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

2. 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

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

4. 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

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

6. 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

7. 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

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

9. 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)

10. 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

11. 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

12. 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

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

14. 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

15. 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

16. 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

17. 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

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

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

20. 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

21. … … 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

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

23. 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

24. Simulation results cont.
A characteristic set of synthetic data

25. 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

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

27. 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

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

29. 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

30. 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

31. 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

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

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

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

35. 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

36. Thank you