Toward Analytical Cadastre: A Basis for Efficient Land Management Anna Shnaidman Yerach Doytsher Mapping and Geo-Information Engineering Technion – Israel Institute of Technology

Outline The problem at hand The proposed algorithm Introduction The problem at hand The proposed algorithm Implementation of GAs – cadastral analogy Simulation Results Case Studies Summary

Introduction The problem at hand The proposed algorithm Implementation of GAs – cadastral analogy Simulation results Case studies Summary

Introduction recording the redefinition and updates of boundaries Cadastral measurement is a continuous process of recording the redefinition and updates of boundaries Cadastre System is a legal frame which embodies people, land and law The cadastre is of a dual nature: Legal and Spatial The most common registration system is Torrens The registration is based on measurements Cadastre is a vital factor in proper management of land properties and the overall economy of a country

Introduction The problem at hand The proposed algorithm Implementation of GAs – cadastral analogy Simulation results Case studies Summary

The problem at hand The cadastre in many countries is of an analogic nature Different measurements of inconsistent and low accuracy stored mostly on paper The current cadastre is not satisfactory and precludes: efficient and computerized management of real estate faster planning of development projects minimizing border conflicts to employ technological innovations and respond to the impelling reality of the modern world The transition to a coordinate – based cadastre is both crucial and inevitable

The problem at hand cont. Due to factors such as: population growth, globalization, urbanization, affordable housing and sustainable development - an automated and reliable land management system is urgently required Analytical cadastre is one of the concrete topics being discussed and researched in many countries Most customary solutions are based mainly on the deterministic Least Square (LS) method

Introduction The problem at hand The proposed algorithm Implementation of GAs – cadastral analogy Simulation results Case studies Summary

The proposed algorithm The conventional methods are mainly analytical and straightforward The proposed method is based on biological optimizations and is known as Genetic Algorithms (GAs) Characteristics: Stochastic method Founded on evolutionary ideas and Darwin's principles of selection and survival of the fittest A natural selection which operates on a population of solutions – chromosomes (individuals)

The proposed algorithm cont. The generic framework of GAs: Encode the Given Problem – a computerized definition or representation of the problem at hand Create the initial population of n vectors Evaluate the Initial/Current individuals by assigning a fitness value Create the next population by applying variation- inducing operators: selection, crossover and mutation Repeat the steps

The proposed algorithm cont. Genetic operators - Selection: Two parent chromosomes are selected from a population according to their fitness Guiding principle – selection of the fittest Superior individuals are of higher probability to be selected Selection method – Roulette Wheel selection Roulette slots’ size is determined by the fitness value The chromosome grades (fitness values) are translated to probability, normalized and summarized A number is picked arbitrarily, the segment which the number falls into is the chosen parent

The proposed algorithm cont. Genetic operators - Crossover: Two offspring are created using single point crossover Parents chromosomes children chromosomes Genetic operators - Mutation: The new offspring are changed randomly to ensure diversity

Introduction The problem at hand The proposed algorithm Implementation of GAs – cadastral analogy Simulation results Case studies Summary

Implementation of GAs – cadastral analogy A generation of individuals - vectors of turning points coordinates of parcels Each individual - a set of block/mutation plan coordinates stored in an array (vector) structure Parcel areas and lines - provide the cadastral and geometrical constraints An Objective function - minimizes the differences between the legal (registered) coordinates and those provided by the solution under the specified conditions

Implementation of GAs – cadastral analogy cont. With each generation the vectors are altered according to the best solution provided Every individual may assumed to be a set of coordinates, representing acceptable observations received from different sources Early stages – GAs were evaluated using synthetic data Advanced stages - GAs were applied to real data

Implementation of GAs – cadastral analogy synthetic data cont. Definitions: The preliminary population of N vectors is produced by randomly altering an "ideal" cadastral block A registered area criteria, straight, parallel and perpendicular lines were chosen for analyzing the GAs' competence and effectiveness in the cadastral domain After the population is generated, a primary test is performed according to the SOI regulations

Implementation of GAs – cadastral analogy cont. Cadastral conditions: Objective function employs Cartesian area calculation and a desirable MSE of parcel coordinates Fitness function considers parcel size to determine its weight Geometrical conditions: Objective function uses turning point angles, line segment length and the perpendicular distance Fitness function computes line weight using the number of points in both lines and the total line length Total grade

