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We propose the first accurate digitization and color reconstruction process for historical lenticular film that is robust to artifacts. Lenticular films emerged in the 1920s and were one of the first technologies that permitted to capture full color information in motion. The technology leverages an RGB filter and cylindrical lenticules embossed on the film surface to encode the color in the horizontal spatial dimension of the image. To project the pictures the encoding process was reversed using an appropriate analog device. In this work, we introduce an automated, fully digital pipeline to process the scan of lenticular films and colorize the image. Our method merges deep learning with a model-based approach in order to maximize the performance while making sure that the reconstructed colored images truthfully match the encoded color information. Our model employs different strategies to achieve an effective color reconstruction, in particular (i) we use data augmentation to create a robust lenticule segmentation network, (ii) we fit the lenticules raster prediction to obtain a precise vectorial lenticule localization, and (iii) we train a colorization network that predicts interpolation coefficients in order to obtain a truthful colorization. We validate the proposed method on a lenticular film dataset and compare it to other approaches. Since no colored groundtruth is available as reference, we conduct a user study to validate our method in a subjective manner. The results of the study show that the proposed method is largely preferred with respect to other existing and baseline methods.