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…

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…

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…

In the article Color QR Codes Done Right, I’ve tried to convince you to create your color QR codes in a way that keeps them easily scannable. This week, I’ve discovered Visualead, a startup that is currently in Public Beta, that lets you combine any artwork with a QR code. Graphically, they have nailed it. They seem to have found out that…

To the guys that stole my car: I feel that your action was suboptimal with respect to building a better society. Also, breaking open a locker while a guy is in the swimming pool is not generally considered a nice thing to do. I do agree with your point of view that…

Following my article on pinhole phography, I’ve implemented a calculator that you can use to compute the optimal pinhole size for your own camera. Go to the tool.

Quite a while ago, I briefly reported on the spectacular Mars Science Laboratory mission that is currently under way. As you are probably aware, the Curiosity rover has now safely landed, and is already exploring the Red Planet. In this article, I want to tell you about the spectacular way in which the rover was put down on the surface. For previous Mars rovers like…

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.

The concept of a fractal dimension is based on the idea of measuring things with differently sized rulers, as already mentioned in the article on the Mandelbrot Mandelbrot set. Mathematically (but very loosely), the fractal dimension is defined as: if I cover an object with…

The Mandelbrot set is named after Benoît Mandelbrot, a French American mathematician. The set is a part of the complex plane. It is created by iterating the complex quadratic polynomial \(f_c(z)=z^2+c\). For each point \(c\) of the complex plane…