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Segmentation is a widely used operation in very high resolution remote sensing processing such as object based image analysis. Since the available memory resource might be limited, it is often impossible to process a whole satellite image without using piece-wise processing, which in the case of segmentation introduces a huge amount of artifacts. The work presented in this paper introduce a solution to this problem in the case of the Mean-Shift algorithm, which guarantees that piece-wise segmentation results matches exactly those of full image processing at once. First, we define a new property of segmentation algorithms called stability. After proposing a methodology to measure the stability of segmentation algorithms, we demonstrate that among the Mean-Shift, watershed and connected components algorithms, only the latter is stable. Then, we propose a stabilized version of the Mean-Shift algorithm and use it to build a rigorous and exact solution for piece-wise processing of this algorithm. Last, we present some examples demonstrating the usefulness of the proposed method. This method is available in the Orfeo ToolBox free software, and documented in the software guide. [ABSTRACT FROM AUTHOR]