#histogram manipulation

Grayscale Enhancement

I know we’ve all experienced excessive shadows in pictures. They can come from the shot being in a poorly-lit area, from a side effect of using the flash without a reflector or diffuse, or from backlight. Here’s a photo illustrating the first example.

We may never know what lies in the void I was sticking my hand into; or so I thought at first, but it turns out those shadows still contain information. We just have to force it out, and that’s where histogram manipulation comes in.

First, we test it on the image in grayscale. Since we only have one channel here, the normalized histogram of the image corresponds to its probability distribution function or PDF.

From this, we use the cumulative sum function to allow us to obtain the image’s cumulative distribution function or CDF.

This is what we will use to modify the image’s histogram. We’ll want to pick a CDF to backproject onto the PDF. For this activity we’ll try both a linear CDF and a nonlinear sigmoid CDF, generated using an exponential Gaussian function.

And with no further ado, here are the results from the modified PDFs:

I’d say that while the linear CDF produces a brighter image, it seems a bit overwhelming in its brightness. The sigmoid CDF gives an image that doesn’t go as bright, but it reveals enough detail.

Colour Enhancement

Alright, let’s get to it. The modification we made to the image’s histogram on the grayscale level was basically modifying the “intensity” of each pixel, with high intensity being closer to white.

For coloured images, we use our knowledge of normalized colour coordinates (NCC) to obtain the intensity I, as well as the previously used r, g, and b values for each pixel in the image.

From here, it’s just a matter of applying histogram modification to the intensity matrix of the image, then using it to compute for the new RGB values of the matrix from NCCs r, g, and b. I used both the linear and sigmoid CDFs for this, and the results look pretty good.

I had to try it on something else, and so I found this picture of my niece’s furby I had for.... some reason.

Working on this was pretty straightforward. I had a problem when I tried to apply my grayscale code to the coloured image, but somehow I managed to fix it by starting the code again from scratch. I assume I just missed something while modifying it. I delivered what the activity required, and my images are all there so I say I get a 10 out of 10 for this one.

Here are my acknowledgements and references:

Roland Romero, for helping me troubleshoot my code

My niece, Keira Paulino, for having that furby