Image Processing

Tomography, Part 3: Reconstruction

Fourier slice theorem

At the end of the second article on tomography, I left you with a very blurry reconstruction of the scanned object. Indeed, naive backprojection is not sufficient to create high-quality reconstructions. Why is that so? Intuitively, a simple backprojection cannot be expected to create a perfect reconstruction, since the contribution of…

Submitted on 25 November 2012

Tomography, Part 2: Yes, You Can

Sinograms of box with ball

This article shows that it is possible to reconstruct the inside of a person or object from (lots of) projections of that person or object. Mathematically, tomography is based on the fact that the function values of a two-dimension functional \(f(x,y)\) can be calculated from projections of that function. This basic fact was discovered…

Submitted on 11 November 2012

Tomography, Part 1: Projections

Projection of box with ball

Have you ever wondered how a CT (or CAT) scanner creates an image of the inside of a person? The answer is computing. CT and CAT are short for computed (axial) tomography. Computing is the secret sauce that is poured over the hundreds or thousands of X-ray photos that make up a CT scan, to merge them into a single image. This first article on tomography explains projections, the essential input data for tomography…

Submitted on 29 October 2012

Lena

Lena test image

There are two kinds of people in the world. The first have seen the Lena (or Lenna) image before; most of them have done at least some work in image processing, or happen to have read the November 1972 issue of Playboy magazine. The second have probably never seen it.

Submitted on 30 August 2012

Beware of Silently Assuming Linear Intensity in Astronomical Images

Demo of the effect of screen gamma

This article points out the danger of assuming that astronomical images are encoded using linear intensity. It is meant for the many people that are performing astronomical observations using regular cameras. Not because there’s something wrong with that, but because those cameras are optimized for “normal” photography and video, not for numerical calculations on their images. The illustration below…

Submitted on 17 September 2011