Journal of Signal and Information Processing, 2013, 4, 308-313

http://dx.doi.org/10.4236/jsip.2013.43039 Published Online August 2013 (http://www.scirp.org/journal/jsip)

Application of PDE and Mathematical Morphology in the

Extraction Validation of the Roads

Fabricio Leonardi, Viviane Sampaio Santiago, Carolina Dias Chaves, Erivaldo Antônio da Silva

Department of the Cartography, Faculdade de Ciências e Tecnologia-FCT/UNESP, Presidente Prudente, Brasil.

Email: Leonardibr@gmail.com, vivisamp@gmail.com, carolina.dias.chaves@gmail.com, silva.erivaldo@gmail.com

Received June 13th, 2013; revised July 13th, 2013; accepted August 10th, 2013

Copyright © 2013 Fabricio Leonardi et al. This is an open access article distributed under the Creative Commons Attribution License,

which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

ABSTRACT

The digital images generated by remote sensors often contain noises that are inherent in the process of imaging and

transmission. The application of digital processing techniques greatly enhan ces the ability to extract information on sur-

face targets from remote sensing data. When digital images are used with high spatial resolution, one of the problems

emerging the high variability of targets presents in such images. From the computational point of view, the use of partial

differential equations is favored by the large number of numerical methods showed in the literature. Many of the models

are considered non-complex both from the mathematical and computational standpoints, due to the characteristics of

explicit equations. This work u ses techniques of the partial differential equations (PDE) and mathematical morphology

to extract cartog raphic featur es in digital images of the remo te sensing. The selected study ar ea correspond s to an image

containing part of the Mário Covas Ring Road, located in the metropolitan reg ion of São Paulo (SP), Brazil. The results

are promising and show the high potential of using mathematical morphology in the field of cartography.

Keywords: Extraction Roads; Partial Differential Equations; Mathematical Morph ology

1. Introduction

With the intense modifications that are occurring in the

cities, highways and the agricultural zone, the carto-

graphic update appears as the basic element for the map-

ping of the perimeters urban and agricultural as well as

of the road mesh.

In this direction, it is essential to search a way for the

accomplishment of these updates, so that the same ones

occur in the objective and satisfactory form. The extrac-

tion of highways using images of remote sensing has

been developed in some works in the area of picture

processing, contributing to the management of traffic and

planning of urban and industrial areas.

According to [1], in the area of cartographic sciences,

the problem of extraction of features has been of basic

importance for over two decades, in the automation of

processes of collection of cartographic features, as build-

ings, rivers, roads, etc.

Being like this, the highways are cartographic features

that need constant update, due to its dynamism in func-

tion of modifications in its form or texture.

In this work a sub-picture, is acquired through the

Quickbird satellite, high resolution spacially.

Due to the high spatial resolution offered by satellite,

several applications can be performed, highlighting the

mapping of urban and agricultural areas such as registra-

tion, transportation, telecommunications and planning.

A problem when working with the high resolution of

images is the complexity of its structure, that is, the di-

versity of targets with different forms, tonalities and tex -

tures, such as houses, shades of buildings, automobiles

and trees [2].

In this direction, the use of PDE in picture processing

of remote sensing, associated with the techniques of

mathematical morphology produces satisfactory results

in the extraction of roads, since that they are used in mod-

els of PDE and by appropriate morphol ogic operators.

The model of PDE used in the process of smoothing of

the image in this work was developed by [3]. This model,

part of an only structure, was formulated from the model

of Malik and Perona. Although simple, the model of

Malik and Perona is of great importance, the main idea

suggests a smoothing selection of the image, where the

diffusion is more intense in homogeneous regions and

less in regions of edges.

Through substitutions and additions of terms, the mo-

del of Barcelos and Chen explores the structures of PDEs

Copyright © 2013 SciRes. JSIP