On the use of morphological alternated sequential filters

for the classification of remote sensing images from urban areas.

JOCELYN CHANUSSOT JON ATLI BENEDIKTSSON MARTINO PESARESI

Signal & Images Laboratory Dpt of Elec. & Computer Engineering INFORM srl

LIS / INPG - BP 46 University of Iceland TSA Area, Digital Mapping Sector

38402 St Martin d’Heres 107 Reykjavik 56 via Savelli, 35129 Padova

FRANCE ICELAND ITALY

jocelyn.chanussot@lis.inpg.fr benedikt@hi.is PesaresiM@Informsrl.it

Abstract – The problem of classification of high-resolution

remotely sensed images from urban areas is addressed. Previous

studies have shown the interest of exploiting the local geometrical

information of each pixel to improve the classification. This is

performed using the derivative morphological profile obtained

with a granulometric approach using respectively opening and

closing operators. We propose to replace this by a morphological

alternated sequential filter, where the openings and the closings

are applied alternately. The results and the robustness provided

by the ASF are presented on IKONOS panchromatic data.

Keywords : mathematical morphology, classification, alternated

sequential filters, high resolution imagery.

I. INTRODUCTION

Segmentation is a key operation in automatic image understanding and analysis. Traditionally, two kinds of strategies are considered:

- The contour-based approaches aim at detecting dissimilarities between pixels (i.e.: edges). A region is then defined as the interior of a closed contour.

- The region-based approaches aim at detecting similarities between pixels. A region is then defined as a connected set of pixels sharing some common properties.

Among the region-based approaches, segmentation by classification is very popular in the field of remote sensing. It basically consists in assigning each pixel to a semantically meaningful class. The decision is generally taken by only considering the value of the pixel (the “physical” nature of each pixel is inferred from its value). A region is then defined as a set of connected pixels that have been assigned to the same class, and a class is divided into several regions. In many applications, this leads to satisfactory results. But when one is not only interested in the “physical” nature of each pixel, but also in the structure of the image features, more information is needed. In this paper, we address the case of the analysis of urban areas, using panchromatic high-resolution remotely sensed images. In this case, some local geometrical information is clearly required to enable an accurate classification: for instance, pixels belonging to the roof either of small or of large houses will have the same value and a classification based on these values will not be able to distinguish between these two classes (resp. small and large houses). To solve this problem, a

classification method has been proposed in [1] and [2]. This original method is composed of two main steps :

- Feature extraction: It is based on the construction of a derivative morphological profile, which characterizes each pixel both in terms of intensity and in terms of local geometry. This step is detailed in Section II.A. In this paper, we propose to use alternated sequential filters (ASF) for the construction of the morphological profile of each pixel, instead of the classical granulometric approach. This is presented in Section II.B and discussed in Section II.C.

- Classification: This step is based on a neural network. It is briefly presented in Section III.

The results obtained on high resolution IKONOS remote sensing data are presented in Section IV. Figure 1 presents one original panchromatic image from Reykjavik (1m resolution, size 975x639). Six classes are considered: Large buildings, small buildings, streets, open areas, residential laws and shadows. See [2] for more details. For the evaluation, we focused on the robustness against noise provided by the proposed approach. We compare it with the previous method.

II. FEATURE EXTRACTION

A. Granulometry : the classical approach

In [1] & [2], the concepts of a morphological profile and of the derivative of the morphological profile are presented. These concepts are used to create a feature vector for each pixel from one single image. Two profiles are actually constructed:

- One profile is obtained by successively applying morphological opening operators with an increasing size of structuring element (SE). A progressive simplification of the image is obtained by removing at each step the dark features that are smaller than the SE.

- The other profile is obtained by applying morphological closing operators. A progressive simplification of the image is obtained by removing at each step the clear features that are smaller than the SE.

