This paper presents a new deep regression model, which we call DeepDistance, for cell detection in images acquired with inverted microscopy. This model considers cell detection as a task of finding most probable locations that suggest cell centers in an image. It represents this main task with a regression task of learning an inner distance metric. However, different than the previously reported regression based methods, the DeepDistance model proposes to approach its learning as a multi-task regression problem where multiple tasks are learned by using shared feature representations. To this end, it defines a secondary metric, normalized outer distance, to represent a different aspect of the problem and proposes to define its learning as complementary to the main cell detection task. In order to learn these two complementary tasks more effectively, the DeepDistance model designs a fully convolutional network (FCN) with a shared encoder path and end-to-end trains this FCN to concurrently learn the tasks in parallel. For further performance improvement on the main task, this paper also presents an extended version of the DeepDistance model that includes an auxiliary classification task and learns it in parallel to the two regression tasks by also sharing feature representations with them. DeepDistance uses the inner distances estimated by these FCNs in a detection algorithm to locate individual cells in a given image. In addition to this detection algorithm, this paper also suggests a cell segmentation algorithm that employs the estimated maps to find cell boundaries. Our experiments on three different human cell lines reveal that the proposed multi-task learning models, the DeepDistance model and its extended version, successfully identify the locations of cell as well as delineate their boundaries, even for the cell line that was not used in training, and improve the results of its counterparts. (C) 2020 Elsevier B.V. All rights reserved.