## Posts

Showing posts from July, 2018

### Another crack at the RX algorithm in Python

At the request of a commentor on a former post, I decided to write an updated Python implementation of the RX algorithm with NumPy (which actually out-performs my naive C implementation). You can download and install the module from GitHub.

At the heart of it all is the Mahalanobis distance metric,
\begin{align}d(\,\tilde{X},X_{i}\,)&=\sqrt{(\,X_{i}-\tilde{X}\,)^{\text{T}}\,\Omega\,(\,X_{i}-\tilde{X}\,)},\end{align}where $$X_{i}$$ is some vector in the image's space (many times RGB), $$\tilde{X}$$ is the average (or approximately average) vector along each channel, and $$\Omega=\Sigma^{-1}$$ is the precision matrix.

I've found it's not really necessary to have the exact precision matrix in practice, so we may reduce the overhead of computing an average vector and covariance if the image is largely one color.  This computation can be neatly expressed with numpy.einsum.

### Scaling an image to an appropriate number of pixels for your project

Today I'm writing a Python module that works with image data (check back in a few days for my post about it) and I wanted to arrive at the optimal dimensions an image must be to have a certain number of pixels.

For example, if I want to see how fast my algorithm is for, say, 1 million RGB vectors, then I want to scale my example image to 1 megapixel.

In this post I'm working with an image that has dimensions $$(3840,2160)$$, or a size of about 8.3 million pixels. But what should the $$X$$ and $$Y$$ dimensions of my image be then, if I want it to be as close to 1 million pixels as possible?
First Attempt Let's write a Python function that preserves the aspect ratio of an image's dimensions and allows us to vary its size. from typing import Tuple def scale(X: int, Y: int, factor: float =1.0) -> Tuple[float, Tuple[float, float]]: """ Scale our image's dimensions by some factor, preserving aspect ratio. """ X_, Y_ = fa…