Kadastro paftalarının geometrik niteliğinin yükseltilmesinde ve yenilenmesinde homojenleştirme algoritmaları

Abstract

Arazi bilgi sistemi oluşturmaya yönelik projelerde kadastro parsellerine ilişkin bilgiler merkezi öneme sahiptir. Günümüzde parsel bazlı bilgilerin çoğu analog formdadır. Her gün bu bilgilere yenileri eklenmektedir. Harita ve harita benzeri altlıkların sayısallaştırma yöntemleri ile depolanması ve güncelleştirilmesi bu tür altlıkların yeniden üretiminden daha ucuz ve hızlıdır. Bilgi sisteminin sayısal veri tabanını oluşturan özellikle geometrik veriler; jeodezik kontrol sistemindeki, ölçme yöntemlerindeki, ölçekteki, pafta açılışlarındaki, ölçme- çizim doğrululuklarındaki ve yapılış zamanlarındaki farklılıktan dolayı homojen değildir. Homojen yapıda olmayan kadastro paftalarının yan yana getirilip yalnızca sayısallaştırılmaları ve ülke koordinat sistemine transformasyonları yeterli değildir. Homojenleştirmenin amacı; kadastro koordinat sistemi ile en iyi uyum sağlayan, yani çakıştırma artığı içermeyen ve detay noktaları ile dayanak noktaları arasındaki komşuluk ilişkilerini koruyan pafta veya paftalar elde etmektir. Homojenieştirme iki aşamada gerçekleştirilir, ilk aşamada sistematik olarak tüm model alanına yayılmış çakıştırma artıkları, global etki gösteren afin transformasyon yardımı ile belirlenir, ikinci aşamada çakıştırma artıkları, etkisini lokal olarak gösteren interpolasyon algoritması ile tamamen yok edilirken, noktalar arasındaki komşuluk ilişkileri de korunur. Çakıştırma artıkları giderilmiş homojen yapılı bilgiler kullanılarak, geometrik koşulların bir kategori sırasında gerçekleştirilmesi ile kusursuz bir sayısal veri tabanı oluşturulması amaçlanmaktadır. iki test bölgesine ait paftalar üzerinde yapılan araştırma, sayısallaştırılan paftalara uygulanan homojenleştirme ve geometrik koşulların sağlanması işlemi ile bu paftaların azımsanamayacak düzeyde geometrik olarak iyileştikleri ve eskisine oranla daha iyi bir geometrik altlık özelliği kazandıkları sonucuna götürmektedir.

