VERY HIGH SPATIAL RESOLUTION IMAGE SEGMENTATION BASED ON THE 
MULTIFRACTAL ANALYSIS 
M. Voorons^ *, Y. Voirin", G. B. Bénié", K. Fung® 
“ Centre d'applications et de recherches en télédétection (CARTEL), 2500 boul. de l'Université Sherbrooke (Québec) 
JIK 2RI - matthieu.voorons@USherbrooke.ca 
? Centre Canadien de télédétection, Division Acquisition des données, 588 rue Booth Ottawa (Ontario) K1A 0Y7, 
ko.fung@cers.nrcan.gc.ca 
KEY WORDS: Remote Sensing, Vision, Analysis, Algorithms, Texture Segmentation, High Resolution, Multifractal, CDROM 
ABSTRACT: 
The availability of very high spatial resolution images in remote sensing brings the texture segmentation of images to a higher level 
of complexity. Such images have so many details that the classical segmentation algorithms fail to achieve good results. In the case 
of IKONOS images of forest areas, a texture can be so different within a same class that it becomes very difficult even for a human 
to segment or interpret those images. The study of the high frequency content of the data seems to be a good way to study those 
images. We work on a new method which uses the singularity information to achieve the segmentation. It is based on the 
computation of the Hólder regularity exponent at each point in the image. From this parameter we can compute the local Legendre 
or the large deviation multifractal spectrum which gives information about the geometric distribution of the singularities in the 
image. So we use global and local descriptors of the regularity of the signal as input parameters to a k-means algorithm. The whole 
algorithm is described and applied to IKONOS images as well as to an image made of brodatz textures. The segmentation results are 
compared to those obtained from the laws filters and the co-occurrence parameters techniques. The proposed method gives better 
results and is even able to segment the image in tree density classes. 
1. INTRODUCTION have any a priori information about the nature of the grey level 
distribution of those objects. Pentland, (Pentland, 1984), 
Very high spatial resolution images provide a huge amount of showed that the fractal dimension is a good tool to study natural 
details and information. Thus, it is possible to extract new scenes, but this kind of analysis reach its limits when the image 
thematic classes and to detect smaller objects. But all those is strongly irregular. On the opposite, the multifractal analysis 
advantages are strongly tied to a major drawback from an image is the perfect tool to analyze signals having a highly varying 
processing point of view. The processing of such images regularity from point to point. 
becomes very tricky; the local variability of the grey level 
values and the large number of data is a limiting factor for most It is to circumvent all these problems and to bring a new 
of the classical analysis tools. Even the visual interpretation is approach to the segmentation of remote sensing images that we 
not obvious and needs experience to recognize each region. propose a method based on the analysis of the fractals 
Therefore, new segmentation algorithms have to be created in components of the image. No a priori knowledge of the image 
order to achieve good classification results with high spatial is required and it enables to study simultaneously the local and 
resolution images. Classical segmentation tools fail to give global regularity of a signal by the means of the Holder 
homogeneous segments and usually give very sparse results exponent and the multifractal spectrum. The singularities often 
where the classes are not compact. To overcome those issues, it carry most of the information contained in a signal. It is 
seems appropriate to use a textural analysis approach. Thus, for generally possible, for a human being, to determine the nature 
each pixel, we study the neighbourhood and not only the grey of an object only from its boundaries and its texture. Many 
level value. works are dedicated to the analysis of the "high frequencies" 
components of an image. Edge density, Zero crossing analysis 
Image segmentation based on texture is a complex problem. ^ and every method based on the gradient of an image are not 
Many theories were developed but their all result in partial ^ efficient to characterize textures sufficiently well to give 
solution to the problem. None can fully characterize all the kind ^ satisfactory segmentation results for this type of image. They do 
of textures. Even the definition of a texture is not clearly ^ not take into account the nature of the singularities of the signal 
defined. Depending on the field of application and the nature of nor even their spatial distribution, while the multifractal 
the image, the definition of a texture can be very different. Co- analysis does. 
occurrence matrices (Haralick e/ al, 1973), Markov random 
fields (Chellappa and Chatterjee, 1985), Gabor filters (Turner, ^ In a first section we will recall the basics of the multifractal 
1986), the fractal analysis (Kaplan, 1999), etc. are tools which analysis, then we will describe the proposed segmentation 
are not able to analyze all the textures. In the particular case of method and finally, before concluding, we will comment and 
very high spatial resolution images, the high variability of the expose some results which are compared to classical 
grey level of each thematic objects prevent from using the segmentation results. 
previously quoted analysis methods. Furthermore, we do not 
  
* Corresponding author. 
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