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Good afternoon. Thank you for your nice introduction. Before I’ll start my

presentation, I want to introduce myself. I’m an Assistant Professor at Computer

Science Department of Karabuk University-Turkey. Currently, I’m working on Post

doctoral research at 3D GIS research Lab at Universiti Teknologi Malaysia. My

collaques Prof Batuk is from YTU in Turkey. And Prof Abdul-Rahman is also from

UTM.

//////// So, what are the topological problems in a vector data and why we need to

correct them?

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In a GIS project, data collection is very time consuming and expensive task; it still

consumes up to fifty percent of the available resources. Data gathering from

existing archives is a frequently applied method for reducing project costs. The

one of the most beneficial useful method of achieved spatial analogue data is

scanning the maps and than converting to vector forms. However, the data which

has been obtained after the vectorization process cannot be used in a GIS

without the geometrical and topological corrections. And needs post processing.

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Topology is a branch of mathematics science and it is related with relationships

between the entities, but not with metric properties. Topology doesn’t care size or

shape of entities, but interested with properties which they don’t change even

though shapes change. Topology is kind of mathematical statement of manifest

content by human.

In terms of GIS, topology expresses how geographical features connect and

relate to each other that are unchanged after distortion and without geometry.

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It’s very important to configure topologic relationships in a GIS. Configuring

topology is based on connectivity. Connectivity is prerequisite for structuring the

topological network. However, unconnected and some unnecessary lines will be

occurred after the vectorization process./////

This is the our vectorization program. It was developed by us based on our

MUSLE Model. We published this model somewhere else. Graphical user

interface of the program is like in Figure. I will mention here,,, topological

correction module of this program.

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In this modul, to remove connectivity errors, firstly, the program needs some information from the user. //// What are they? Before the vectorization process, the user is expected to define the some specified criteria. Two of these criteria are interested with topological corrections; Maximum Joint Distance and Overshoot/Undershoot Distance.

Maximum Joint DistanceDuring the topological correction of the vectorized data, the ending points of the lines that were closer to each other must have been merged for joining the broken lines. For achieving this, the user is allowed to define and input a maximum joint distance value. Consequently, if the distance between ending points of the lines are less than the input value, the model connects these points at a shared intersection point.

Overshoot and Undershoot DistanceThe user is allowed to define and input a distance value for correcting the undershoot and the overshoot errors during the vectorization process. For example, if a user assigns the value of “three” for this criterion, dangles and gaps which are smaller than “three pixels” would be eliminated and geometrically corrected as explained in following section.

How can be performed the correction by using these criteria?..

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Connecting End Points of the Lines. //// This circumstance occurs especially at

the corner points. “Maximum joint distance” criterion determined by user is used

for this correction. The adjacent lines in the determined distance are connected at

the algorithm. Then, the end points are joined by calculating the mean value of

coordinates for two or more nodes, like in the Figure.

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Calculation of intersection point coordinates

In this process, the coordinates of the intersection points between the lines arecalculated.

Firstly, AB and CD lines are defined by using their beginning and ending pointscoordinates as you see (DOĞRU DENKLEMLERİNİ GÖSTER.) The line equations are like this.

Then, the coordinates of K intersection point for these two lines can be calculated by the formulations like this (GÖSTEREREK)

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And then, the distances from K intersection point, to the ending points of the

intersecting lines, A-B-C-D, can be calculated by using this equation. D distances.

(GÖSTER)

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After these calculations, ending points are examined to determine either there arean overshoot or undershoot error.

1. If the length of a line, (d’yi GÖSTEREREK) is equal to sum of the distances from two ending points, (d1 ve d2’yi GÖSTEREREK) to K intersection point….

2. And one of these distances is shorter than the user defined “overshoot/undershoot distance” value… (oud), (d2’nin oud’den KÜÇÜK OLDUĞUNU GÖSTER)

Ending point is defined as overshoot point like as figure. (C’Yİ GÖSTER. YENİ YERİNE KAYIŞINI GÖSTER)

And then, the algorithm corrects the overshoot error by moving the ending point to the intersection point.

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1. If the length of a line, (d’yi GÖSTEREREK) is shorter than the sum of the distances from two ending points, (d1 ve d2’yi GÖSTEREREK) to K intersection point…

2. And one of these distances is shorter than oud… (d2’nin oud’den KÜÇÜK OLDUĞUNU GÖSTER)

Ending point is defined as undershoot. (C’Yİ GÖSTER. YENİ YERİNE KAYIŞINI GÖSTER)

And then, like overshoot, the algorithm corrects the undershoot error by moving the ending point to the intersection point.

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1. If there is a case where the length of a line (d’yi GÖSTEREREK) is equal to sum of the distances from two ending points to intersection point…

2. And both of these distances were longer than oud value,

Ending point is not defined as neither overshoot or undershoot.

In this case, intersection point is assigned to be a new point and the lines aredivided into four new lines, as you see in the figure.

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PROGRAMI GÖSTER

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In this study, topological and geometrical errors which have been occurred after

the vectorization process were described.

Also, correction module of our R2V program and the mathematical basics of its

algorithm which has been developed to remove these errors were detailed.

The results indicate that the algorithm can be successfully used to

generate data-set which suitable for spatial analyses in GIS.

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