consttutes a complex task due to dscrepances between the adnng parcellatons. These dscrepances, sgnfcant n terms of ther magntude and characterstcs, are manly caused by the cadastral parcellaton process based on separate cadastral measurng proects on the one hand, and lmted accuracy of the measurng technques n prevous decades (manly n the frst half of the 20th century) on the other hand. The paper ntroduces a new algorthm based on the exstng mathematcal model, customary n photogrammetrc mappng, amed at connectng the adnng photographs nto blocks based on Block Adustment by Independent Models. The proposed adustment method (named the "Cadastral Trangulaton") s executed based on the classc

2 54 Cadastral Trangulaton: A Block Adustment Approach for Jnng Adustment of Indrect Observatons combned wth the Chaned Smlarty Transformaton. Ths adustment process whch s carred out by a global transformaton mechansm, enables obtanng both optmal transformaton parameters of all the separate parcellatons, as well as optmal coordnates of the cadastral boundary turnng pnts. The ntal results of the proposed method ndcate ts effectveness n connectng the adnng cadastral blocks, effectveness expressed by a sgnfcant decrease of systematc and random errors compared to ther pre-adusted stuaton. Addtonally, the proposed method enables brngng the adusted cadastral boundary turnng pnts maxmally close to ther theoretcal true (and unknown) locatons and, n any case, much closer than locatons computed by currently practced methods. Therefore, the proposed method may effectvely be used as a prmary computatonal algorthm for mplementng a natonwde coordnate based legal cadastre. Keywords: coordnate based cadastre, boundary matchng, least squares adustment, block adustment by ndependent models 1 Introducton Cadastre s a systematc method of land property regstraton and management that ncludes nformaton about land parcels, e.g. ther boundares, areas, ownershp, mortgages, pledges, etc. (Henssen, 1995, Dale & McLaughln, 1988). Cadastre consttutes essental factor n natonal economy establshng strong bass to the exstence of human socety (Dale, 1997, Kaufmann & Steudler, 1998, Kaufmann, 1999). Good practce n land property admnstraton, whch ncludes development of modern cadastral systems, gves rse to a strong foundaton of sustanable natonal development (Wllamson, 2001, Bennett et al., 2008). Accordng to the customary prncples n the Israel cadastre - Torrens prncples (Dale, 1976), parcel boundares and areas are determned based on ground surveyng, offcally managed, controlled and approved by the state. Ground surveyng s executed based on a natonal geodetc control network, and thus the X, Y planar coordnates defne every parcel turnng pnt. Untl now, the Israel cadastre was based on block maps, feld measurements books, computaton fles and physcal markngs on the ground of the parcel turnng pnts. These turnng pnts have legal valdty whenever parcels boundary restoraton s needed. Notwthstandng ther legal status, the orgnal cadastral documents suffer consderably from lack of completeness, and physcal markng s mostly based on ground surveyng of low accuracy (especally that carred out durng the frst decades of the modern cadastral era n Israel the frst half of the 20th century). As a result, the coordnates of parcel turnng pnts are of low accuracy and there s great dffculty n ntegratng adnng blocks nto a spatal cadastral contnuty. Addtonally,

