nonparametric normalization I would like to normalize some of my data based on images to compare the relative brightness of some pixels compared to another image, (with different scalings)
say I have an image in Matlab (in reality spanning from 0 to 255)
im=magic(5);

the simplest way I can come up with to normalize the image data is:
normalizer=@(x) ( x-min(x) ) / (max(x) - min(x))
normalizer(im)

However, similar to to mean (vs median) this method is highly influenced by outliers. What would be a good or even standard way to approach this in a  nonparamatric way?
 A: 'Robust' normalization might be a more fitting term for what you want than 'nonparametric', since normalization methods don't typically involve distributional assumptions. Here are a couple possibilities.
As an alternative to min-max scaling (described in the question), you could replace the minimum with a small quantile and the maximum with a large quantile. Given data values $X = \{x_1, \dots, x_n\}$, let $q_{low}$ denote the $\left( \frac{\alpha}{2} \right)$th quantile and $q_{high}$ denote the $\left( 1 - \frac{\alpha}{2} \right)$th quantile, where $\alpha$ is some small fraction. The normalized data is $\tilde{X} = \{\tilde{x_1}, \dots, \tilde{x}_n\}$ where:
$$\tilde{x}_i = \frac{x_i - q_{low}}{q_{high} - q_{low}}$$
Normalization will be unaffected by outliers, as long as they make up a fraction less than $\alpha$ of the data points. Note that $\alpha=0$ corresponds to the standard min-max scaling. Also, note that normalization will map inputs less than $q_{low}$ to negative values,  and inputs greater than $q_{high}$ to values greater than $1$.
Standardization is a another common form of normalization, which maps inputs to Z scores (i.e. subtract the mean, then divide by the standard deviation). To construct a robust version of this procedure, the mean and standard deviation can be replaced with robust estimates of location and scale. For example, the median can be used in place of the mean and the median absolute deviation (MAD) can be used in place of the standard deviation. Alternatively, trimmed or Winsorized estimates could be used.
A: If you're seeking to compare individual pixels, you can also remap each pixel's brightness to the portion of pixels (in its original image) which are dimmer.  For an image M which is a collection of pixels p, and for N(M|c) which calculates the number of pixels in M satisfying condition c:
p :-> N(M|p' < p) / N(M|True)

This will give output on [0, 1], but should provide an overall brightening to dim images, and a dimming of bright images. If most pixels cluster near the mean, that mean will be shifted to near 0.5 and the high and low anomalies will be evenly distributed on either side.
