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Interests in synthetic aperture radar (SAR) data analysis is driven by the constantly increased spatial resolutions of the acquired images, where the geometries of scene objects can be better defined than in lower resolution data. This paper addresses the problem of the built-up areas extraction in high-resolution (HR) SAR images, which can provide a wealth of information to characterize urban environments. Strong backscattering behavior is one of the distinct characteristics of built-up areas in a SAR image. However, in practical applications, only a small portion of pixels characterizing the built-up areas appears bright. Thus, specific texture measures should be considered for identifying these areas. This paper presents a novel texture measure by combining the proposed labeled co-occurrence matrix technique with the specific spatial variability structure of the considered land-cover type in the fuzzy set theory. The spatial variability is analyzed by means of variogram, which reflects the spatial correlation or non-similarity associated with a particular terrain surface. The derived parameters from the variograms are used to establish fuzzy functions to characterize the built-up class and non built-up class, separately. The proposed technique was tested on TerraSAR-X images acquired of Nanjing (China) and Barcelona (Spain), and on a COSMO-SkyMed image acquired of Hangzhou (China). The obtained classification accuracies point out the effectiveness of the proposed technique in identifying and detecting built-up areas. [ABSTRACT FROM AUTHOR]