A Model-Based Approach to the Automatic

Extraction of Linear Features from Airborne

Images.

A. Katartzis, H. Sahli, V. Pizurica, J. Cornelis

Abstract

We describe a model-based method for the automatic extraction of linear features, like roads and paths, from aerial images. The paper

combines and extends two earlier approaches for road detection in SAR satellite images, and presents the modi�cations needed for the

application domain of airborne image analysis, together with representative results.

Keywords

Mathematical morphology, Markov random �elds, linear features, airborne images.

I. Introduction

THE identi�cation of linear features by means of digital image analysis is a generic task in remote sensing. Several

approaches have been proposed in the literature, most of them dealing with the problem of road extraction from

either synthetic aperture radar (SAR) images or optic (visible range) images. Usually they are based on two criteria: a

local criterion involving the use of local operators and a global criterion incorporating additional knowledge about the

structure of the objects to be detected. Local operators evaluate properties of the image by using either edge or line

detection [1] [2] [3] [4] or morphological operations [5]. The performance of these methods can be greatly increased by

using techniques that introduce some global constraints in the image analysis process. These techniques minimize a cost

function by using dynamic programming [3] [6], tracking [7] or the Bayesian framework [4] [8] [9].

In this paper we propose a method that combines both local and global criteria for the identi�cation of the medial axis

of roads and paths in aerial images [10]. Our work is part of the European pilot project 'Airborne Mine�eld Detection

in Mozambique', and its main objective is the identi�cation of mine�eld indicators that correspond to linear structures,

which designate safe passage areas [11]. The proposed method is model-based and follows certain assumptions concerning

the geometry and radiometry of the linear structures of interest. It is based on the combination of the concepts of two

previously published methods for road detection using SAR images (Chanussot and Lambert [5], Tupin et al. [4]).

Chanussot and Lambert proposed a simple and fast unsupervised method for road network extraction, based on a series

of morphological processing steps that do not require any threshold. The only parameters that have to be set correspond

to the model dimensions of the feature which has to be extracted. Unfortunately, the lack of contextual knowledge in [5]

results in partial detection of the road network, together with several spurious detections. On the other hand, the work

of Tupin et al. [4] uses both local and global techniques for linear feature extraction. The �rst part of their algorithm

performs a local detection of linear structures based on the fusion of the results from two line detectors, both taking into

account the statistical properties of speckle in SAR images. The masks of the line detectors have widths ranging from 1

to a maximal number of 5 pixels [4]. The produced candidate road segments, together with an additional set of segments

that correspond to all possible connections between them, are then organized as a graph and the road identi�cation is

solved by the extraction of the best graph labeling based on a MRF model for road like structures and a maximum a

posteriori (MAP) criterion.

Our approach consists of two steps. During a local analysis step, the detection of elongated structures is performed

using a set of morphological operators, similar to the ones proposed in [5], and a dedicated algorithm for line segment

extraction [12]. We introduce some modi�cations that enhance the performance of the morphological �ltering in the

case of heavily noisy environments and partially disconnected roads. The local analysis scheme can be extended for a

wide range of images and its computational complexity is relatively small, even in cases where the widths of the roads

vary from a few pixels, up to more than 20 pixels. A segment linking process is then performed in the global analysis

step of our method. This is based on the Bayesian framework of Tupin et al [4]. We present some modi�cations that

improve the road model, and make the process more robust and exible. These changes include the incorporation of

a new observation measure that re ects more eÆciently the likelihood value of each segment as belonging or not to a

road, a di�erent formulation of the potential functions that describe the probability distributions of our model, and the

reduction of the number of potential parameters.

The paper is organized as follows. Section II describes the morphological approach of [5] for road detection and our

local analysis scheme. In section III we present the MRF model-based formulation for road identi�cation and describe

the di�erences between our line grouping scheme and the approach of [4]. The validation of our method, which includes

the parameter setting and some representative results, is presented in section IV. Finally a discussion and directions for

future research are given in section V.