This is very similar to the classical granulometric approach for morphological image analysis. See [3,4] for more information on mathematical morphology; see [5] for an application-oriented book presenting morphological image analysis from the principles to recent developments. See [6] for a recent

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survey paper investigating the use of advanced morphological operators in the general frame of satellite remote sensing.

The derivative for the two obtained profiles is then computed. The maxima of these derivative profiles indicate the local characteristic sizes of the different features of the image. These vectors are then concatenated to build the feature vector on which the classification is performed.

It is important to note that connected operators are used: each opening and closing is followed by a geodesic reconstruction, enabling a perfect preservation of the remaining features edges [7]. No shape noise is introduced. In the following, we also use connected operators.

B. Granulometry using alternated sequential filters

In this paper, we propose the following modification of the

previously described method. Instead of constructing a two

sided morphological profile using the classical granulometric

approaches (resp. with openings and closings), we propose to

construct directly a one sided profile by applying alternately

opening and closing operators with increasing SE sizes. The

results provided by the two methods are different. The

alternated sequential filter (ASF) provides a nice

progressive simplification of the image, but since it does not

separate the processing of the dark features and the clear

features, it better fits our intuitive understanding of the image.

Furthermore, the ASF is known for its robustness against

noise (this will be evaluated in Section IV).

The ASF leads to the construction of the following

morphological profile (MP):

MP0(x) = I(x)

MP1(x) = γs[I(x)]

MP2(x) = ϕs ογs[I(x)] … ➲ …

MP2p-1(x) = γpsοϕ(p-1)sογ(p-1)sο…οϕs ογs[I(x)]

MP2p(x) = ϕpsογpsοϕ(p-1)sογ(p-1)sο…οϕs ογs[I(x)]

Where p is the number of openings applied (there are also p

closings), s is the radius increment of the SE between two

steps, I(x) denotes the original image, γn denotes an opening

by reconstruction with a disk SE of radius n, and ϕn denotes

the closing.

Then, the derivative morphological profile (DMP) can be

constructed for each pixel. This 2p-dimensional vector, which

is used in the decision step to classify each pixel is defined by

DMPk(x) = MPk(x) - MPk-1(x) ; k=1,…,2p.

C. Lost self-duality

In the previous definition of the ASF, an arbitrary choice was made. We decided to start with an opening operator, followed by a closing. The inverse choice (closing first, then opening) was also possible. That choice results in the loss of the self-duality property, which was ensured by the former approach (two sided MP). Consequently, the same operator

applied to one image or its negative does not lead to the same result.

Nevertheless, we can observe that this arbitrary choice is not so significant in most practical cases. The two possibilities (opening and closing, or closing and opening) in general lead to “visually” very similar results. This is not always true and that is depending on what kind of land pattern / satellite data are processed. For example, NIR 20m resolution data can contain some patterns of narrow dark structures (like small water channels) and/or light narrow structures (like roads). Starting with an opening, the roads may be suppressed first, whereas starting with a closing the water channels may disappear first, resulting in a clear visual difference. But the key point is that this may not disturb the classification process. It is important to know for which size of SE one feature has been suppressed, and to know if that was during an opening or a closing: this information will most of the times remain unchanged in any case. Furthermore, this potential problem is more important when the spatial resolution of the dataset is close to the dimension of the structures assumed as relevant (size of detection target). If the resolution is much higher than the minimum target size, we believe that self-duality is not an absolute requirement. Nevertheless, the results can be really different. For instance, imagine that the picture is strongly corrupted and that every second pixel turns black. An opening with a SE of size 3 will provide a completely black picture; all the information is lost during the first processing and no classification is possible. On the contrary, starting with the closing will remove all the black pixels and the rest of the profile will be constructed with no further problem, enabling a correct classification.

To conclude with this point, the main idea is that the arbitrary choice changes the results; that the changes are difficult to estimate a priori since the operators are non linear. In all our experiments, we obtained the same classification performances with very small differences (approx 1% of the average accuracy), but the induced bias can be significant in some specific cases / applications. In these cases, the appropriate choice should be made.

