Topological representation of input data for DTM

Petr Rapant
Institue of Economics and Conrol Systems
HGF VŠB - Technical University of Ostrava
tř. 17. listopadu, 708 33 Ostrava - Poruba
Czech Republic
Tel.: +420 69 699 5470, Fax: +420 69 691 8589
E-mai
l: petr.rapant@vsb.cz

 

Abstract:

There are many problems related to generation, tuning and analysis of DTMs. Checking input data for validity and completeness of terrain relief description, generation of correct high quality TINs, and morphological analysis of DTMs are some of them. Presented paper discusses the possibility to generate topological representation of terrain relief data from DTM input data and the possibility to use this topological representation for DTM input data checking, TIN generation and DTM analysis. This representation is based on transformation of DTM input data to form of nodes and links weighted graphs. The necessary conditions the data have to fulfill is to use terrain description at least in the form of contours.

 

Introduction

One from the basic problems related to DTM generation is how to ensure consistency and validity of input data used. Procedures to ensure and check internal and external consistency of data describing terrain relief were studied for a long time.

Internal consistency means logical validity of data which (if it is reached) guarantees that for example there are no contours crossings, no missing contours, no erroneously tagged contours, no gaps in contours, etc. It is possible to develop data validation procedures permitting automatic validation of internal data consistency.

External consistency means coincidence of the input data with reality. It is very difficult to find out procedures for automatic checking of this consistency. But in the case we ensure internal consistency of data it undoubtedly let us to reach also better external consistency.

There are some procedures for internal consistency checking today, but these procedures are designed only for TIN and grid data structures. Any procedures for validating of complex data, containing different kind of features describing terrain relief are not developed nowadays.

 

Features used for terrain relief description

There are many kinds of features used for terrain relief description. It is possible to sort them to three basic classes by their graphic representation:

  1. points
  2. lines
  3. areas.

Point features describe phenomena located on the terrain surface which are described by the set at least of three coordinates [x,y,h]. It is possible to sort point features to two main groups:

- points carrying information only about an elevation of terrain in a given point, which are described by the set of three coordinates [x,y,h]. There are two kinds of these points:

- points carrying information about elevation of terrain and information about behavior of terrain surface in this point. It possible to describe these points by a set of four data [x,y,h,i] (where i is an additional information):

Line features represent one-dimensional phenomena on the terrain surface which are described by a succession of sets of at least three coordinates [x,y,h]. They can be sortet to following classes:

- line features carrying information about terrain elevation in the points describing lines only:

- line features representing sudden changes of terrain surface course (edges), which are described by a succession of sets of at least three coordinates [x,y,h] and additional information i, meaning of which is dependent on the kind of feature:

line features representing so called structure lines, which are described by a succession of sets of at least three coordinates [x,y,h] and additional information i, meaning of which is dependent on the kind of feature:

Area features represent two dimensional phenomena on the terrain surface, which are described by a succession of sets of at least three coordinates [x,y,h] defining border line of the area, and additional information i which closely describe nature of heights in this area. We can sort these features to following classes:

It is possible to divide digital terrain models to three main classes based on the set of features used for terrain relief description:

 

Topological representation of data describing terrain relief

Topological representation of data describing terrain relief is such representation of input data which describes their mutual spatial relations and make possible to check their inner consistency.

Topological representation is presented in the form of usual nodes and links weighted graphs. Nodes represent features or their parts, links their spatial relationships like adjacency and continuity.

Nodes have assigned attributes describing represented features. There are defined these attributes in the case of point features (Fig. 1):

Fig. 1

Abbreviation

Kind of feature

PE

peak

PI

pit

PS

spot height

PR

regular point

PO

point of outlet from watershed

PD

saddle point

PC

check point

Table 1

Abbreviation

Kind of feature

opened

closed

OC

CC

contour

OP

CP

profile

OG

CG

general line

OR

-

ridge

OD

-

drain

OS

-

slope vector

OB

CB

break line

-

CE

edge

Table 2

Abbreviation

Kind of feature

AC

plane with constant elevation

AP

area with unknown elevation

Table 3

Symbol

Kind of Edge

edge describing relation of neighborhood of two features; assigned attribute is equal to elevation growth between two features in the direction of arrow

edge describing relation of contiguity of two features; assigned attribute is equal to elevation of both features

Table 4

There are defined these attributes in the case of line features:

- type of feature

- starting feature elevation

- ending feature elevation

- closeness

- attribute meaning starting/through/finishing

- pointer to original feature.

There are defined these attributes in the case of area features:

- type of feature

- feature elevation

- pointer to original feature.

Two attributes are assigned to edges:

- type of spatial relation

- elevation growth.

Attributes do not include horizontal position of features. Knowledge of horizontal feature positions is important in the phase of topological representation generation. Following analysis are made in topological space.

 

Examples of topological representation

Some examples of line graphs representing some typical cases of contours successions follows. These graphs represents contours describing peak, pit and saddle. Each example is documented partly by contour image and partly by line graph.

Peak

Fig. 2 displays contours describing peak and Fig. 3 related line graph:

Fig. 3

Pit

Fig. 4 displays contours describing pit and Fig. 5 related line graph:

Saddle

Fig. 6 displays contours describing two peaks and Fig. 7 related line graph.

Fig. 6

 

More complex example

Finally, more complex example is described (see Fig. 8). This situation can be described by relatively simple line graph, dealing with only contours, edge of the model and two peaks, as displayed on Fig. 9. In this case we would be able to deal also with structure lines (ridges and drains). More complex line graph can be derived, which describes also spatial relationships of contours and structure lines.

The second kind of the line graph tax input data heavily. We need to know structure lines and their points of intersection with contours explicitly. But it looks it would be possible to derive structure lines from above mentioned simple line graph. It would permit to derive so called Warntz networks from the input data.

 

Conditions for deriving topological representation of input data

Data used to derive topological representation of input data have to meet some conditions. Those cases, which do not meet them, can be indicated as errors in the input data.

 

 

 

Contours have to meet these conditions:

- either they have to be closed, or

- they have to be terminated by:

- rising succession of closed contours has to be finished by peak

- digressive succession of closed contours has to be finished by pit.

Intersection points of structure lines with contours have to be known.

Input data would contain full set of point features like peaks, pits and saddle points.

 

What can be derived from topological representation of input data

It is possible to derive from topological representation of input data:

Fig. 10 and Fig. 11 describe some of these cases.

 

Conclusions

This paper represents only first look into this problem. Ideas presented (if they survive professional discussion, which is welcomed) need more detailed research. By my opinion, this approach can contribute to solution of many problems in the sphere of DTM development, analysis and usage. Especially in the case when vectorised contours from existing analog maps are used as input data for DTM.

 

 

 

 

Fig. 8

Fig. 10

Fig. 11