II. LOCAL ANALYSIS

A. The morphological approach of Chanussot and Lambert

The approach of Chanussot and Lambert for road detection in SAR images [5] is based on a geometrical and radio-

metrical road model. The model is based on three assumptions: 1) the roads appear on the image as thin, elongated

structures with a maximum width wmax, 2) they are locally rectilinear, with each road pixel belonging to a line segment

that is longer than a minimum length `0, and 3) each road segment is considered as a dark structure with respect to

its surroundings. All this information is integrated and extracted using mathematical morphology. A series of morpho-

logical operators is used in order to retain elongated structures with a speci�c width. The sequence of morphological

�ltering consists of: (a) an opening by reconstruction (removal of non at peaks), (b) a directional closing in 40 successive

directions (removal of non-linear valleys), (c) an opening (removal of remaining peaks), and (d) a closing Top-hat oper-

ator (removal of wide valleys). At every step, at structuring elements (SE) have been used, and their size is speci�ed

according to the a priori information about the road's maximum width and curvature. At a last stage, the roads are

extracted by a simple thresholding applied to the response of the morphological operators. Unfortunately, this approach

yields incomplete detection of the road network and several spurious detections.

B. The proposed scheme for local analysis

B.1 Morphological �ltering

We retain the advantages of the operators of [5], and at the same time introduce some modi�cations that �rst enhance

their performance under noise, and secondly, produce additional outputs that are used in the next steps of our method.

We suppose that the roads satisfy the �rst two assumptions of the road model of section II-A. As far as the third

assumption is concerned, because of the nature of our images we consider the roads as being bright structures with

respect to their background. This simply implies that each morphological operation must be replaced by its dual

counterpart (closing is replaced by opening and vice-versa).

In our case, the structuring elements used in the morphological �ltering steps (a), (c) and (d) are squares with

sizes wmax=4, wmax=4 and wmax, respectively. One of the proposed modi�cations refers to the directional operator

of step (b). According to [5], the elimination of non-linear structures can be obtained by using a directional opening

in a speci�ed number of successive directions. The resulting value at each pixel should be the supremum of all these

directional openings. Unfortunately, the minimum and maximum operations of the standard morphological opening are

very sensitive to noise and small variations in the shape of the objects (these changes can be small gaps in the road

segments). In order to overcome this problem, we use a soft morphological �lter based on weighted order statistics [13].

This operator is a soft opening with an order index equal to 5 and a linear, non- at SE of size `0, successively oriented in

32 di�erent directions. The SE consists of a hard center with a value equal to `0=2+1 and a soft boundary with linearly

decreasing values (from `0=2+1 to 1), starting from the center, towards both ends. These parameters have been chosen

empirically, based on several experiments, using a large set of test images. The result of the soft directional opening is

an image where bright structures that do not belong to any line segment with minimum length `0 have been eliminated,

and small gaps between linear objects are bridged. During this processing step, an orientation image is also produced

by assigning to each pixel the direction where the soft directional opening gave the maximum value.

As an additional last step, we use a closing with a square SE of size wmax=4, in order to homogenize the regions inside

the roads. The �nal result is considered as the response (R) of our morphological road detector. Figures 1 and 2 show

the grey value version of an airborne optical image with a size of 800 x 800 pixels and the morphological road detector's

response (negative image), respectively. In this particular example we have chosen wmax = 30 and `0 = 35.

B.2 Line segment extraction

One pixel width line segments are produced by extracting from the response image (R) the pseudo-medial axis of the

roads, over which we apply a line-following algorithm [12]. The pseudo-medial axis is found by performing the watershed

transformation on the response image. The objective of the line-following process is the creation of a list of line segments

with a minimum prede�ned length `min. Each medial-axis pixel is considered as the starting point of a line segment.

