Image-based plant phenotyping is a growing application domain of computer vision in agriculture. A key task is the segmentation of all individual leaves in images. Here we focus on the most common rosette model plants Arabidopsis and young tobacco. Although leaves do share appearance and shape characteristics, the presence of occlusions and variability in leaf shape and pose, as well as imaging conditions, render this problem challenging. The aim of this paper is to compare several leaf segmentation solutions on a unique and first of its kind dataset containing images from typical phenotyping experiments. In particular, we report and discuss methods and findings of a collection of submissions for the first Leaf Segmentation Challenge (LSC) of the Computer Vision Problems in Plant Phenotyping (CVPPP) workshop in 2014. Four methods are presented: three segment leaves via processing the distance transform in an unsupervised fashion, and the other via optimal template selection and Chamfer matching. Overall, we find that although separating plant from background can be achieved with satisfactory accuracy (>90% Dice score), individual leaf segmentation and counting remain challenging when leaves overlap. Besides, accuracy is lower for younger leaves. We find also that variability in datasets does affect outcomes. Our findings motivate further investigations and development of specialized algorithms for this particular application, and that challenges of this form are ideally suited for advancing the state of the art. Data are publicly available (http://www.plantphenotyping.org/CVPPP2014-dataset) to support future challenges beyond segmentation within this application domain.