Graph Unfolding and Sampling for Transitory Video Keyframe Selection via Gershgorin Disc Alignment

User-generated videos (UGVs) uploaded from mobile phones to social media sites like YouTube and TikTok are short and non-repetitive. We summarize a transitory UGV into several keyframes in linear-time via fast graph sampling based on Gershgorin disc alignment (GDA). Specifically, we first model a sequence of N frames in a UGV as an M-hop path graph G° for M ≪ N, where the similarity between two frames within M time instants is encoded as a positive edge based on feature similarity. Towards efficient sampling, we then "unfold" G° to a 1-hop path graph G, specified by a generalized graph Laplacian matrix L, via one of two graph unfolding procedures with provable performance bounds. We show that maximizing the smallest eigenvalue λ_min(B) of a coefficient matrix B = diag(h) + μL, where h is the binary keyframe selection vector, is equivalent to minimizing a worst-case signal reconstruction error. We maximize instead the Gershgorin circle theorem (GCT) lower bound λ- _min(B) by choosing h via a new fast graph sampling algorithm that iteratively aligns left-ends of Gershgorin discs for all graph nodes (frames). Experiments on multiple short video datasets show that our algorithm achieves comparable or better keyframe selection performance compared to state-of-the-art methods, at a substantially reduced complexity.