Pixels are added into a line segment by using a dedicated tracking algorithm, that follows a direction � indicated by

the orientation image. The line-following stops when an angle deviation greater than d� is reached. Figure 3 shows the

�nal result of this process (detected line segments) superimposed on the orientation image. The parameters `min and

d� are set to `min = `0=2 and d� = 30o, respectively.

III. GLOBAL ANALYSIS

The second part of our work concerns the reconstruction of the roads from the previously detected line segments.

Several methods have been developed for grouping lines using contextual constraints about the linear features of interest.

Markov random �eld theory provides an eÆcient framework to model these constraints [8] [14]. Our line grouping

approach is based on [4].

A. The line grouping approach of Tupin et al.

The method of Tupin et al. for line grouping [4] falls within the scope of the Bayesian framework. It is applied on

a set S of line segments, consisting of the set of detected line segments (Sdet) that are the result of a dedicated line

detection algorithm for SAR images, and all the possible connections between them (Scon). These additional segments

are produced by using certain connectivity criteria. The elements of S are then organized as a graph G = (S;A). To

each node i 2 S is associated a normalized segment length (`i 2 [0; 1]), an observation value di, which corresponds to

the mean line detection response value along the segment, and a label li = 1 if i belongs to a road, li = 0 otherwise. An

arc, Aij 2 A, between two nodes i and j, corresponds to a shared extremity. To each arc Aij is associated the angle

�ijmod� between the two segments. A neighborhood system is de�ned on G, with its cliques being all the subsets of

segments sharing an extremity. The neighborhood Ni of each node i is given by:

Ni =�j 2 S=9(k; p) 2 f1; 2g2;Mk

j=M

p

i; j 6= i

(1)

where Mkj, for k 2 f1; 2g, denote the endpoints of a segment j.

The identi�cation of the roads is carried out with an appropriate labeling of the graph, in accordance with the

observation process d = (d1; d2; :::; dm) (where m is the cardinality of S). A Markov random �eld is de�ned on the graph

and the optimum con�guration (labeling) l = (l1; l2; :::; lm) of the segments of S, given the observation process d, can be

estimated based on the Bayes rule and a MAP criterion that maximizes the posterior probability P (ljd). The conditional

probability distribution p(djl) depends on the observation measurements, whereas the prior probability of labelings P (l)

is based on a Markovian model of road-like objects. From the equivalence between MRF and Gibbs �elds, both of

them can be described with a set of potentials that associate an energy function to the di�erent con�gurations. The

minimization of this energy function gives the optimal solution to the problem.

Under the assumption that each observation di is only conditioned by the corresponding label li, the conditional

probability distribution p(djl) is expressed by:

p(djl) =

mYi=1

p(dijli) / exp

�

mXi=1

(V (dijli) + logZ0)

!(2)

where V (dijli) denotes the conditional potential of segment i and Z0 a normalization factor that ensures the condition

R1

0p(d = xjl)dx = 1. The potentials V (dijli) were chosen experimentally after a manual segmentation of roads and

depend on two parameters t1 and t2:

V (dij0) =

8>>>>>><>>>>>>:

0 if di < t1

di�t1

t2�t1if t1 < di < t2

1 otherwise

and V (dij1) = 0; 8 di (3)

The prior probability of labelings and the corresponding clique potentials re ect three main assumptions about the

road structure: (i) roads are long structures, (ii) they have low curvature, and (iii) intersections between roads are rare.

For every clique c, the de�ned clique potentials depend on the current con�guration:

� Null situation : 8i 2 c; li = 0; Vc(l) = 0 (4)

� Assumption (i) : 9!i 2 c=li = 1; Vc(l) = Ke �Kl`i(5)

� Assumption (ii) : 9!(i; j) 2 c2=li = lj = 1; Vc(l) = �Kl(`i + `j) +Kcsin(�ij) (6)

� Assumption (iii) : in all other cases; Vc(l) = KP

i=i2cli

(7)

Positive values for the parameters Ke and Kl ful�ll assumption (i) and favor long roads, whereas positive values for Kc

and K ful�ll the assumptions (ii) and (iii) of the road model, respectively.

