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I need to take table data out of a handwritten paper form and convert it to digital data in a useful format like CSV. My current thinking is to create an image file of the form and run it through an OCR program. Bonus points if it's free and online or automatible with, say, an API interface, ideally.
Is there anything like this? Maybe an open source project?
Handwriting recognition is a hard problem as a general issue. However you mention forms, in this case assisted recognition may be possible if the form consists of character fields in groups with limited possible valid inputs. By assisted I mean every time it is unsure it pops up a image of that section for manual input
You can develop such a system using OpenCV as demonstrated in the pyImageSearch blog possibly by training a expert system. You are unlikely to find one that is already written.
I would suggest looking at Microsoft's Computer Vision API, specifically the handwritten OCR part. Their docs currently state: "Note: this technology is currently in preview and is only available for English text."
I got impressive results when I tried it out. You can road-test it without installing anything, just upload a sample image at https://azure.microsoft.com/en-us/services/cognitive-services/computer-vision/ (scroll down the page to find "Preview: Read handwritten text from images")
Example code shows how to use this from python and other languages:
