Topological line-region relations are generally defined by DE-9DIM in GIS. But some distinguish topological line-region relations cannot be identified in DE-9DIM. In the paper, Segmental operator model is introduced to solve this problem. Let a region A filter a curve L and produce a set of sub curves within the exterior, the interior or the borders of A. The topological relations between a sub curve and A can be mapped into eight categories: across, cutsinto, along, ringof, around, sticksto, inside and disjoint. Segmental operator model is based on counting the number of sub curves that belongs to each of the eight categories. Any topological relations defined in DE-9DIM can be expressed in segmental operator model when knowing whether A has holes or not. In segmental operator model, L is atomic to A when only a single sub curve is produced, simplex to A when all sub curves belongs to the same category, or L is complex to A.