III. CLASSIFICATION STEP

The feature extraction provides for each pixel a vector of

attributes (the DMP). Eventually, the dimension of this vector

can be reduced by selecting the most significant features.

Different strategies are discussed in [2] (picking the largest

indexes in the DMP, use of a decision boundary feature

extraction…). In this paper, we kept the entire DMP. To

classify each pixel using this vector, we used the same neural

vector as in [2] (10 hidden neurons, training sample test ratio

was approximately 1)

IV. RESULTS

In our experiments, we used the following parameters: s=3

and p=8. This is a trade-off to obtain both a feature vector

with a reasonable size (2*p = 16) and an analysis going from

small sizes (3) to rather big ones (p*s=24). The structuring

elements are therefore disks with increasing radius (resp. 3, 6,

9, 12, 15, 18, 21 & 24).

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We present here the results obtained on the original

IKONOS image and test the robustness of the method against

a different kind of noise. Figure 3 presents the results obtained

when Gaussian noise is added. The three curves represent the

average classification accuracy versus the standard deviation

of the corrupted data in the following cases:

- When only the grey-level of the pixels are used: The

performances quickly deteriorate when the noise is added.

- The original method (“morpho classic”) presented in [2]:

The results are excellent when there is no noise but the method

is rather sensitive and the performances also deteriorate when

the noise is added (we rapidly reach the floor value around

35% which is not better than random in this case).

- The proposed method (“morpho ASF”): The results are

worse than the “classic” method when the image is not

corrupted, but the performances decrease much slower when

the noise is added. Similar results are obtained in the case of impulse noise

(see Figure 4). The “morpho ASF” approach is even more robust. For instance, the average accuracy is still over 70% with a strongly corrupted image (standard deviation = 85. The corresponding picture is presented Figure 2).

V. CONCLUSIONS

In this paper, we presented an evolution of the classification

algorithm proposed in [2] for the segmentation of

panchromatic high-resolution remote sensing images from

urban areas. Keeping the same idea of characterizing each

pixel both in terms of intensity and in terms of local geometry,

we proposed to use an ASF instead of the two-sided

morphological profile. Although the new method turned out to

be sub-optimal in the case of noiseless images, an interesting

robustness to noise was achieved. This opens the door to other

applications, like active imagery systems (radar, sonar) where

high-resolution images are acquired but the data are highly

corrupted.

VI. REFERENCES

[1] M. Pesaresi & J.A. Benediktsson – A new approach for the morphological segmentation of high resolution satellite imagery – IEEE Transactions on Geoscience and Remote Sensing, vol. 39 n. 2, pp. 309-320, 2001

[2] J.A. Benediktsson, M. Pesaresi & Kolbein Arnason - Classification and feature extraction for remote sensing images from urban areas based on morphological transformations – to appear in IEEE Transactions on Geoscience and Remote Sensing, Sept. 2003.

[3] J. Serra – Mathematical morphology, Theoretical advances, vol. 2 – Academic press, London, 1988

[4] E. Dougherty – Mathematical morphology in image processing– Marcel Dekker, New York, 1993

[5] P Soille – Morphological image analysis, principles and applications – Springer, Berlin, 1999

[6] P. Soille & M. Pesaresi - Advances in mathematical morphology applied to geoscience and remote sensing - IEEE Transactions on Geoscience and Remote Sensing, vol. 40, no 9, pp2042-2055, 2002

[7] J. Crespo, J. Serra & R. Schafer – Theoretical aspects of morphological filters by reconstruction – Signal Processing, 47, pp. 201-225, 19995

Fig. 1: Original IKONOS panchromatic image (Reykjavik, Iceland)

Fig. 2: Strongly corrupted image (impulse noise, std. dev.=85)

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grey level

morpho classic

morpho ASF

Fig. 3 : Average accuracy vs std. deviation (Gaussian noise)

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grey level

morpho classic

morpho ASF

Fig. 4: Average accuracy vs std. deviation (impulse noise)

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