We consider curve evolution based on comparing distributions of features, and its applications for scene segmentation. In the first part, we promote using cross-bin metrics such as the Earth mover's distance (EMD), instead of standard bin-wise metrics as the Bhattacharyya or Kullback-Leibler metrics. To derive flow equations for minimizing functionals involving the EMD, we employ a tractable expression for calculating EMD between one-dimensional distributions. We then apply the derived flows to various examples of single image segmentation, and to scene analysis using video data. In the latter, we consider the problem of segmenting a scene to spatial regions in which different activities occur. We use a nonparametric local representation of the regions by considering multiple one-dimensional histograms of normalized spatiotemporal derivatives. We then obtain semisupervised segmentation of regions using the flows derived in the first part of the paper. Our results are demonstrated on challenging surveillance scenes, and compare favorably with state-of-the-art results using parametric representations by dynamic systems or mixtures of them.