3 Nordc Journal of Surveyng and Real Estate Research Specal Seres Vol. 4, 2009 most of ground mark pnts no longer exst n the feld due to urban development actvty and constructon. Ths stuaton, whch s qute common to varous countres all over the world, has stmulated awareness of the urgent need to transform the exstng paper-based cadastre nto a coordnate based cadastre, a process whch would be characterzed by optmally determned turnng pnt postons and mproved accuracy. The coordnate based cadastre wll enable usng turnng pnts coordnates as a legal bass for parcel boundares restoraton. In order to acheve ths goal t s necessary to: () develop an optmal method of orgnal cadastral documents processng referrng to separate parcellatons (separate cadastral proects); and, () develop a model enablng nng the separate parcellatons nto a cadastral contnuty mantanng a rgd topologcal structure. We approached the frst task (Klebanov & Doytsher, 2008) by applyng the Least Squares Adustment as an optmal method of defnng the parcel turnng pnts poston, consderng all avalable nformaton recorded n the orgnal cadastral documents. The current paper presents a soluton of the second task. 2 Motvaton The soluton proposed n our recent work (Klebanov & Doytsher, 2008), enabled obtanng optmal postons of parcel turnng pnts (and as a byproduct, ther accuraces) based on orgnal cadastral document processng. The soluton, based on the Gauss-Markov adustment model, has assured ganng mnmally possble dfferences between observatons made durng ground surveyng and ther values, analytcally calculated from adusted coordnates. The latter qualty meets one of the essental requrements n cadastral documents processng keepng adusted values of observatons maxmally close to ther measured values of legal valdty. Addtonally, the proposed soluton enabled consderng other knds of nformaton (geometrcal and cadastral constrants) n defnng the optmal poston of the turnng pnts. Applyng the aforementoned method allows obtanng the optmal poston of turnng pnts n separate cadastral blocks (or other cadastral parcellatons,.e., mutaton plans). However, dffcultes arse when one tres to ntegrate adnng blocks. Practce shows that despte the ablty to optmally process separate parcellatons, ther optmal connecton nto a homogeneous seamless space remans a very complcated task (Shmutter & Doytsher, 1992), manly due to the accuracy problems pnted out n the prevous secton. Though some attempts have already been made to fnd local solutons (Doytsher & Gelbman, 1995, Nmre & Doytsher, 2000, Takash et al, 2001), a comprehensve soluton of the ssue has not as yet been acheved.

4 56 Cadastral Trangulaton: A Block Adustment Approach for Jnng Hstorcally, the Israel cadastre conssts of a numerous proects based on dfferent geodetc grds of relatvely low accuracy (from several decmeters up to few meters), as well as of local grd systems wthout any connecton to the natonal geodetc. Nowadays, when an accurate geodetc grd (IG05) exsts n Israel, based on satellte geodesy and permanent ground statons (Stenberg & Even-Tzur, 2004), a techncal possblty exsts to determne pnt postons on a sub-decmeter level whch s undoubtedly an approprate accuracy level for a future coordnate based cadastre. Thus, the man problem n formng a homogeneous cadastral space s fndng the approprate transformaton model and parameters of the numerous cadastral mult-grd based proects to be merged nto a contnuous seamless cadastral realty. The dffculty arses because only a small part of the parcel pnt ground marks have survved n the feld due to urban development actvty and constructon. Ths stuaton prevents ther drect ground re-surveyng, amed at obtanng accurate planar coordnates. Consequently, some knd of transformaton s requred to convert the pnt coordnates computed n the orgn grd, to coordnates n the current updated Israel grd (IG05). As a result, new cadastral proects, based on old materals, should be accompaned by a transformaton of the coordnates of parcel turnng pnts, whch have not been located n the feld. The transformaton ssue becomes even more complcated when one tres to compute the approprate transformaton parameters for two or more adnng cadastral parcellatons amng to obtan dentcal coordnates of perpheral common turnng pnts. These dentcal perpheral coordnates wll ensure contnuous cadastral realty wthout gaps or overlaps between adacent cadastral proects. The purpose of the current work s to develop a comprehensve model of global coordnate transformaton amed at creatng a homogeneous seamless cadastral space of hgh accuracy based on separate cadastral proects optmally pre-processed. 3 Proposed method The proposed method adopts and follows the customary prncples n photogrammetrc mappng - prncples of aeral trangulaton (Kraus, 1993). Accordng to these prncples, the separate aeral photographs are connected nto blocks by common te pnts n overlappng regons of adacent photographs. The photogrammetrc model s transformed from a model space to a ground coordnate system based on pre-defned control pnts. A commonly used computatonal model, Block Adustment by Independent Models (Mkhal et al., 2001, Lnder, 2006) enables obtanng ground coordnates of a large-scale topographc area from numerous aeral photographs based only on a lmted number of ground control pnts. The theory of Block Adustment method and ts mplementatons have been

