## Valentine Filtering

Happy Valentine’s Day! This is a bit of a trick post; after luring you in with the cute heart, I’ll explain in this article how image filtering can be implemented in frequency space… read more

There is a fundamental difference between *adding Gaussian noise* and *applying Poisson noise*. In practice, people often talk about *adding* Poisson noise anyway, but this is not accurate. I will be looking at this from the image processing perspective in this article, and I’ll show purely visual examples. An application of this could be… read more

When taking a picture with a camera, the “true” image is *convolved* with the *point spread function* (PSF) of that camera, potentially producing a blurred image. *Deconvolution* is the process of removing the effect of this PSF again. In this article, I demonstrate that this is not an easy thing to do… read more

After computing The PSF of a Pinhole Camera and showing Some Wacky Pinholes and Their PSF in previous articles, the next step towards ever more realistic PSFs is adding color. A DSLR camera has detector pixels that are sensitive to red, green, and blue, and, since the size of the PSF depends on… read more

After simulating a round pinhole and showing the resulting point spread function (PSF) both far away (equivalent to the Airy disk) and close by (resulting in a realistic PSF for a DSLR pinhole camera) in The PSF of a Pinhole Camera, I show the PSFs of some more wacky pinholes here… read more

After introducing the Airy pattern in The Perfect Camera, I will show in this article how the PSF of a pinhole camera looks. A camera with a classical lens focuses the image that would be at infinity on the detector, which means that you actually get (approximately) the Airy pattern as the image of a point source there. This is not true for a pinhole camera, so… read more

The perfect camera is *diffraction limited*. This article is written strictly from an optical point of view, so don’t expect a Nikon / Canon / Leica comparison here… Optically, a camera (or telescope or other optical instrument) can be described by its *point spread function* (PSF), which… read more

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