## 1 Introduction and Motivation  
A human watching a video of closely-packed cells can usually identify each individual and reconstruct events far better than existing algorithms, which is why armies of biology students spend an inordinate amount of time tagging individual cells one-at-a-time, frame-by-frame in videos of cell cultures. Though expensive, this method is used because humans are good at interpreting what is happening in a scene based upon our common-sense knowledge of what is physically possible; we effectively _simulate_ the scene \"in our heads\", allowing us to readily distinguish signal from noise and eliminate interpretations that are physically implausible. Accordingly, in this paper we introduce _Cell Universe_, a simple proof-of-concept algorithm that builds a physics-based simulation model (the \"universe\") of all the members of a colony of cells; like a human, our model is based on simple common-sense rules of what cells can do across the short interval of time between frames: they can move a bit, rotate a bit, grow a bit, and occasionally split into two daughter cells. They cannot disappear into thin air, appear out of nowhere, or jump great distances in a short amount of time. These simple physical rules tightly constrain what is possible and what is not, _greatly_ increasing the robustness of _Cell Universe_'s output compared to existing algorithms. We represent a single bacterium as a rectangle with rounded ends; each cell thus has a length, width (with the rounded ends being semi-circles with a diameter equal to the width), and an orientation; if sufficiently long, it is allowed one \"bend\" near the middle which requires two rectangles with joined ends. An example synthetic image of such bacteria is depicted in the top image of Figure 1.  
We initialize the simulation using positions and orientations of cells in the first video frame; at each frame \(i\) we duplicate and perturb the simulated universes into an ensemble of nearly-identical universes, each member of which is advanced stochastically via simple physics-based rules to plausible futures at frame \(i+1\). At frame \(i+1\), a synthetic image is generated depicting the state of each simulated universe in the ensemble. These synthetic images are each compared to the real video frame \(i+1\) using an objective function based on image subtraction (cf. Figure 1). The top few universes ranked by this objective are  
Figure 1: **Fitting a synthetic image to the corresponding video frame. ** We use Frame 26 (cf. Figure 2). (**Top**) synthetic image derived from the positions, sizes, and orientations of the bacteria in one of the many stochastically simulated “universes”at the time of Frame 26, drawn as a binary image of equal dimensions to the real video image. (**Second image**) the “clean” image of Figure 2. (**Residual image**) the pixel-by-pixel difference, in absolute value, between the real and synthetic images; black is zero difference. (**Bottom**) the outline, drawn in red, of the synthetic bacteria of the top image, overlaid on top of the “clean” video frame of Figure 2.  
kept, while the rest are discarded. This process of fitting a simulation to reality is called \"data assimilation\". Then we iterate: these top-scoring universes are duplicated, perturbed, and propagated forward to frame \(i+2\). Currently our \"laws of cell physics\" allow only Brownian motion, small stochastic rotations, slow linear growth, and possible cell division; the laws are easily adaptable to other situations. As [PERSON]'s quote above alludes to, our program _creates_ universes that follow simple physics-based \"laws\"; those simulated universes that are observationally compatible with the real one essentially _understand_ what is happening in the real Universe to a level of detail far beyond current methods: simulation output variables can be interpreted as _measurements_ of the current and historical position, orientation, size, and family tree of _every_ cell in the simulation.