5 Nordc Journal of Surveyng and Real Estate Research Specal Seres Vol. 4, 2009 wdely dscussed n professonal lterature (Jacobsen, 1998, Trggs et al., 2000, Cothren, 2005, Baz et al., 2007). The proposed method Cadastral Trangulaton (CT) Method refers to separate cadastral proects, optmally pre-processed, determned n varous local coordnate systems (orgn grds). The perpheral common turnng pnts belongng to adnng cadastral parcellatons play the role of te pnts. Pnts measured at the tme when the cadastral proects were carred out and remaned n the feld, and can now be re-measured n the current grd system (IG05), serve as control pnts. The latter pnts ganed the name of "authentc" pnts. It should be mentoned that due to the rapd urban development, not many authentc pnts can be presently located n the feld, and these are not necessarly dspersed n an optmal manner, especally n reference to the old cadastral proects. As these authentc pnts have two sets of coordnates n the orgn grd from analytcal pre-processng of the old measurements, and n the new grd (IG05) from modern re-surveyng the authentc pnts play the role of the control pnts n the photogrammetrc aeral trangulaton and a central role n the global transformaton of the cadastral proects. The proposed CT method, based on Block Adustment by Independent Models, treats the separate cadastral proects, amng to create a homogeneous seamless space by applyng the global transformaton mechansm. The proposed method uses the Chaned Smlarty Transformaton (Kraus, 1993) as a model of global adustment amed at achevng a mnmum sum of weghted squared resduals of perpheral common te pnts and authentc control pnt coordnates by applyng the Least Squares Adustment. We consdered smlarty transformaton to be the most approprate type of cadastral transformaton, as ts conformal qualtes have legal mportance. We also consdered ts general case, usng four transformaton parameters for each parcellaton. Addtonal research can be consdered regardng the chce of optmal number of transformaton parameters and the effect of the number of authentc pnts and ther dsperson on the fnal results. Mathematcal model The lnearzed mathematcal model of planar smlarty transformaton has the followng expresson (Kraus, 1993): Yt X t where a = b b Y a X o o + c d (1)

6 58 Cadastral Trangulaton: A Block Adustment Approach for Jnng Y t, X t - pnt coordnates n target grd Y X o, o - pnt coordnates n orgn grd a, b - parameters of scale m and rotaton K calculated as a = m* cos K, b = m* sn K c, d - shft parameters Due to pre-processng of the separate parcellatons, the pnt coordnates n the orgn grd are always known both for te and control pnts. Transformaton parameters of separate parcellatons are always unknown. Pnt coordnates n the target grd are unknown for te pnts and known for control pnts. The mplementaton of the aforementoned model (1) n the process of Chaned Smlarty Transformaton, whch nvolves numerous pnts and parcellatons, enables computng the estmates of poston resduals εˆ of pnt based on estmates of adusted transformaton parameters of the separate parcellaton to whch pnt belongs: ˆ ε ˆ ε y x = aˆ = aˆ * Y * X bˆ + bˆ * X * Y + cˆ + dˆ ~ Yt ~ X t where ^ - stands for Least Squares Estmator ~ Note: Y t, X ~ t stands for: () coordnate estmates of te pnts n target grd Yˆ, Xˆ ); or, () known coordnates of authentc pnts n target grd ( t t ( t X t Y, ). As mentoned before, the obectve of the proposed CT method s to obtan durng a global adustment process such estmates of transformaton parameters of the orgnal cadastral parcellatons (treated as ndependent models) that would mnmze pnt poston resduals (2) whle applyng LS Adustment: p ˆ ε 2 = mn (3) where p are the weghts of pnts coordnates computed nversely to ther accuraces Equatons (1) determne the functonal relatons between known observatons and unknown adustment parameters, whch accordng to the model of Adustment of Indrect Observatons, may be expressed n general form as: (2)

