## 1 Introduction  
Cell spheroids as a 3D in vitro model are highly important for primary as well as translational research and considered the gold standard, especially for chondrogenic differentiation [1, 2]. One major drawback of standard spheroid formation methods is the time and costs required for the procedure steps, as well as the reagents required to generate and cultivate the spheroids and generate the final readouts. Furthermore, the cultivation time for chondrogenicity is quite long, but there is no possibility of generating early readouts before the endpoint analysis. To address this problem, a new technology (SpheroWell) has been developed that enables the creation of multiple spheroids from cell monolayers by self-assembling within a single vessel by segregating the growth surface of a standard cell culture surface such as Petri dishes [3]. Additionally, media consumption is reduced through the self-assembly of cell monolayers.  
The growth surface is segregated into single compartments by a CNC-guided CO\({}_{2}\) laser. The engravings produce a grid-like structure of repeating equidistant crossed lines spanning a grid containing multiple compartments. The engraved surface possesses anti-adhesive properties to prohibit the compartments' attachment, allowing self-assembly. Since the culture surface is flat standard culture plastic and not curved or intransparent as in many spheroid systems, it is possible to monitor the assembly of single spheroids over time.  
With (microscopy) imaging, the resulting spheroids and formation behavior can be assessed to identify the effect of treatments like anti-inflammatory compounds. Systematic quantitative assessment of spheroid formation stages can be highly tedious and time-consuming due to large amounts of spheroids over large numbers of images. An automated approach is crucial to extracting knowledge about the formation stage and important metrics efficiently during these experiments.  
Macroscopic images of Petri dish plates that were seeded with adipose-derived stem-cells were used to monitor the spheroid formation process over time. The images were taken using a digital of the shelf camera (Olympus OM-D E-M1).  
The spheroid formation process can be separated into multiple states, which is significant, as this differentiation facilitates the possibility of detecting treatment effects in early-stage readouts compared with only identifying fully formed spheroids. The three different states of spheroid formation are referred to and described as follows [3]:  
1. A monolayer is described as a compartment with a fully attached cell layer filling 100% of the compartment.
2. The stage of formation (aggregation) is described by compartments with cells in the interim state between fully attached (monolayer) and fully formed (spheroid). The aggregation is described as a compartment where >50% of the cell layer remains attached. The formation of the late stage is described as a compartment where <50% of the cell layer remains attached but is not yet fully developed (not circle-shaped).
3. Fully formed is described as a circle-shaped spheroid. Due to detachment, spheroids can also move to other compartments, and two or more spheroids can appear in one compartment.  
Our workflow combines state-of-the-art methods based on image processing and artificial neural networks with a reliable and adaptive extraction of the grid structure in SpheroWell Petri dishes through an evolution strategy. Combining these methods provides an improved and automatic methodology for quantifying the spheroid stages in the compartments of the Petri dish images. As described in the methods section, several steps are necessary to enable automatic information extraction and subsequent quantification. These include segmenting and classifying a cell compartment's content to extract one of the three classes mentioned above. Furthermore, evolution-based grid extraction reduces segmentation errors, improving the resulting accuracy of the segmentation and classification results.