A fine segmentation algorithm is proposed for extracting objects in an image, which have both weak boundaries and highly non-convex shapes. The image has simple background colors or simple object colors. Two concepts, geometric attraction-driven flow (GADF) and edge-regions are combined to detect boundaries of objects in a sub-pixel resolution. The main strategy to segment the boundaries is to construct initial curves close to objects by using edge-regions and then to make a curve evolution in GADF. Since the initial curves are close to objects regardless of shapes, highly non-convex shapes are easily detected and dependence on initial curves in boundary-based segmentation algorithms is naturally removed. Weak boundaries are also detected because the orientation of GADF is obtained regardless of the strength of boundaries. For a fine segmentation, we additionally propose a local region competition algorithm to detect perceptible boundaries which are used for the extraction of objects without visual loss of detailed shapes. We have successfully accomplished the fine segmentation of objects from images taken in the studio and aphids from images of soybean leaves.