7 Nordc Journal of Surveyng and Real Estate Research Specal Seres Vol. 4, 2009 y = F(β ) (4) where observatons y are the coordnates of authentc control pnts computed n target grd on the bass of modern ground surveyng, and unknowns β are parcellaton transformaton parameters and perpheral te pnts coordnates n the target grd. As an adustment model of equatons (4), we use the Gauss-Markov model (Koch, 1999), whch ensures obtanng the best unbased soluton regardng the estmates of unknown parameters and adusted te pnts coordnates, provded condton (3) wth resduals (2), computed n general form as: ˆ ε = X ˆ β y (5) F( β ) where X = - Jacoban matrx of partal dervatves of equatons (2); β F (β ) - the rght sde of equatons (2). Note: observatons vector y ncludes known coordnates for authentc pnts n target grd ( Y t, X t ) and zeros for te pnts. Followng are the fragments of Jacoban matrx X, observatons vector y T and transposed vector of unknowns β for pnt belongng to parcellaton : For authentc pnt: (β ) T = [ a b c d ] Y X 1 0 [ ] = t X, [ y ] = X For te pnt: ) T (β = [ a Y b 0 c 1 d Y X Y X [ ] = X Y t Y t X t ] 0 0 y = 1 0 X, [ ] F(β ) The aforementoned model (4) s lnear ( = const ); therefore, the β soluton for vector of unknowns β s obtaned durng one teraton accordng to followng expresson (Koch, 1999):

8 60 Cadastral Trangulaton: A Block Adustment Approach for Jnng ˆ T 1 T β = ( X PX ) X Py (6) P - s the weght matrx defned nversely to the accuracy estmates of pnts coordnates computed durng pre-processng (Klebanov & Doytsher, 2008) n the orgn grd. Matrx P has a block dagonal structure composed of submatrces referrng to separate parcellatons: P = ( Σˆ x ) 1 = ( where for parcellaton ˆ σ 0x ( N x ) ) = N ˆ σ x 2 0x Σ x - covarance matrx of pnts coordnates estmates n orgn grd 2 ˆ 0x σ - unt varance estmate N x - normal matrx Covarance matrx of unknown parameters estmates s computed as T ˆ ˆ ε P ˆ ε T 1 Σ β = ( X PX ), where r s the system redundancy. r 4 Smulaton of proposed method In order to be able to analyze the results and the accuracy of the proposed CT method, t was tested on synthetc data. The smulaton of the synthetc sample was composed as an array of 300 rectangular cells (10x30) (Fgure 1a). Every cell had the dmensons of 200x300 meters and thus, the entre synthetc sample covered the area of 2x9 km. Every sngle cell represented a separate cadastral block (or separate parcellaton). The ntal array was used as an "deal" stuaton where a complete topologcal accordance of boundares between adnng cadastral parcellatons exsts (Fgure 1b). Addtonally, some nodes (61 turnng pnts), evenly dstrbuted on the synthetc sample, were chosen as the "authentc" pnts (marked on Fgure 1 wth a double crcle) wth the coordnates computed n a target geodetc grd based on newly performed ground surveyng. Afterwards, the "true" nodal coordnates of ntal stuaton were "spled" (dstorted) by applyng a normal (Gauss) dstrbuton error mechansm. The dstorton process was performed n two steps. In the frst step, every cell was ndependently shfted, rotated and scaled by applyng β β, Σ normally dstrbuted conformal transformaton parameters: ( ) T where = [ a = m b = K c d ] [ ] = 1 0 β, β and standard mn devatons σ β : σ m = , σ K = 10, σ c = σ d = 0. 3 meter (Fgure 1c).

9 Nordc Journal of Surveyng and Real Estate Research Specal Seres Vol. 4, 2009 Ths step smulated the accuracy problem of geodetc grd, whch was very common n old cadastral proects. The values of standard devatons were chosen accordng to the statstcally obtaned accuraces of geodetc control pnts coordnates. In the second step, the cell nodes were ndependently (a) (b) (c) (d) Fgure 1. Smulaton of proposed method: a) general chart; b) fragment of "deal" stuaton; c) fragment of dstorted stuaton; d) scheme of dstorton

