  In this paper, we consider the knot matching problem arising in computational
forestry. The knot matching problem is an important problem that needs to be
solved to advance the state of the art in automatic strength prediction of
lumber. We show that this problem can be formulated as a quadripartite matching
problem and develop a sequential decision model that admits efficient parameter
estimation along with a sequential Monte Carlo sampler on graph matching that
can be utilized for rapid sampling of graph matching. We demonstrate the
effectiveness of our methods on 30 manually annotated boards and present
findings from various simulation studies to provide further evidence supporting
the efficacy of our methods.
