A vine pruning robot uses stereo cameras to build a 3D model of vines. The robot's 3D reconstruction scheme requires the 2D structure of the vine to be extracted from each image. This paper describes how the 2D structure is extracted. We propose an image grammar-based model for how a vine generates an image. We extract cane edges from each image, then apply a bottom-up parse of the cane edges to find a vine structure explaining the image. The method is efficient and accurate, and the 2D structures are complete enough that complete 3D models of vines can be reconstructed. The scheme demonstrates the power of the image grammar model for solving complex image interpretation problems.