10 62 Cadastral Trangulaton: A Block Adustment Approach for Jnng moved from the transformed values n the frst step poston Y 1, X 1 (Fgure T T 1d) by shft values normally dstrbuted: [ Y 2 X 2 ] ([ Y1 X 1],ΣdY, dx ) wth standard devatons σ dy = σ dx = m whch are double the standard devatons obtaned n smulated pre-processng (Klebanov & Doytsher, 2008). Ths step smulated the accuracy problem of ground surveyng (drect feld observatons) n carryng out cadastral proects. After the two aforementoned dstorton steps, the fnal standard devaton of cell nodes poston was obtaned, computed accordng to error propagaton (Anderson & Mkhal, 1998), as equal to σ Y = σ X = m, whch s close to commonly encountered dfferences between turnng pnts coordnates belongng to adnng old cadastral proects. Followng the dstorton process, the synthetc sample was processed accordng to the CT method as proposed n secton 03 wth the orgnal "deal" coordnates of the pnts used as the known coordnates of authentc pnts n the target grd. Cell transformaton parameters and unknown nodes coordnates were computed accordng to (6). Amng to acheve consstent results, the proposed method was processed 10 tmes, changng each tme the smulatve dataset by reactvatng the aforementoned dstorton process each tme. The accuracy evaluaton results of these 10 runs computed before and after the adustment are depcted n Table 1. Table 1. Pnt poston accuracy computed by the proposed method Accuracy factor Sum of varances p ε (sq. meters) ˆ 2 (1) Before adustment (2) After adustment Improvement Rato (1) vs. (2) p ˆε MSE σ 0 =, r (meters) Max resduals ε, (meters) Notes: () Varances before adustment (after dstorton) were computed as squared dfferences between dstorted pnts postons and ther average poston; varances after adustment were computed accordng to (5).

11 Nordc Journal of Surveyng and Real Estate Research Specal Seres Vol. 4, 2009 () r s the system redundancy computed as the dfference between the number of all pnt appearances n all parcellatons and the number of unknowns. In order to analyze the stablty of the solutons, the results of the 10 runs were statstcally evaluated and the standard devatons of the parameters n Table 1 (Sum of varances, MSE, Max resduals) were computed. These standard devatons results are depcted n Table 2. Table 2. Stablty results (standard devatons of runnngs accuracy factors) Accuracy factor Before adustment After adustment MSE of sum of varances (sq. meters) MSE of MSEs (meters) MSE of Max resduals (meters) As can be seen from Tables 1 and 2, the proposed CT method enabled reducng drastcally the dscrepances between adnng cells and brngs them to the level that approaches the requrements of a legal coordnate based cadastre (sub-decmeter level). Moreover, the stablty of the dfferent smulatons s very hgh, whch pnts out the valdty and correctness of the proposed method. Table 3. Dfferences between "true" coordnates and coordnates computed accordng to the proposed and the "average" methods Accuracy factor (1) "True" coordnates vs. adusted coordnates (2) "True" coordnates vs. "average" coordnates Improvement Rato (2) vs. (1) Y X Y X Y X Average (meters) MSE (meters) Max dfference (meters) It should be mentoned that the currently wdely used n practce method of boundary matchng between adnng parcellatons s: () computng average pnt poston (by means of plan or weghted average) between the approprate adnng pnts; or, () acceptng one of parcellatons as an

12 64 Cadastral Trangulaton: A Block Adustment Approach for Jnng anchor and attachng the adnng parcellatons to t. The frst method provdes reduced pnts poston errors compared to the second one; accordngly, t was chosen as the method for comparson wth the proposed CT method. Adusted pnts coordnates computed accordng to the proposed CT method and coordnates computed by average method of adnng boundares matchng were compared wth ntal "true" coordnates. For comparson purposes, the dfferences between: () "true" coordnates and adusted coordnates; and, () "true" coordnates and "average" coordnates, were computed. The comparson results are depcted n Table 3. In order to analyze the stablty of the solutons, the results of the 10 runs have been statstcally evaluated and the standard devatons of the parameters n Table 3 (average, MSE, max dfferences) were computed. These standard devatons results are depcted n Table 4. Table 4. Stablty results (standard devatons of runnngs accuracy factors) Accuracy factor MSE of Averages (meters) MSE of MSEs (meters) MSE of Max dfferences (meters) (1) "True" coordnates vs. adusted coordnates (2) "True" coordnates vs. "average" coordnates Y X Y X As can be seen from Tables 3 and 4, n both methods the coordnate dfferences converge to zero, meanng that both adusted and average coordnates converge to ther true values wth a mnor advantage to proposed method. However, the dsperson of pnts around ther "true" poston n the proposed CT method s much closer (3-4 tmes) than n the average" method. Ths means that n a real stuaton, after applyng the proposed adustment process, specfc parcels turnng pnts would be defned qute close (on sub-decmeter accuracy level) to ther true (and unknown) postons and, n any case, much closer than by currently practced methods. Moreover, the stablty of the dfferent smulatons s very hgh, whch ndcates the valdty and the correctness of the proposed method. An addtonal test has been performed on a synthetc dataset wth the smulatve array reduced to 100 parcels that accordngly ncluded less authentc pnts stll evenly dstrbuted on synthetc sample. The test was