B. The proposed scheme for line grouping

We propose a line grouping scheme that is an enhanced version of the method described in the previous section. The

main modi�cations include the incorporation of a new observation measure, the reduction of the number of potential

parameters and the improvement of the clique potential functions.

B.1 Graph creation

The graph structure G, associated to the augmented set of segments S, together with the attributes attached to it

are the same as in the scheme of [4], described in the previous section. We introduce a new observation �eld d that

depends both on the morphological road detection response and orientation information, and re ects more eÆciently

the likelihood value of each segment as belonging to a road. The observation di of each segment i is a function of a

saliency measure ri de�ned as:

ri = Ri=(j�i � �ij+ 1) (8)

where Ri and �i are the mean values, along the line segment, of the morphological road detection and orientation

responses (as described in section II-B.1) respectively, and �i is the line segment orientation. A high value ri for a

segment i, together with the presence of other segments with a high saliency in the neighborhood of i, are considered as

cumulated evidence that this segment is part of a road. The observation values di are de�ned as:

di = maxj2Ni

f(ri + rj)=2g (9)

The observation values d1; d2; :::; dm, associated to S, are then normalized between 0 and 1.

B.2 Conditional probability distribution

By assuming that the observation di is only conditioned by the corresponding label li, and that the dependencies

between the di�erent observations are exclusively determined by the dependencies between the labels li (as described

by the MRF model), the conditional probability distribution p(djl) can be derived from equation 2. Using the proposed

observations di (equation 9), manual segmentation of road images showed that road segments may have almost any

observation value d, while nonroad segments have observations with values smaller than a threshold t. As opposed

to the conditional potentials proposed in [4], the chosen potential functions that describe the conditional probability

distributions p(dijli) depend only on one parameter:

V (dj0) =

8>><>>:

d

tif d < t

1 otherwise

and V (dj1) = 0; 8 d (10)

Based on these functions, the normalization factor Z0 in equation 2 is found to be equal to Z0 = (1� t)(1=e)� t(1=e�1)

with e = exp(1).

B.3 Prior probability of labelings

A priori knowledge is introduced with the creation of a geometrical model of road-like structures. In our case, this

model is based on the three assumptions of [4] described in section III-A. We have modi�ed the form of the clique

potentials proposed in [4] by using a reduced number of potential parameters and by making a clear distinction between

the elements of Sdet and Scon, which provides additional a priori information about the nature of each segment. The

optimal con�gurations have long and collinear detected line segments with short connections between them. Every

clique contains one segment belonging to Sdet (with length `det), along with segments of Scon (with length `

con) that

share the same extremity. For every clique c, the chosen clique potentials have the following form:

� Null situation : 8i 2 c; li = 0; Vc(l) = 0 (11)

� Assumption (i) : 9!i 2 c ^ i 2 Sdet=li = 1; Vc(l) = K1 + 1� `det

i+ logZ0

(12)

� Assumption (ii) : 9!(i; j) 2 c2 ^ i 2 Sdet; j 2 Scon=li = lj = 1;

Vc(l) = sin(�ij) + 1� `det

i+ `

con

j+ 2logZ0

(13)

� Assumption (iii) : in all other cases, Vc(l) = K2

Pi=i2c

li(14)

By choosing K1 > 0 in equation 12 we penalize short roads (assumption (i) in section III-A), i.e. the clique potential is

high for a clique with only one isolated segment, except when this isolated segment has a high normalized length `det

i

(close to 1). High values of K1 favor more connected con�gurations. Equation 13 satis�es assumption (ii) of section

