## 1 Introduction
For instance, CellCognition aims at annotating complex cellular dynamics in live-cell microscopic movies [19] by combining Support Vector Machines with hidden Markov models to evaluate the progression by using morphologically distinct biological states. More recently, it has been shown that methods based on Deep Convolutional Neural Networks (DCNNs) [20; 21] can successfully address detectionand segmentation problems otherwise difficult to solve by exploiting traditional image processing methods [22]. Further, an ensemble of DCNNs defined to segment cell images was presented in [23], where a gating network automatically divides the input image into several sub-problems and assigns them to specialized networks, allowing for a more efficient learning with respect to a single DCNN. With regard to the most popular architectures for object detection and instance segmentation, such as Faster Region-CNN (R-CNN) [24] and You Only Look Once (YOLO) [25], these approaches require a considerable amount of labeled images and yield only a coarse-grained segmentation in cell imaging [26] and medical image analysis [27]. This does not ensure a precise separation between adjacent cells. Even though transfer learning (i.e., the use of pre-trained CNNs on large-scale datasets of natural images) could be applied, hundreds of accurately annotated input samples should be available [28]. Therefore, parameter-efficient architectures, including simple trainable activation functions [29] or mixed-scale dense CNNs [30], might be beneficial to deal with the paucity of manually labeled and validated datasets. Alternatively, also data augmentation techniques based on Generative Adversarial Networks (GANs) [31; 32] or interactive solutions [33], require time-consuming annotation by experts. Traditional image segmentation approaches often require experiment-specific parameter tuning, while DCNNs require large amounts of high-quality annotated samples or ground truth. The ground truth, representing the extent to which an object is actually present, is usually delineated by a domain expert, via a tedious, cumbersome and time-consuming visual and manual approach. The annotated samples for one dataset may not be useful for another dataset, so new ground truth generation may be needed for a new dataset, thus limiting the effectiveness of DCNNs. The authors of [22] proposed an approach for automatically creating high-quality experiment-specific ground truth for segmentation of bright-field images of cultured cells based on end-point fluorescent staining, then exploited to train a DCNN [34]. In general, applying DCNNs to microscopy images is still challenging due to the lack of large datasets labeled at the single cell level [34]; moreover, [PERSON] et al. [16] showed that watershed-based methods can achieve performance comparable to DCNN-based approaches. Thus, unsupervised techniques that do not require a training phase (i.e., data fitting or modeling) represent valuable solutions in this practical context [19; 35]. In this work, we present a novel method named Automated Cell Detection and Counting (ACDC), designed for time-lapse microscopy activity detection of fluorescent-labeled cell nuclei. ACDC is capable of overcoming the practical limitations of the literature approaches, mainly related to the training phases or time constraints, making it a feasible solution for the laboratory practice. Recent developments of automated microscopy imaging systems has allowed for the generation of very large datasets [36], which are typically \(\sim\)3 TB, including over 300,000 images, for each experiment. Each dataset produces novel features due to differences in the cells used, their fluorescence label intensity, and their specific responses to anti-cancer treatment conditions. This variation poses challenges to using deep learning-based segmentation [37] that is trained without including the new data: for any comparisons across datasets, the segmentation would need to be repeated/updated to include every new dataset and re-applied to all previous data.