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I have a large dataset of skin images, each one associated with a hydration value (percentage).

Now I'm looking into predicting the hydration value from an image. My thinking: train a CNN on the dataset and evaluate the model with a mean square error regression.

First, does this sound like a sensible way to try this?

Second, I'd like to run the model on mobile. Can you recommend any examples with Caffe2 (or alternatively TensorFlow) or diagrams that might explain a similar task?

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Your initial idea seems about right. Before creating your own classifier you might want to try transfer learning, using some pretrained network like VGG16 that is incorporated in most of machine learning frameworks.

As to inference on mobile devices, TensorFlow offers some tutorials in this subject: https://www.tensorflow.org/mobile/tflite/

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