III-A and at the same time penalizes con�gurations with short detected and long connecting segments. Finally, K2 > 0,

in equation 14, has the same properties as the parameter K in equation 7. The additional parameters logZ0 and 2logZ0,

in equations 12 and 13 respectively, are factors that facilitate the comparison between the clique potential values and

the conditional potentials of the null con�gurations (where all the segments of the current clique are labeled as 0). In

the case of a clique with one segment labeled as 1, the factor K1+1� `det

iin equation 12 is directly compared with the

conditional potential component V (dij0) of the current segment i. In the case of a clique with two segments i, j labeled

as li = lj = 1, the factor sin(�ij) + 1� `det

i+ `

con

jof equation 13 is compared with the sum of the conditional potential

components V (dij0), V (dj j0).

B.4 Posterior probability - Energy minimization

The posterior probability P (ljd) can be also expressed in terms of a global energy function U(ljd) (P (ljd) =/

exp(�U(ljd))), which can be deduced from the potentials functions:

U(ljd) =

mXi=1

V (dijli) +Xc2C

Vc(l) (15)

The MAP con�guration of the line segments is estimated by minimizing the energy function U(ljd). As minimization

scheme, a simulated annealing specially adapted to our problem is used [12]. We chose an eÆcient label generation

mechanism in order to speed up the evolution of the system towards the optimal solution (global minimum). Instead of

sequentially updating the label of each node, we consider three adjacent segments and apply the Metropolis acceptance

criterion [15] to each of their eight possible con�gurations. Based on the conjecture that it is not possible to have a

connecting segment with label li = 1 if one of the adjacent detected segments has label lj = 0, we reject beforehand

con�gurations of this type. For the annealing process, we used the polynomial-time cooling schedule proposed in [15].

IV. VALIDATION

A. Parameter setting

In this section, we investigate the parameters that in uence the probability distributions and their corresponding

potential functions. Our scheme for parameter setting is inspired from the one presented in [4]. As a reference, we will

use a set of three connected segments s1, s2, s3 (s1; s3 2 Sdet and s2 2 Scon). By comparing the energy components of

two possible con�gurations of these segments, we can derive the accepted range of the parameter K1.

� "Connected" con�guration: l1 = l2 = l3 = 1.

Ucon = 2K1 + sin�12 + sin�23 + 4� 2`1 � 2`3 + 2`2 + 6logZ0 (16)

� "Unconnected" con�guration: l1 = l3 = 1 and l2 = 0.

Uuncon = V (d2j0) + 4K1 + 4� 2`1 � 2`3 + 4logZ0 (17)

The energetic variation �U = Ucon �Uuncon should be positive in the case of a long connecting segment s2 (`2 ! 1)

with a poor observation value (V (d2j0)! logZ0), even if the three segments are perfectly aligned. This condition limits

the connecting power of the a priori model in poor observation areas. Based on the restriction �U > 0, the following

condition should be ful�lled:

K1 <2 + logZ0

2(18)

The parameter K2 has been empirically set to a value equal to 0.1. Finally, the optimal value of the parameter t (in

equation 10), for the type of airborne images used in our application, is found to be around 0.15 (logZ0 � �0:89).

B. Results

This section demonstrates the performance of our method in two diÆcult cases of airborne images. The �rst image

contains roads with a big variety of widths, while the second one has small paths in a heavily textured environment. In

both examples, the road detection results have been produced using the following values for the potential parameters:

t = 0:15, K1 = 0:5 and K2 = 0:1.

Figure 4 shows the result of our method related to the airborne image of �gure 1. Most of the false-alarm detections

of �gure 3 have been suppressed, whereas the linear features corresponding to roads and paths have been successfully

reconstructed, independently of their size. Figure 5 illustrates the in uence of the angular information in the de�nition

of the saliency measure r (equation 8). The choice of a saliency measure depending only on the mean response value

along each segment (ri = Ri) produces several spurious detections due to imperfections in the response image.

