Get, or calculate the entropy of an image with Ruby and imagemagick

Question

How to find the "entropy" with imagemagick, preferably mini_magic, in Ruby? I need this as part of a larger project, finding "interestingness" in an image so to crop it.

I found a good example in Python/Django, which gives the following pseudo-code:

image = Image.open('example.png')
histogram = image.histogram() # Fetch a list of pixel counts, one for each pixel value in the source image

#Normalize, or average the result.
for each histogram as pixel
  histogram_recalc << pixel / histogram.size
endfor

#Place the pixels on a logarithmic scale, to enhance the result.
for each histogram_recalc as pixel
  if pixel != 0
    entropy_list << log2(pixel)
  endif
endfor

#Calculate the total of the enhanced pixel-values and invert(?) that.
entropy = entroy_list.sum * -1

This would translate to the formula entropy = -sum(p.*log2(p)).

My questions: Did I interprete the Django/Python code correct? How can I fetch a histogram in ruby's mini_magick if at all?

Most important question: is this algorithm any good in the first place? Would you suggest a better one to find the "entropy" or "amount of changing pixels" or "gradient depth" in (parts of) images?

Edit: Using a.o. the resources provided by the answer below, I came up with the working code:

# Compute the entropy of an image slice.
def entropy_slice(image_data, x, y, width, height)
  slice = image_data.crop(x, y, width, height)
  entropy = entropy(slice)
end

# Compute the entropy of an image, defined as -sum(p.*log2(p)).
# Note: instead of log2, only available in ruby > 1.9, we use
# log(p)/log(2). which has the same effect.
def entropy(image_slice)
  hist = image_slice.color_histogram
  hist_size = hist.values.inject{|sum,x| sum ? sum + x : x }.to_f

  entropy = 0
  hist.values.each do |h|
    p = h.to_f / hist_size
    entropy += (p * (Math.log(p)/Math.log(2))) if p != 0
  end
  return entropy * -1
end

Where image_data is an RMagick::Image.

This is used in the smartcropper gem, which allows smart slicing and cropping for images with e.g. paperclip.

Answer 1

Entropy is explained here (with MATLAB source, but hopefully the qualitative explanation helps):

Introduction to Entropy (Data Mining in MATLAB)

For a more formal explanation, see:

"Elements of Information Theory" (Chapter 2), by Cover and Thomas