We expected that the minority-phase domains would preferably accumulate and fuse at the free regions to decrease line tension. Membrane deformation such as budding, which also contributes in the line tension decrease, can also favorably occur in these wall-free, unconstrained regions. Conversely, at the confined region, we expected a less favorable fusion of the domains due to the imposed two-dimensional flat geometry and hindrance of domain deformation due to the close contact of the membrane with the rigid channel walls.