Long-Term Tracking of Group-Housed Livestock Using Keypoint Detection and MAP Estimation for Individual Animal Identification

Tracking individual animals in a group setting is a exigent task for computer vision and animal science researchers. When the objective is months of uninterrupted tracking and the targeted animals lack discernible differences in their physical characteristics, this task introduces significant challenges. To address these challenges, a probabilistic tracking-by-detection method is proposed. The tracking method uses, as input, visible keypoints of individual animals provided by a fully-convolutional detector. Individual animals are also equipped with ear tags that are used by a classification network to assign unique identification to instances. The fixed cardinality of the targets is leveraged to create a continuous set of tracks and the forward-backward algorithm is used to assign ear-tag identification probabilities to each detected instance. Tracking achieves real-time performance on consumer-grade hardware, in part because it does not rely on complex, costly, graph-based optimizations. A publicly available, human-annotated dataset is introduced to evaluate tracking performance. This dataset contains 15 half-hour long videos of pigs with various ages/sizes, facility environments, and activity levels. Results demonstrate that the proposed method achieves an average precision and recall greater than 95% across the entire dataset. Analysis of the error events reveals environmental conditions and social interactions that are most likely to cause errors in real-world deployments.

Sets with Few Differences in Abelian Groups

Let $(G, +)$ be an abelian group. In 2004, Eliahou and Kervaire found an explicit formula for the smallest possible cardinality of the sumset $A+A$, where $A \subseteq G$ has fixed cardinality $r$. We consider instead the smallest possible cardinality of the difference set $A-A$, which is always greater than or equal to the smallest possible cardinality of $A+A$ and can be strictly greater. We conjecture a formula for this quantity and prove the conjecture in the case that $G$ is an elementary abelian $p$-group. This resolves a conjecture of Bajnok and Matzke on signed sumsets.