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

arXiv:2408.01859v2 Announce Type: replace Abstract: 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^o for M ll 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^o 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 lambda_{min}(B) of a coefficient matrix B = iag{h} + mu L, 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 lambda^-_{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.

Source: arXiv cs.CV | 2026-06-29