Graph Convergence Through Motion
This research shows that a moving object can be extracted by treating image motion as a connectivity problem on a weighted Region Adjacency Graph. The frame is first divided into homogeneous regions; every region becomes a node and every shared boundary becomes an edge.
The central observation is that the moving object does not have to be fully visible as motion in every single instant. Across the time axis, repeated comparisons accumulate evidence until the true object becomes a stable connected graph component.
Proof that the graph converges
The convergence follows from the difference between persistent object evidence and temporary occlusion evidence. For object edges, high change probability remains stable across multiple comparisons; for occluded edges, the evidence appears only as a temporary peak and then declines. The GCP mapping preserves the first behavior and suppresses the second.
LCPet,t+i = |e|-1Σpxlt,t+i measures boundary change on each graph edge.
LCPet,t+i ≈ high for many iterations, because the object's original boundary keeps producing change evidence.
LCPet,t+k = GM only near a temporary coverage event; therefore its distribution is unstable.
GCPei = μ(LCP) − σ(GM − LCP) rewards persistent evidence and penalizes temporary peaks.
D(∂Obji, ∂Obji−1) → ε, so the connected node set stabilizes into an accurate object representation.