Count the number of a number in the picture area

Question

Your goal is to write a full program or function that takes 5 positive integers and a string with an image filename as input [X1,Y1], [X2,Y2], N, image.jpg in any reasonable format, where:

• First couple [X1,Y1] are the top left X,Y coordinates (<=20) of the blue rectangle area in the example picture (16,11).
• Second couple [X2,Y2] are the bottom right X,Y coordinates (<=20) of the blue rectangle area in the example picture (20,22).
• Fifth number N such 0 <= N <= 9 is the number that has to be found.
• Sixth parameter is a string with the filename of this JPG picture.

Output how many of N's are present in the indicated area (outlined in blue in the picture for this example):

Click here to obtain a bigger clean version of the same image.

In the picture there are 500 numbers from 0 to 9 (included) arranged in 20 columnns per 25 rows, in monospaced Courier New font. Each different number has a different color (you can take advantage of this fact or ignore it and consider or convert the image in monocrome if that helps you).

Test cases:

[4,4],[13,5],1,image.jpg    > 4  (outlined in red)
[4,4],[13,5],4,image.jpg    > 2  (outlined in red)
[17,5],[17,5],2,image.jpg   > 1  (outlined in magenta)
[17,5],[17,5],9,image.jpg   > 0  (outlined in magenta)
[20,8],[20,9],3,image.jpg   > 1  (outlined in cyan)
[20,8],[20,9],2,image.jpg   > 0  (outlined in cyan)
[16,11],[20,22],0,image.jpg > 8  (outlined in blue)
[16,11],[20,22],3,image.jpg > 9  (outlined in blue)
[3,14],[11,20],7,image.jpg  > 6  (outlined in green)
[3,14],[11,20],5,image.jpg  > 6  (outlined in green)
[3,14],[11,20],8,image.jpg  > 8  (outlined in green)
[1,1],[20,25],0,image.jpg   > 47 (whole picture)
[1,1],[20,25],8,image.jpg   > 50 (whole picture)
[1,1],[20,25],1,image.jpg   > 55 (whole picture)

Rules:

• This is code-golf so the shortest code wins.
• You must take as input this JPG file.
• You are not allowed to hardcode the matrix of numbers represented in the JPG, or the results.
• Standard loopholes are forbidden.

Answer 1

Mathematica, 92 bytes

Count[Take[Characters@StringSplit@TextRecognize@Binarize[Import@#4,.9],#2,#],ToString@#3,2]&

Unnamed function taking the arguments in this format: [{X1,X2}, {Y1,Y2}, N, "image.jpg"]. (Indeed, the fourth argument can be either the local file name or the URL http://i67.tinypic.com/6qh5lj.jpg.)

Import@#4 imports the image file, Binarize[...,.9] darkens all of the numbers to black, and TextRecognize (the function clearly doing the heavy lifting here!) extracts a multi-line string from the resulting image, which is split into a nested list of characters with Characters@.

Take[...,#2,#] keeps only the characters corresponding to the outlined rectangle, and Count[...,ToString@#3,2] counts the number of occurrences of N in the result.

Answer 2

Python 3 + pillow + pytesseract, 239 bytes

from PIL.Image import*
from pytesseract import*
def c(a,b,n,f):w,h=b[0]-a[0]+1,b[1]-a[1]+1;return len([1for i in range(h*w)if image_to_string(open(f).convert('L').point(lambda x:[9,0][x<250],'1')).split()[i//w+a[1]-1][i%w+a[0]-1]==str(n)])

This is horribly inefficient as for each number tile, the whole file is parsed. The much faster and slightly longer 243 bytes solution would be

from PIL.Image import*
from pytesseract import*
def c(a,b,n,f):s=image_to_string(open(f).convert('L').point(lambda x:[9,0][x<250],'1')).split();w,h=b[0]-a[0]+1,b[1]-a[1]+1;return len([1for i in range(h*w)if s[i//w+a[1]-1][i%w+a[0]-1]==str(n)])