Image Processing

Happy Valentine’s Day! I might not be very romantic, but I had to do something with it. Imaging the heart is an important application of tomography and other techniques in medical imaging. Since hearts are everywhere on Valentine’s Day, let’s scan one. This article builds on… read more

The first three articles on tomography focused on analytic techniques, in which the reconstruction problem is attacked using mathematical analysis. When the step to real world scanners is made, the problem is discretized. Both the projections and the reconstruction area are divided into pixels, and a numerical approximation of the true mathematical technique is introduced. The algebraic techniques assume… read more

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… read more

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… read more

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… read more

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. read more

After trying to explain how to correctly add color to a QR code, I went all the way and implemented a QR code generator that actually does this in practice. Go to the tool. At this time, the tool is limited to adding a logo or image. read more

Color is a straightforward way to make those boring QR codes special. This seems to have caught on with quite a few people, as a quick Google image search reveals. But, there’s a problem. Deviating from the ideal black-and-white makes the QR code more difficult to scan. In this article, I show a way to… read more

After the fun with the “doctored” photo from a previous article, I thought it would be nice to show another example of a photo that “fades to gray” if you’re not careful. This time the image disappears if it is converted to grayscale in the wrong way. This is… read more

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… read more