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The extraction of component line segments and circular arcs from freehand strokes along with their relations is a prerequisite for sketch understanding. Existing approaches usually take three stages to segment a stroke: first identifying segmentation points, then classifying the substroke between each pair of adjacent segmentation points, and, finally, obtaining graphical representations of substrokes by fitting graphical primitives to them. Since a stroke inevitably contains noises, the first stage may produce wrong or inaccurate segmentation points, resulting in the wrong substroke classification in the second stage and inaccurately fitted parameters in the third stage. To overcome the noise sensitivity of the three-stage method, the segmental homogeneity feature is emphasized in this paper. We propose a novel approach, which first extracts graphical primitives from a stroke by a connected segment growing from a seed-segment and then utilizes relationships between the primitives to refine their control parameters. We have conducted experiments using real-life strokes and compared the proposed approach with others. Experimental results demonstrate that the proposed approach is effective and robust.