Convert ASCII art numbers to integers

Question

Inspired by this game

Challenge:

Given an ASCII art string representing a number, output that number.
Example:

Input:

  &&&&      #####    .====..    .&&&
 $$$$$.    %%   %%   %    % .   +. .
   @@@  .      @@ .  = .  =   . ????
   +++.    &&   &&.  %    %     =   =
   $$$    . @@@@@    #    #  .  ===.
 .$$$$$              .????.

Output: 1306

Input:

  ====     .$$..      &&&&&&.    .@@@@    ?????
 +++++     &. &           $$    %%   %%  &&   &&
   $$$     .==.          @@ .   @@   @@ .    ??
.  ### .   @  @  .      ==     $$$$$$$$  ??. .??
. .@@@.    .%%.        ==           .$$   &&&&&  .
  $$$$$. .            .%        .    @@ .

Output: 18743

Periods are interference, you can ignore them
The complete list of numbers:

 &&&& 
%    %
=    =
%    %
#    #
 ????

 &&&&
$$$$$
  @@@
  +++
  $$$
 $$$$$


 #####
++   ++
 #  ##
   @@
  @@    
???????


 #####
%%   %%
    @@
&&   &&
 @@@@@  


   @@@@
 %%   %%
 @@   @@
$$$$$$$$
      $$
      @@ 


###### 
$  
#### 
    + 
    ? 
$$$$$ 


 &&&
+ 
????
=   =
===

&&&&&&
    $$
   @@
  ==
 ==
 %

 $$
&  &
 ==
@  @
 %%


 &&&&
@    @
 &&&&
    $
    &
  + 

Rules:

• Your input is a string unless your language doesn't have a string type.
• The input is guaranteed to be exactly 6 characters "high." Numbers such as 8 and 3 have a whitespace buffer UNDER the number.
• If you write a function, it MUST return a numerical type.
• The ASCII art can be composed of ANY printable characters in no particular order (remember, you can ignore periods).
  
• No standard loopholes.
  
• Your program must handle any arbitrary ASCII number of reasonable length (as long as the result fits within a 32-bit signed integer).
  
• Input is guaranteed valid, undefined behavior is allowed with bad input.
  
• This is code-golf, shortest program wins.
  
  More tests:

  $$$$     ######     @@@@  . .  .%%%%    #####
 #####     $ .       =====..  . ##   ##  ++   ++
   +++     ####.       +++.     ==   ==   #  ##
   ===     .   +       ###  .  ========.    @@
  .&&&    .  . ?   . . @@@           ##    @@    .
  %%%%%    $$$$$      #####          @@  ???????

> 15142

 .&&&&.    ??????     @@@@@      .++++
 @    @    + .       ==   ==    %%   %%
 .&&&&.    ####..     =  == .   ++   ++
  .. $         &        $$     $$$$$$$$.
 .   &.      . #       && .          ##
   +.   .  #####     $$$$$$$        .==

> 9524

Answer 1

Jelly, 35 33 34 bytes

Ỵe€€⁾ .¬ZḄṣ0§ḟ0%29“h½sØ?X’ḃ26¤iⱮ’Ḍ

Try it online!

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

Answer 2

05AB1E, 34 bytes

'.ð:.B€SðÊøJC0¡O0K29%•!aˆM©м•₂вskJ

Port of @NickKennedy's Jelly answer, so make sure to upvote him!
PS: Knowing the width of the digits is pretty useless if the amount of space columns in between digits can vary..

Try it online.

Explanation:

'.ð:                              '# Replace all dots with spaces
    .B                             # Split on newlines
      €S                           # Convert each line to a list of characters
        ðÊ                         # Check of each character if it's NOT equal to a space
          ø                        # Zip/transpose; swapping rows/columns
           J                       # Join each column together
            C                      # Convert each from binary to an integer
             0¡                    # Split on 0s
               O                   # Sum each inner list
                0K                 # Remove 0s
                  29%              # Take modulo-29 on each
                     •!aˆM©м•      # Push compressed integer 102583844953589
                             ₂в    # Converted to Base-26 as list: 
                                   #  [18,23,6,5,1,19,13,21,8,25]
                               sk  # Index the earlier number into this list
                                 J # Join everything together (and output implicitly)

See this 05AB1E tip of mine (sections How to compress large integers? and How to compress integer lists?) to understand why •!aˆM©м• is 102583844953589 and •!aˆM©м•₂в is [18,23,6,5,1,19,13,21,8,25].

Answer 3

Jelly, 29 bytes

⁾. yỴ=⁶s€⁵ZẎ€Ḅ:434ị“¡£:E’Œ?’¤

A monadic Link accepting a list of characters which yields a list of digits, or a full program accepting a single text argument which prints the digits.

(Requires padding on the right with spaces such that each digit has a width of ten characters, including the right-most one, which I believe is OK.)

Try it online! ...or try the other test case here.