In this paper, the gauge structure of non-Abelian Chern–Simons model is investigated. Non-Abelian Chern–Simons model, unlike first class constraints systems is not a gauge theory, primarily due to the appearance of two second class constraints in its algebra. These two second class constraints were converted into first ones using gauge unfixing formalism. The model Lagrangian and Hamiltonian were obtained, aiming to satisfy first class algebra and hence making it into a fully gauge theory. Partition function of the model was finally evaluated and presented here.

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A key step in understanding animal behaviour relies in the ability to quantify poses and movements. Methods to track body landmarks in 2D have made great progress over the last few years but accurate 3D reconstruction of freely moving animals still represents a challenge. To address this challenge here we develop the 3D-UPPER algorithm, which is fully automated, requires no a priori knowledge of the properties of the body and can also be applied to 2D data. We find that 3D-UPPER reduces by $$>10$$ > 10 fold the error in 3D reconstruction of mouse body during freely moving behaviour compared with the traditional triangulation of 2D data. To achieve that, 3D-UPPER performs an unsupervised estimation of a Statistical Shape Model (SSM) and uses this model to constrain the viable 3D coordinates. We show, by using simulated data, that our SSM estimator is robust even in datasets containing up to 50% of poses with outliers and/or missing data. In simulated and real data SSM estimation converges rapidly, capturing behaviourally relevant changes in body shape associated with exploratory behaviours (e.g. with rearing and changes in body orientation). Altogether 3D-UPPER represents a simple tool to minimise errors in 3D reconstruction while capturing meaningful behavioural parameters.