In an encoder, a high-dynamic range (HDR) image is encoded using a family of local forward reshaping functions selected according to an array of forward mapping indices (FMI) indicating which local forward reshaping function needs to be used for each pixel in the HDR image to generate a reshaped standard dynamic range (SDR) image. A decoder, given the reshaped SDR image, iteratively generates a reconstructed HDR image and estimated reshaped SDR images by adjusting a local FMI array and a local array of backward mapping indices (BMI) until an error metric related to the difference between the local BMI and FMI arrays and the difference between the estimate SDR images and the reshaped SDR image satisfy a convergence criterion. Techniques for generating families of local forward reshaping functions and local backward reshaping functions based on a global forward reshaping function are also presented.