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Cataloged from PDF version of article. Thesis (Master's): Bilkent University, Department of Computer Engineering, İhsan Doğramacı Bilkent University, 2023. Includes bibliographical references (leaves 51-57). Multi-task learning proved to be an effective strategy to increase the performance of a dense prediction network on a segmentation task, by defining auxiliary tasks to reflect different aspects of the problem and concurrently learning them with the main task of segmentation. Up to now, previous studies defined their auxiliary tasks in the Euclidean space. However, for some segmentation tasks, the complexity and high variation in the texture of a region of interest may not follow the smoothness constraint in the Euclidean geometry. This thesis addresses this issue by introducing a new multi-task network, MTFD-Net, which utilizes the fractal geometry to quantify texture complexity through self-similar patterns in an image. To this end, we propose to transform an image into a map of fractal dimensions and define its learning as an auxiliary task, which will provide auxiliary supervision to the main segmentation task, towards betterment of left atrium segmentation in computed tomography images. To the best of our knowledge, this is the first proposal of a dense prediction network that employs the fractal geometry to define an auxiliary task and learns it in parallel to the segmentation task in a multi-task learning framework. Our experiments revealed that the proposed MTFD-Net model led to more accurate left atrium segmentation, compared to its counterparts. by Aziza Saber Jabdaragh M.S.