Image Processing Fundamentals

When do optical imaging, it is always a certain "smearing" of resulting image compared to what is shown. This Deterioration of the image can be characterized by explaining what the imaging system to a single point means, that is, as it lubricates from then. A feature characterizing this is known as a point Function (PSF spread).

In the above applet, we image two points (or at least two point-like Sources.) As we can see in the bottom half of the applet are the Sources (with a PSF with a width) smeared. The larger The PSF, which need further apart two points for us, they can visually to be separated in the image. The upper part of the applet shows a 1-D function of the center segment of the image. In a classical imaging system, no matter how well, we focus the image, or to optimize the lens diffraction caused a certain width and shape of the PSF If we Diffraction this effect alone , We can approach an analytical expression for the minimum distance between Point sources obtained which can be resolved.

A typical approach to store an image on a digital computer, is through the image in a rectangular grid sampling. The color or Intensity of each of these points to a numeric value converted and Computer-stored. Aside from the color / intensity of these specific Points, everything else is discarded when the image is stored in the computer.

If it's digital picture, we again form a continuous image by interpolation between the stored samples. One way to Interpolation to do is to say that for every point ('continuous'), we only the value to select the next sample. This is known as the next Neighbor interpolation, and causes each sample digital image on the screen as a sharply defined square are drawn. Bilinear or higher order Interpolation, is continuous, smooth and 'real' image reconstruction.

Regardless of the reconstruction, as we of the picture when there are not enough digital Samples used, ie, not enough samples per image area, we can not the continuous original image to be reconstructed. In this case, contains the digital image is not the same information as the original image. The spatial frequency content of the original image leads to another geographic Frequency content in the digital image. This is called aliasing.

In order to reconstruct the original image can (ie avoid aliasing) we have a spatial frequency that is higher than twice the highest spatial frequency of the original image example. This result is as Shannon's sampling theorem Nyquistschen (or simply the sampling theorem) known. The above applet is (re) try it and a picture of painting each sample as an (extended) square reconstruct. In areas where the original image has a high spatial frequency (or a high resolution, or a high level of information), aliasing is apparent, and the captured image contains different content than what is in the original image.