Two Monte Carlo-based simulators for imaging-system modeling and projection simulation of flat-panel X-ray source

The advantages of a flat-panel X-ray source(FPXS)make it a promising candidate for imaging applications.Accurate imaging-system modeling and projection simulation are critical for analyzing imaging performance and resolving overlapping projection issues in FPXS.The conventional analytical ray-tracing approach is limited by the number of patterns and is not applicable to FPXS-projection calculations.However,the computation time of Monte Carlo(MC)simulation is independent of the size of the patterned arrays in FPXS.This study proposes two high-efficiency MC projection simulators for FPXS:a graphics processing unit(GPU)-based phase-space sampling MC(gPSMC)simulator and GPU-based fluence sampling MC(gFSMC)simulator.The two simulators comprise three components:imaging-system modeling,photon initialization,and physical-interaction simulations in the phantom.Imaging-system modeling was performed by modeling the FPXS,imaging geometry,and detector.The gPSMC simulator samples the initial photons from the phase space,whereas the gFSMC simulator performs photon initialization from the calculated energy spectrum and fluence map.The entire process of photon interaction with the geometry and arrival at the detector was simulated in parallel using multiple GPU kernels,and projections based on the two simulators were calculated.The accuracies of the two simulators were evaluated by comparing them with the conventional analytical ray-tracing approach and acquired projections,and the efficiencies were evaluated by comparing the computation time.The results of simulated and realistic experiments illustrate the accuracy and efficiency of the proposed gPSMC and gFSMC simulators in the projection calculation of various phantoms.

Conflict-free Incidence Coloring of Outer-1-planar Graphs

An incidence of a graph G is a vertex-edge pair(v,e)such that v is incidence with e.A conflict-free incidence coloring of a graph is a coloring of the incidences in such a way that two incidences(u,e)and(v,f)get distinct colors if and only if they conflict each other,i.e.,(i)u=v,(ii)uv is e or f,or(iii)there is a vertex w such that uw=e and vw=f.The minimum number of colors used among all conflict-free incidence colorings of a graph is the conflict-free incidence chromatic number.A graph is outer-1-planar if it can be drawn in the plane so that vertices are on the outer-boundary and each edge is crossed at most once.In this paper,we show that the conflict-free incidence chromatic number of an outer-1-planar graph with maximum degree△is either 2△or 2△+1 unless the graph is a cycle on three vertices,and moreover,all outer-1-planar graphs with conflict-free incidence chromatic number 2△or 2△+1 are completely characterized.An efficient algorithm for constructing an optimal conflict-free incidence coloring of a connected outer-1-planar graph is given.

Incidence Coloring of Outer-1-planar Graphs

A graph is outer-1-planar if it can be drawn in the plane so that all vertices lie on the outer-face and each edge crosses at most one another edge.It is known that every outer-1-planar graph is a planar partial3-tree.In this paper,we conjecture that every planar graph G has a proper incidence(Δ(G)+2)-coloring and confirm it for outer-1-planar graphs with maximum degree at least 8 or with girth at least 4.Specifically,we prove that every outer-1-planar graph G has an incidence(Δ(G)+3,2)-coloring,and every outer-1-planar graph G with maximum degree at least 8 or with girth at least 4 has an incidence(Δ(G)+2,2)-coloring.