Implementation of GAs – cadastral analogy cont. – Objective function Areas Lines

Implementation of GAs – cadastral analogy cont. – Fitness function Areas Lines Total grade

Implementation of GAs – cadastral analogy cont. Iterations – creation of successive generation: Parent selection - for each parcel and line/lines in the block two parents are selected - Tournament Selection Crossover - a single point crossover is performed Process repetition - until the original population size (N) is reached Averaging - mean coordinates are calculated Mutation

… … The proposed algorithm - graphical illustration Set 1 Set 2 Set N Parcel 1 Lines 1 Parents selection Parent 1 Single point crossover Offspring 1 Offspring 2 next generation –Averaging coordinates, adding mutation, creation of new sets … New set 1 New set 2 New set N

Introduction The problem at hand The proposed algorithm Implementation of GAs – cadastral analogy Simulation results Case studies Summary

Simulation results examined by performing simulations on the The proposed method's quality and accuracy were examined by performing simulations on the synthetic data The main purpose of these simulations is to test the ability of the GAs to return to the initial theoretical state - an ideal, errorless solution For comparison an Least Square iterative adjustment was applied as well

Simulation results cont. A characteristic set of synthetic data

Simulation results cont. 3 characteristic examples of the solution accuracy (meters) Param- eters Min dX Min dY Max dX Max dY  X  Y Initial -0.500 -0.758 0.742 0.700 0.225 0.233 GAs -0.113 -0.169 0.182 0.163 0.039 0.043 LS -0.490 0.526 0.202 0.190 -0.563 -0.702 0.684 0.601 0.216 0.243 -0.111 -0.195 0.147 0.120 0.040 0.044 -0.592 0.583 0.558 0.200 0.184 Initial -0.619 -0.704 0.630 0.497 0.216 0.224 GAs -0.168 -0.190 0.154 0.134 0.044 0.043 LS 0.569 0.456 0.184 0.173

Introduction The problem at hand The proposed algorithm Implementation of GAs – cadastral analogy Simulation results Case studies Summary Future work

Case Studies parcellation plans (alternative solution) Case Studies based on legitimate parcellation plans (alternative solution) Features considered: number of parcels parcels' shapes and sizes lines’ topology numerical ratio

Case Studies cont. - Figures Ex. # 5 Ex. # 6 Ex. # 4 Ex. # 3 Ex. # 1 Ex. # 2 Ex. A Ex. C Ex. B

Case Studies cont. 17 18 20 25 26 111 8 2 7 5 3 9 1 11 Parameters No. of Constra ints Ex. #1 Ex. #2 Ex. #3 Ex. #4 Ex. #5 Ex. #6 Parcels 17 18 20 25 26 111 Straight Lines 8 2 7 5 3 9 Pairs of Lines 1 11

Case Studies cont. Case Studies’ Fitness Values Fitness Values Example A Example B Example C LS Init. GAs Total 88 67 95 44 77 90 94 Parcels 84 66 31 34 72 89 70 Straight Lines 93 65 100 98 99 46 Pairs of Lines 69 36

Case Studies cont. – Results Analyses Parameters [m] Example A Example B Example C Initial Final 0.078 0.002 0.122 0.177 0.003 0.076 0.288 0.010 0.305 0.009 0.300 0.014 0.281 0.286 0.008 0.315 0.921 0.038 0.892 0.035 0.936 0.041 0.941 0.043 0.795 0.042 1.075 0.046 -0.863 -0.054 -0.803 -0.036 -1.042 -0.045 -0.837 -0.049 -0.874 -0.029 -1.123 -0.044

Case Studies cont. – Results Analyses Coordinates’ STD Distributions Ex. A Final Values Initial Values

Case Studies cont. – Results Analyses Coordinates’ Differences Distributions Ex. A Final Coordinates’ Differences Distribution Initial Coordinates’ Differences Distribution

Introduction The problem at hand The proposed algorithm Implementation of GAs – cadastral analogy Simulation results Case studies Summary

Summary coordinates by using evolutionary algorithms – GAs was An innovative method for achieving homogeneous coordinates by using evolutionary algorithms – GAs was presented Several cases of different characteristics were discussed The GAs method provides better results than those of the traditional LS approach GAs hold the potential of realizing a coordinate-based cadastral system (CBCS) CBCS will serve as platform for an efficient land management basis

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