.. _sec-ImageStretching:

Contrast Stretching
===================

Consider a scalar (gray value) image $f$ with values $f(\v x)$ that
are only in a subset of the possible scalar values (of course
dependent on the range of the image). E.g. consider a gray value image
$f$ with possible range $R=[0,1]\subset\setR$ but whose values are in
the range from $a$ to $b$.

.. ipython:: python
   :suppress:

   from pylab import *
   a = loadtxt('images/lowcontrast.npy')
   N=32; bins = linspace(0,1,N+1)
   ha, ea = histogram(a.flatten(), bins=bins)
   b = (a-a.min())/(a.max()-a.min())
   hb, eb = histogram(b.flatten(), bins=bins)
   figure(1); clf();
   subplot(221); imshow(a,cmap=cm.gray,vmin=0,vmax=1); axis('off')
   title("Low contrast orginal")
   subplot(223); imshow(b,cmap=cm.gray,vmin=0,vmax=1); axis('off')
   title("Contrast Stretched")
   subplot(222); bar(ea[:-1], 1.0*ha/sum(ha), width=diff(ea)[0] ); xlim(0,1)
   title("Histogram of low contrast image")
   subplot(224); bar(eb[:-1], 1.0*hb/sum(hb), width=diff(eb)[0] ); xlim(0,1)
   title("Histogram of contrast stretched image")
   @savefig contraststretch.png width=99%
   show()



The point operator:

.. math::
   g(\v x) = \phi(f(\v x))

with:

.. math::
   \phi(v) = \frac{v-a}{b-a}

results in an image $g$ that uses the entire range of gray values from
0 to 1.

Assuming we have overloaded the arithmetical operators to work on images we may write:

.. math::
   g = \frac{f-f_\text{min}}{f_\text{max}-f_\text{min}}

In Python/Numpy we can write:

.. code:: python

   g = (f-f.min())(f.max()-f.min())



Exercises
---------

   #. Given an 8-bit gray value image $f$, i.e. $f(\v
      x)\in[0,255]\subset\setZ$, what is the point operator that
      stretches the contrast of the image to the entire possible range.

   #. Explain why contrast stretching of a digital image cannot always
      lead to satisfactory results when the original image was very
      very dark (or very very light).

   #. Contrast stretching of color images is not a trivial
      generalization of what is discussed for scalar images.

      a. Explain that scalar constrast stretching of the Red, Green
         and Blue channels (images) independently is not a good idea.

      #. Let's first change the color model from RGB to HSV. And then
         stretch the contrast in the V image and use the new V values
         together with the original H and S values. Implement this
         contrast stretching algorithm. Why is this contrast
         stretching method leading to reasonable results?