How to compensate for uneven illumination in a photograph of a printed page?

Question

I am trying to teach my camera to be a scanner: I take pictures of printed text and then convert them to bitmaps (and then to djvu and OCR'ed). I need to compute a threshold for which pixels should be white and which black, but I'm stymied by uneven illumination. For example if the pixels in the center are dark enough, I'm likely to wind up with a bunch of black pixels in the corners.

What I would like to do, under relatively simple assumptions, is compensate for uneven illumination before thresholding. More precisely:

• Assume one or two light sources, maybe one with gradual change in light intensity across the surface (ambient light) and another with an inverse square (direct light).

• Assume that the white parts of the paper all have the same reflectivity/albedo/whatever.

• Find some algorithm to estimate degree of illumination at each pixel, and from that recover the reflectivity of each pixel.

• From a pixel's reflectivity, classify it white or black

I have no idea how to write an algorithm to do this. I don't want to fall back on least-squares fitting since I'd somehow like to ignore the dark pixels when estimating illumination. I also don't know if the algorithm will work.

All helpful advice will be upvoted!

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EDIT: I've definitely considered chopping the image into pieces that are large enough so they still look like "text on a white background" but small enough so that illumination of a single piece is more or less even. I think if I then interpolate the thresholds so that there's no discontinuity across sub-image boundaries, I will probably get something halfway decent. This is a good suggestion, and I will have to give it a try, but it still leaves me with the problem of where to draw the line between white and black. More thoughts?

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EDIT: Here are some screen dumps from GIMP showing different histograms and the "best" threshold value (chosen by hand) for each histogram. In two of the three a single threshold for the whole image is good enough. In the third, however, the upper left corner really needs a different threshold:

Answer 1

Well. Usually the image processing I do is highly time sensitive, so a complex algorithm like the one you're seeking wouldn't work. But . . . have you considered chopping the image up into smaller pieces, and re-scaling each sub-image? That should make the 'dark' pixels stand out fairly well even in an image of variable lighting conditions (I am assuming here that you are talking about a standard mostly-white page with dark text.)

Its a cheat, but a lot easier than the 'right' way you're suggesting.

Answer 2

This might be horrendously slow, but what I'd recommend is to break the scanned surface into quarters/16ths and re-color them so that the average grayscale level is similar across the page. (Might break if you have pages with large margins though)

Answer 3

i would recommend calibrating the camera. considering that your lighting setup is fixed (that is the lights do not move between pictures), and your camera is grayscale (not color).

take a picture of a white sheet of paper which covers the whole workable area of your "scanner". store this picture, it tells what is white paper for each pixel. now, when you take take a picture of a document to scan, you can reload your "white reference picture" and even the illumination before performing a threshold.

let's call the white reference REF, the picture DOC, the even illumination picture EVEN, and the maximum value of a pixel MAX (for 8bit imaging, it is 255). for each pixel:

EVEN = DOC * (MAX/REF)

notes:

• beware of the parenthesis: most image processing library uses the image pixel type for performing computation on pixel values and a simple multiplication will overload your pixel. eventually, write the loop yourself and use a 32 bit integer for intermediate computations.
• the white reference image can be smoothed before being used in the process. any smoothing or blurring filter will do, and don't hesitate to apply it aggressively.
• the MAX value in the formula above represents the target pixel value in the resulting image. using the maximum pixel value targets a bright white, but you can adjust this value to target a lighter gray.

Answer 4

You could try using an edge detection filter, then a floodfill algorithm, to distinguish the background from the foreground. Interpolate the floodfilled region to determine the local illumination; you may also be able to modify the floodfill algorithm to use the local background value to jump across lines and fill boxes and so forth.

Answer 5

I assume that you are taking images of (relatively) small black letters on a white background.

One approach could be to "remove" the small black objects, while keeping the illumination variations of the background. This gives an estimate of how the image is illuminated, which can be used for normalizing the original image. It is often enough to subtract the illumination estimate from the original image and then do a threshold based segmentation. This approach is based on gray scale morphological filters, and could be implemented in matlab like below:

img = imread('filename.png');
illumination = imclose(img, strel('disk', 10)); 
imgCorrected = img - illumination; 
thresholdValue = graythresh(imgCorrected); 
bw = imgCorrected > thresholdValue;

For an example with real images take a look at this guide from mathworks. For further reading about the use of morphological image analysis this book by Pierre Soille can be recommended.

Answer 6

You could also try a Threshold Hysteresis with a rate of change control. Here is the link to the normal Threshold Hysteresis. Set the first threshold to a typical white value. Set the second threshold to less than the lowest white value in the corners.

The difference is that you want to check the difference between pixels for all values in between the first and second threshold. Ideally if the difference is positive, then act normally. But if it is negative, you only want to threshold if the difference is small.

This will be able to compensate for lighting variations, but will ignore the large changes between the background and the text.

Answer 7

Two algorithms come to my mind:

• High-pass to alleviate the low-frequency illumination gradient
• Local threshold with an appropriate radius

Answer 8

Why don't you use simple opening and closing operations? Try this, just lool at the results: src - cource image

src - open(src) close(src) - src

and look at the close - src result using different window size, you will get backgound of the image. I think this helps.