A second example is presented in �gure 6. The image has a size of 800x800 pixels and represents a heavily textured

scene, with several small paths that are partially disconnected, mainly because of image degradation. The parameters

used in the local analysis step are the following: wmax = 5, `0 = 20, `min = `0=2 and d� = 30o. The �nal result,

presented in �gure 7, contains most of the linear features of interest together with a small number of wrongly classi�ed

line segments. Finally, we demonstrate the importance of the introduced soft morphological operators during the local

analysis phase. Figure 8 represents the detected linear structures from �gure 6, using merely the morphological operators

of Chanussot and Lambert [5], without the proposed modi�cations. The paths in the image have been partially detected,

mainly due to the fact that the result of the morphological �ltering contains several disconnected linear regions, which

are gradually vanished during the ooding process of the watershed transformation (extraction of the pseudo-medial

axis of the roads).

The computational time of our method is rather demanding, mainly because of the optimization step (simulated

annealing) of section III-B.4. Nevertheless, the proposed optimization scheme is stable and converges, in most cases

that were investigated, to a global minimum solution, independently of the initial realization of labelings. For a 800 x

800 image on a Pentium III at 500MHz, the local analysis phase lasts around 5 min. Due to the eÆciency of our line

detector, for our test set of images, the total number of road segment candidates is not more than 1500. For this number

of segments the labeling stage lasts approximately 10 min.

V. DISCUSSION - CONCLUSIONS

We describe a model-based technique for linear feature extraction, in digitized airborne images, which combines both

local and global criteria, and illustrate its application on the problem of road and path detection. Its main advantage is

the good detection performance in heavily textured environments along with its ability of identifying elongated structures

independently of their size. It can be considered as the combination and extension of two earlier approaches [5] [4].

As far as the local analysis step is concerned, the improvement of the morphological �ltering scheme of [5], mainly due

to the use of a soft operator, together with the proposed line-following algorithm, result in a better detection of roads

with a large variety of sizes, and in the reduction of spurious line segments, even in the presence of heavy noise. Due to

the good performance of our line detector, the produced candidate road segments are long and not too numerous. This

decreases signi�cantly the complexity of the labeling process. The proposed global analysis stage, although it has many

similarities with the one in [4], contains some important modi�cations that make it more exible and robust. These

modi�cations include the incorporation of a new observation measure that re ects more eÆciently the likelihood value

of each segment, the reduction of the number of potential parameters, and �nally the use of di�erent potential functions

that represent better the properties of the geometrical road model.

One of the most important limitations of our method is that it is not entirely unsupervised, due to the setting of

three parameters (t, K1, K2), all of them concerning the connection step. Nevertheless, the proposed ranges of these

parameters, give very good results for the class of environments illustrated in �gures 1 and 6, independently of the size

of the linear features to be extracted. Further analysis should be carried out towards the problem of identifying road

segments with high curvature, especially when the curvature is high compared to the maximum road width found in

the image, and towards the choice of a more eÆcient skeletonization process for the extraction of the road medial axis.

Another interesting aspect for investigation is the incorporation of color information as an extra attribute, in order to

further decrease the number of false-alarm detections.

Acknowledgments

The research is part of the European Pilot Project: "Airborne Mine�eld Detection in Mozambique" (REG/661-

97/2,DG VIII). (Partners: ITC(N), RMA(B), Geograph(P), EOS(UK), Eurosense(B), Aerodata(B), CAE Aviation(L),

VUB(B)). It was funded by the European Commission (DG8) and the involved member states. The authors would like

also to thank Prof. E. Nyssen (VUB) for his comments.

References

[1] J. Canny, \A computational approach to edge detection," IEEE Trans. Pattern Anal. Machine Intell., vol. 8, pp. 679{698, Nov. 1986.

[2] Y. T. Zhou, V. Venkateswar, and R. Chellapa, \Edge detection and linear feature extraction using a 2-d random �eld model," IEEE

Trans. Pattern Anal. Machine Intell., vol. 11, pp. 84{95, Jan. 1989.

