Convert ASCII art numbers to integers
Jelly, 35 33 34 bytes

Ỵe€€⁾ .¬ZḄṣ0§ḟ0%29“h½sØ?X’ḃ26¤iⱮ’Ḍ


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When I started writing this, The question didn’t specify that the width of digits was fixed, so my answer doesn’t make that assumption. 

Input is now a string (which costs a byte over having a list of strings). Output is an integer. 

Explanation:

Ỵ                         | split at new lines
e€€⁾ .                    | For each character check whether it is a
                          | full stop/space or something else
      ¬                   | invert this
       Z                  | transpose
        Ḅ                 | convert from binary to decimal (one number per column of input)
         ṣ0               | split at zeroes (blank columns)
§                         | take the sum of each digit
 ḟ0                       | filter out remaining blank columns
   %29                    | take this number mod 29
      “h½sØ?X’ḃ26¤iⱮ      | look each digit up in a compressed list
                          | [18, 23, 6, 5, 1, 19, 13, 21, 8, 25]
                    ’     | subtract one
                     Ḍ    | convert to decimal