13 Nordc Journal of Surveyng and Real Estate Research Specal Seres Vol. 4, 2009 performed wth a gradually reduced number of authentc pnts from 23 to 6 pnts. Table 5. Dfferences between "true" coordnates and coordnates computed accordng to proposed and "average" methods for a reduced number of authentc pnts Accuracy factor (1) "True" coordnates vs. adusted coordnates (2) "True" coordnates vs. "average" coordnates Improvement Rato (2) vs. (1) Y X Y X Y X 23 authentc pnts Average (meters) MSE (meters) authentc pnts Average (meters) MSE (meters) authentc pnts Average (meters) MSE (meters) As can be seen, reducng the number of authentc pnts led to decreasng the accuracy of the proposed CT method compared to the smple "average" method. Generally, thnnng out authentc pnts caused a convergence of both methods to produce almost smlar results regardng dsperson of pnts around ther "true" poston. Nonetheless, durng a detaled analyss of obtaned results t was notced that wthn the surroundng regons close to the authentc control pnts there remans a strong mprovement of the proposed CT method compared to the "average" method, an mprovement that gradually dmnshes as one moves away from the authentc pnts. Ths ndcates a possblty of defnng the authentc pnt nfluence regons where applyng the proposed CT method mght be effectve. In a real stuaton, cadastral space parttonng on separate nfluence regons would enable transformng the natonwde task of connectng the adnng parcellatons to local (regonal) solutons of reduced extent. The method proposed n ths paper has been tested on a synthetc dataset amng to confrm the convergng of turnng pnt adusted coordnates to ther ntal true values whch are unknown n a real stuaton. In addton to

14 66 Cadastral Trangulaton: A Block Adustment Approach for Jnng the theoretcal mathematcal developments of the CT method, usng smulatve synthetc data has the advantage of beng able to analyze thoroughly the meanng of the dfferent mathematcal steps and the dfferent parameters beng used. In a second phase of the research, the proposed approach s tested on real data of cadastral proects, and the results wll be reported next year (Klebanov & Doytsher, 2009). 5 Concluson and future work Applyng the proposed CT method to global adustment of adnng parcellatons enabled us to: () convert separate cadastral proects prepared n dfferent orgn grds nto cadastral contnuty n a unform geodetc target grd; () reduce consderably poston dscrepances between adnng cadastral parcellatons; and, () ncrease poston accuracy of parcel boundary turnng pnts compared to the exstng boundares matchng method. Applyng the proposed method ensured obtanng parcel turnng pnts postons much nearer ther "true" postons than those obtaned by applyng the exstng matchng methods. An addtonal study should be made to analyze: () the optmal number of transformaton parameters referrng to separate parcellatons durng global transformaton and adnng boundares adustment; and, () optmal dsperson of authentc pnts n the adusted area and ther number. These ssues wll probably drastcally affect the computaton of optmal transformaton parameters and turnng pnt postons and ther accuracy. Applyng the proposed CT method on the natonwde level, ncludng calculaton of tens of thousands of transformaton parameters and mllons of perpheral turnng pnt coordnates, s not a smple task n respect to the requred computatonal resources. Therefore, an addtonal study should be carred out amed at smplfyng the proposed soluton, and mprovng the adustment model n order to acheve the optmal algorthm and ncrease the effectveness of the entre computatonal process. References Anderson, J.M., and E.M. Mkhal (1998). Surveyng: Theory and Practce. McGraw- Hll, New York Baz, I., G. Büyüksalh and K. Jacobsen (2007). Bundle Block Adustment wth Hgh Resoluton ULTRACAMD Images. IntArchPhRS XXXVI, Band 1/W51, Hannover Bennett, R., J. Wallace and I.P. Wllamson (2008). Organsng property nformaton for sustanable land admnstraton. Journal of Land Use Polcy, Vol. 25(1): Cothren, J. (2005). Relablty n Constraned Gauss-Markov Models: An Analytcal and Dfferental Approach wth Applcatons n Photogrammetry. Report #473, Geodetc and GeoInformaton Scence, the Oho State Unversty