The daily rapid increase in population and the fact that the society is becoming more sophisticated are clear indications that there is a need for information to serve both the government and the people. The cadastre (including land registration) is a record (including maps) of ali land parcels within an area (country, region, state); showing location, size, ownership and other legal interests on the persons. The basic information in a cadastre concern is man and his relation to land ör land related objects. The International Federation of Surveyors (FIG) defines Land information System (LIS) as "a tool for legal, administrative and economic decision-making and an aid for planning and development which consist on the öne hand of a data base containing spatially referenced land-related data for a defined area, and on the other hand, of proce- dures and technigues for the systematic collection, updating, processing and distribution of the data. The base of a land information system is a uniform spatial referenc- ing system for the data in the system, which also facili- tates the linking of data within the system with other land-related data." From the definition of LIS and the set of geographic unit (as defined area) it can concluded that the cadastre is a type of LIS where the geographic unit is the land parcel to which as much information related to land as possible can be attached. This information could be used as a tool by the government to carry out the following functions: decision-making, planning, administration, land use policy, land tax, statistics ete.. So the cadastral maps are the most important part for the establishment of a LIS. Cadastre must always give information on these subjects. - Ovraer of the land and his ör her rights, - Location and the dimensions of the parcel. x The first information refer to the land registration providing the legal status of the land (attribute data). The second öne refer to cadastre, providing spatial and guantitative data (geometric data). Digital map base is created and revised by digitizing existing maps, a new survey ör by the combination of these methods. Both accuracy and cost vary widely according to the chosen method. The positional accuracy of detail points obtained by resurveying is higher than the accuracy obtained by digitazition of existing map ör maps. The digitized information will at least have the accuracies depending on the map scale. in many instances the existing maps are much more inaccu- rate, and a careful assessment of map quality is necessary before entering their contents into the digital map base. Despite of its well knovra disadvantages, because of limitation time and cost factors, in the future surveying authorities will only be able to master this task by digitizing the available maps. There are three different methods to digitize the analogous maps: - the automatic (scanning) method, results can be obtained in grey tone of picture elements (pixels), - the semiautomatic digitizer, which automatically follows lines in the analogous maps and has vectorial results, - the manual digitizer -with a digitizing table-, which has vectorial results. The majority of digitized data entry is now done by manual digitizing. The reasons för this are many: öne may not be able to remove the maps to where a scanner is available for doing the actual conversion; records may not be in a form that can be scanned (e.g., the maps are of poor guality, are in poor condition ör have errors); the features may be too few on a single map to make it practical to scan; a scanner may be unable to distinguish the features to be captured from the surrounding graphic information on tho display; scanning may not provide the reguired data precision (for certain applications, relatively high precision is reguired, and lower priced scanners simply do not offer the precision that is required); scanning may be more expensive than manual digitizing, considering ali the cost/performance issues. Manual digitizing has many advantages: low capital cost, low-cost labor and great flexibility and adaptability. While it is a time-consuming procedure, the technigue can be taught to user within hours, and with modern data base error checking software, the quality of the information is quite high. Interactive xi entry and editing can be done while users work on the data; errors on the basic map can be easily discovered and updated while in the process of entering the information; and digitizing devices are very reliable. it should, however, be noted that the present source of maps is in many respects heterogeneous. The heterogeneous actual state is especially charecterized by differences in: temporal origin, the geodetic reference systems, the surveying methods, the scales, the map edges, ete.. in this thesis, the sample maps are digitized by the softvrare for the digitization and geometrical improvement of cadastral maps which is based on comprehensive scientif- ic research work on map homogenization as carried out at the University of Bonn, Institute of Cartography and Topography (IKT). Program components which make such manual map digitization are contained in universal graphic-interactive systems. They support relieve the operatör by dialogue and help function, plausibilty test as well as comprehensive interactive correction feature. On the other hand, the facilities for geometrical improvement of locational data is only primary. Principles of such softwares are summeri- zed below: - Map fitting by means of affine transformation with very few predetermined control points; - coordinate exchange which is replacement of the coordi- nates without environmentally true error removal, for ali reference points not used during fitting; - direct realization of geometrical conditions only during constructional digitization; - in as far as environmentally true residual error distri- bution is possible at ali, it is limited to those control points which were used during map fitting. However, this functions do not correspond with the demands as required by thorough geometrical improvement. Necessary functions to obtain thorough geometrical improvement are summerized below: - During fitting into the national system, the information from ali the reference points should, if possible, be used. Only after completion of the digitization process can the decision be made as to which points may possibly not be used as control ör respectively support points in the homogenization measures. - The errors on the map edge of non-full-sheet maps also have to be minimized. These errors therefore need to be xii taken into consideration during fitting into the national system. - The remaining errors at ali reference points and at the map edge points must be removed whilst at the same time retaining environmental accuracy so that the more precise coordinates of the reference points contribute to the effective improvement of ali other map points. - Geometrical conditions must, as far as possible, be implicitly ör semiautomatically acguired and stored in the course of digitization. Their realization forms the last step in the geometrical improvement of the homogeni- sed data file by means of two-dimensionally effective adjustment techniques. The main subject of this thesis is geometrical improvement of inhomogeneous cadastral maps by using the procedure described below: - Temporary transformation - The preliminary model fitting affine transformation with few control points for each model. - Digitization of models as point, line and area object. -- Semi or/and automatic linking reference and digitized points. - On account of the fundamental importance of reference coordinates for homogenization measures, their linking with digitized points must be free of errors. The procedures available at present are an outlier test using standardized residuals, also knovm as "data snooping". - in addition to those errors at the reference points, there are also some at the model edges. The prerequi- sition for the numerical linking of adjacent models are created by the linking of identical edge points to tie points. If even larger errors are found, then the identically linked edge points may be used to carry out a temporary Helmert transformation of öne model edge with the other. -- Map homogenization is basically undertaken in two steps: - First of ali, the errors which systematically extend över the whole model are registered by means of globally effective transformation process (affine transforma¬ tion). The över determined affine transformations may minimize the errors at the control points and -if present- at the tie points, but they can not fully remove them. More över, there are also errors to be found at the reference points which were not used as xiii control points for transformation. All these points with residual errors are called "support points". The shift required for detail points should be derived from the neighboring support points and include the value and direction of each point. - Then the remaining, at most, systematic residual errors in the vicinity are completely removed by the means of locally effective interpolation methods including some influence of the environment (multiquadric interpolation or distance weighted interpolation). Multiquadric interpolation has proved to be the most suitable technique for residual error removal. The main advantage of these approach lies in its general insensi- tivity towards irregular support point density and distribution. The weaknesses of multiquadric interpola tion are registered during extrapolation. In such cases, distance weighted interpolation is available with various weight approaches. The criteria of distance and weight is only applied to selected support points in a special sector around the interpola tion point, so that this technique also guarantees proper residual error removal. - Realization of geometrical conditions (e.g. straightness of lines, rectangularity, parallelism, distances, relative location, circular continuitity). Homogenisat- ion and condition realization are then carried out making full use of all the information on the basis of the original data. Geometrical conditions adjustment is carried out separately for hierarchically structured object groups. The hierarchy is; model edges, parcel boundary building and other geometrical elements for cadastral maps. The numerical results of this thesis are evaluated in two different pilot area. For the first pilot area, coordinates of cadastral map points are entered manually to system, drawn on the screen and plotted. The plotted sheet is digitized and digitized values of coordinates of 50 points are read. These values are compared with their original coordinates after each process. The results of affine transformation by few and much control points for the test area and the results obtained by two interpolation methods are given -for all process- in Table 1. XIV Table 1: Mean positional errors for first test area. In Table 1 digitizing error is 14.4 cm. After condition adjustment it is reduced to 6.6 cm. In the second test area digitization is realized directly on cadastral map. In this sample only the polygon and grid points are known. Because of this reason, results of condition adjustment can not be compared with original coordinates, in the Table 2. Table 2: Mean positional errors for second test area. In table 2 digitazition error is reduced from 42.4 to 18.4 cm only by multiquadric interpolation. If it could be possible to compare condition adjustment results with original coordinates of detail points, the geometrical improvement would be better than 18.4 cm. As a conclusion it can be said that by means of the method presented in this thesis, it is possible to improve the accuracy of digitized coordinates significantly. With the aid of new measurements, digitized maps in better quality -in other words true digital dynamic cadastral maps- can be obtained.