In this paper we present a method to estimate the radiance map and camera response function for high dynamic range (HDR) imaging which is devoid of free parameters and can reliably recover HDR images with as few as two low-dynamic range (LDR) views acquired at different exposures. To do this, we employ a L1 cost function which lends itself to the use of a Weiszfeld optimisation scheme. We illustrate the utility of the method for computing high-dynamic range images from low-dynamic range imagery. In our experiments, we compare our results with those delivered by alternatives elsewhere in the literature and show that our method can outperform the alternatives with as few as two LDR images. We also apply our method to panorama generation.