[3] M. A. Fischler, J. M. Tenenbaum, and H. C. Wolf, \Detection of roads and linear structures in low resolution aerial imagery using a

multisource knowledge integration technique," Comput. Graph. Image Processing, vol. 15, pp. 201{223, no 3 1981.

[4] F. Tupin, H. Maitre, J. F. Mangin, J. M. Nicolas, and E. Pechersky, \Detection of linear features in SAR images: Application to road

network extraction," IEEE Trans. on Geoscience and Remote Sensing, vol. 36, pp. 434{453, Mar. 1998.

[5] J. Chanussot and P. Lambert, \An application of mathematical morphology to road network extraction on SAR images," Proc.

International Symposium on Mathematical Morphology, Amsterdam, pp. 399{406, 1998.

[6] N. Merlet and J. Zerubia, \New prospects in line detection by dynamic programming," IEEE Trans. Pattern Anal. Machine Intell.,

vol. 18, pp. 426{431, Apr. 1996.

[7] D. Geman and B. Jedynak, \An active testing model for tracking roads in satellite images," IEEE Trans. Pattern Anal. Machine Intell.,

vol. 18, pp. 1{14, Jan. 1996.

[8] J. L. Marroquin, \A Markovian random �eld of piecewise straight lines," Biological Cybern., vol. 61, pp. 457{465, 1989.

[9] M. Barzohar and D. B. Cooper, \Automatic �nding of main roads in aerial images using geometric-stohastic models and estimation,"

IEEE Trans. Pattern Anal. Machine Intell., vol. 18, pp. 707{721, Jul. 1996.

[10] A. Katartzis, V. Pizurica, and H. Sahli, \Application of mathematical morphology and Markov random �eld theory to the automatic

extraction of linear features in airborne images," Proc. International Symposium on: Mathematical Morphology and its Applications to

Image and Signal Processing V, California, USA, pp. 405{414, 2000.

[11] L. van Kempen, A. Katartzis, V. Pizurica, J. Cornelis, and H. Sahli, \Digital signal/image processing for mine detection part1: Airborne

approach," Proc. MINE '99, Euroconference on: Sensor systems and signal processing techniques applied to the detection of mines and

unexploded ordinance, Firenze, Italy, pp. 48{53, 1999.

[12] A. Katartzis and H. Sahli, \A model-based approach to the automatic extraction of linear features from airborne images, using

mathematical morphology and MRF theory," Technical report,VUB: IRIS-TR-0062, 2000.

[13] P. Kuosmanen and J. Astola, \Soft morphological �ltering," Journal of Mathematical Imaging and Vision, vol. 5, pp. 231{262, 1995.

[14] S. Krishnamachari and R. Chellapa, \Delineating buildings by grouping lines with MRFs," IEEE Trans. on Image Processing, vol. 5,

pp. 164{168, Jan. 1996.

[15] E. H. L. Aarts, Simulated annealing and Boltzmann machines, John Wiley & Sons Ltd., 1989.

Figures - Captions

Fig.1. Original airborne image (Bandua region in Mozambique: scale 1:2000; ground resolution 0.22m).

Fig.2. The negative image of the morphological road detection response R.

Fig.3. Detected line segments superimposed on the orientation image.

Fig.4. Road detection result (Bandua region).

Fig.5. Road detection result, using the saliency measure ri = Ri (Bandua region).

Fig.6. Original airborne image (Songo region in Mozambique: scale 1:3000; ground resolution 0.31m).

Fig.7. Road detection result (Songo region).

Fig.8. Road detection result, using the morphological operators of [5] in the local analysis step (Songo region).

Fig. 1. Fig. 2.

Fig. 3. Fig. 4.

Fig. 5. Fig. 6.

Fig. 7. Fig. 8.