perugia voiron

GEOG-AN-MOD 08A Spatio-Morphological Modelling of Spread Predicting

A Spatio-morphological Modelling for Spread Predicting

Christine Voiron – Canicio

UMR ESPACE - University of Nice Sophia Antipolis / CNRS


The aim of the modelling

❑ The aim

i. Predicting the broad outlines of a built-up areas extension

i. Providing decision makers with a tool which allows them to explore spatial consequences of different urbanisation policies

❑ The challenge

Finding a compromise between the level of generalisation and the level of accuracy


Outline

❑ What is a spatio-morphological modelling ?

❑ A model to predict the built-up areas spread in the coastal region of

Languedoc (Southern France)

❑ The stages of the modelling :

1) determining the spatial rules of the model

2) simulating in a retrospective way the progressive extension of

the built-up areas

3) validating the model.

4) using the validated model to simulate the future extension of built-up areas.


What is a spatio-morphological modelling ?

❑ A spatial modelling performed by image processing and algorithms of

Mathematical Morphology. MM is suited to spread models and to

propagation simulations.

❑ In this application, the model is deterministic, it assumes that the

spatial spread depends on both distance and morphology of the built-

up areas.

❑ The spreading process essentially complies with elementary rules of

distance to the built-up areas which are supposed to explain the major

part of the spread.


Stage 1: determining the spatial rules



98% of the new built-up areas have sprawled from the already built-up zones

The spatial diffusion mode is that of « expansion diffusion »

Since 2000, the French law only permits new constructions which are contiguous to already built-up zones.



Spatial rules :

The new built-up areas can spread from the existing built-up elements only.

The spread is forbidden wherever protected natural zones exist.

The extension of built-up areas occurs by the progressive connection of the nearest elements.

These connections are performed by using operators of image analysis.


❑ The spread process is performing by using 3 basic operations of Mathematical Morphology : the dilation, the erosion and the closing

A dilation corresponds to a thickening process of a given size

An erosion corresponds to a thining process

Stage 2: simulating the spread by using image processing

dilation size 1

erosion size 1


❑ A closing is a dilation of a given size + an erosion of the same size

The result of a closing is : i) the clustering of parts in the set under study ii) the hole filling action

The spread process will be performed by using conditional closings of increasing size

=+

a closingsize 2

Stage 2: simulating the spread by using image processing


❑ We deal with bmp images:

Stage 2 : simulating the spread by using image processing


Y

Coefficient simil

Image A1:Built-up areas in 1977

Image B: closing of size i

I = i+ 1

simil is higher

?

Elimination of points falling into sea, ponds, protected zones

Image A2:observed built-up areas in 1990

Image B:result ofclosing

simil (A2,B) = surface of intersection (A2,B) / surface of union (A2,B)

Y

Matching

Flow chart of the spread modellingby image processing

N

The ctiterion for stopping the spread is the value of simil.The matching is performed for all probable sizes of closing,

one takes that which maximizes simil


« The predictive models are not expected to be accurate at the pixel scale but they are expected to predict the approximative shapes and locations of the phenomenon » (Power, Simms and White, 2001)

1) The evaluation of similarity takes into account margins of error of :

1 pixel (37 m)

2 pixels (74 m)

3 pixels (117 m)

by dilating the new predicted surfaces by 1, 2 or 3 pixels successively, before performing the intersection with the new observed surfaces.

The visual comparison can suggest the need of local calibrations

Stage 3: validating the outputs


simil calculated on the new built-up areas = 0.257

71%65%58%48.5%

Margin of error3 pixels


Margin of error1 pixel

Pixel agreement

Application: basic model

Results of the model


Improving the model

Subset 1: « attractive zones »:Stage 1: new spread process

Subset 2:rest of the

built-up areas

Stage 2: protocol used to the 1st model


Application: Improved model

simil calculated on the new built-up areas = 0.41

77%72%65%58%Improved model

71%65%58%48.5%Basic model



Margin of error1 pixel

Pixel agreement

Results of the model


Stage 4: simulating the future extension of built-up areas

This improved model is applied to seek the broad outlines of the future built-up surfaces, up to 2010

2 spread rates have been tested

6 %

3 %


Summary

❑ Modelling by image processing is rich in potential. MM is well adapted to spatial analysis,

especially to spatial propagation simulations.

❑ This model has been performed to measure how much the urban spread depends on

elementary rules of distance and morphology.

❑ The results give the broad outlines of the future urbanisation to be discussed with the local

autorithies.

❑ New spatial rules can be added to take into account the topography and the road network of

the region under study.

❑ This model is deterministic. We are working on a randomisation of the urban spread by

combining both « dilation » operation and Poisson points diffusion.

❑ In other applications as risks the prediction is based on probabilistic approaches and

simulations with random spread models.


Thank you for your attention

perugia voiron

Economy & Finance