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We propose a novel method, the adaptive local window, for improving level set segmentation technique. The window is estimated separately for each contour point, over iterations of the segmentation process, and for each individual object. Our method considers the object scale, the spatial texture, and changes of the energy functional over iterations. Global and local statistics are considered by calculating several gray level co-occurrence matrices. We demonstrate the capabilities of the method in the domain of medical imaging for segmenting 233 images with liver lesions. To illustrate the strength of our method, those images were obtained by either Computed Tomography or Magnetic Resonance Imaging. Moreover, we analyzed images using three different energy models. We compare our method to a global level set segmentation and to local framework that uses predefined fixed-size square windows. The results indicate that our proposed method outperforms the other methods in terms of agreement with the manual marking and dependence on contour initialization or the energy model used. In case of complex lesions, such as low contrast lesions, heterogeneous lesions, or lesions with a noisy background, our method shows significantly better segmentation with an improvement of 0.25+- 0.13 in Dice similarity coefficient, compared with state of the art fixed-size local windows (Wilcoxon, p < 0.001)., Comment: 24 pages, 11 figures, 3 tables