15 Nordc Journal of Surveyng and Real Estate Research Specal Seres Vol. 4, 2009 Dale, P.F. (1976). Cadastral Surveys wthn the Commonwealth. pp , London, HMSO Dale, P.F. (1997). Land Tenure Issues n Economc Development. Urban Studes, Vol. 34(10): Dale, P.F. and J. McLaughln (1988). Land Informaton Management: An Introducton wth Specal Reference to Cadastral Problems n Thrd World Countres. Clarendon Press, Oxford Doytsher, Y. and E. Gelbman (1995). A Rubber Sheetng Algorthm for Cadastral Maps. Journal of Surveyng Engneerng - ASCE, Vol. 121(4): Henssen, J. (1995). Basc prncples of the man cadastral systems n the world. Proceedngs of FIG Commsson 7, Semnar on Modern Cadastres and Cadastral Innovaton, Delft, The Netherlands Jacobsen, K. (1998). Block Adustment. Internal Report, Insttute of Photogrammetry and GeoInformaton, Hannover, Germany Kaufmann, J. (1999). Future Cadastres: Implcatons for Future Land Admnstraton Systems - Brngng the World Together?. Proceedngs of the UN-FIG Internatonal Conference on Land Tenure and Cadastral Infrastructures for Sustanable Development, Melbourne Kaufmann, J. and D. Steudler (1998). Cadastre a Vson for a Future Cadastral System. Internatonal Federaton of Surveyors, Commsson 7, Swtzerland Klebanov, M. and Y. Doytsher (2008). A New Mathematcal Approach to Cadastral Documents Processng for Parcels Boundares Restoraton. Proceedngs of FIG Workng Week, Stockholm, Sweden Klebanov, M. and Y. Doytsher (2009). Establshng an Accurate Contnuous Natonwde Cadastre Based on the Cadastral Trangulaton Method. Proceedngs of FIG Workng Week, Elat, Israel Koch, K.R. (1999). Parameter Estmaton and Hypothess Testng n Lnear Models. Sprnger-Verlag, Berln/Hedelberg/New York Kraus, K. (1993). Photogrammetry Volume 1. Fundamentals and Standard Processes. Dümmler Verlag, Bonn, Germany Lnder, W. (2006). Dgtal Photogrammetry: A Practcal Course. Sprnger-Verlag, Berln/Hedelberg/New York Mkhal, E.M., J.S. Bethel and J.C. McGlone (2001). Introducton to Modern Photogrammetry. John Wley & Sons, Inc. Nmre, S. and Y. Doytsher Y. (2000). An Algnment Process of Master Plans at Large Scale n a GIS Envronment. Proceedngs of FIG Commsson 3 Annual Workshop and Semnar, Athens, Greece Shmutter, B. and Y. Doytsher (1992). Matchng a Set of Dgtzed Cadastral Maps. CISM Journal- ACSGC, 46(3):

16 68 Cadastral Trangulaton: A Block Adustment Approach for Jnng Stenberg, G. and G. Even-Tzur (2004). A State-of-the-Art Natonal Grd Based on the Permanent GPS Statons of Israel. Proceedngs of FIG Workng Week, Athens, Greece Takash, S., S. Yuko and O. Atsuyuk (2001). A Computatonal Procedure for Jnng Separate Map Sheets. GeoJournal 52: , Kluwer Academc Publshers, Netherlands Trggs, B., P. McLauchlan, R. Hartley and A. Ftzgbbon (2000). Bundle Adustment - A Modern Synthess. Vson Algorthms: Theory & Practce, Sprnger-Verlag Vol Wllamson, I.P. (2001). Land Admnstraton Best Practce Provdng the Infrastructure for Land Polcy Implementaton. Land Use Polcy, 18,