In this paper, we present a general convex formulation for global histogram-based binary segmentation. The model relies on a data term measuring the histograms of the regions to segment w.r.t. reference histograms as well as TV regularization allowing the penalization of the length of the interface between the two regions. The framework is based on some $l^1$ data term, and the obtained functional is minimized with an algorithm adapted to non smooth optimization. We present the functional and the related numerical algorithm and we then discuss the incorporation of color histograms, cumulative histograms or structure tensor histograms. Experiments show the interest of the method for a large range of data including both gray-scale and color images. Comparisons with a local approach based on the Potts model or with a recent one based on Wasserstein distance also show the interest of our method.