Undersampling an image can lead to a common artifact known as aliasing, a form of spatial distortion of the minute details present in a digital image. The effects of this common image defect can be minimized with proper sampling of the specimen image by gathering an adequate number of pixels at the proper spatial resolution during capture.

This interactive tutorial explores the relationship between undersampling and aliasing artifacts in digital images. The tutorial initializes with a randomly selected specimen image (captured in the microscope) appearing in the left-hand window entitled Anti-Aliased Image. To the right of the specimen image window is the Undersampled Image window, which displays an undersampled form of the specimen image. To operate the tutorial, select a specimen image from the Select an Image pull-down menu, and vary the image scale factor using the Image Scale Factor slider. As the slider is translated to the right, the image size is simultaneously reduced in both windows. Visitors should compare the two images and observe the spatial aliasing effects that occur in the Undersampled Image as the image size is decreased.

A digital image is acquired through a process often referred to as sampling. The accuracy of each sample depends upon the size of the sampling interval, which is determined by the number of pixels in the image and the distance between each pixel. Each image sample is taken as an average of the image brightness over the sampling interval. The Nyquist Criterion requires a sampling interval equal to just over twice (actually 2.3 times) the highest spatial frequency occurring in the image to avoid losing spatial information. If the sampling interval is larger than the Nyquist limit, then undersampling occurs, and spatial information is lost. Undersampling has the effect of distorting image details, resulting in a phenomenon termed aliasing, which occurs when undersampled high spatial frequencies masquerade as (or "alias" to) lower spatial frequencies.

There are several methods available for suppressing the effects of aliasing. The simplest method is to display objects at a higher resolution, which has the effect of increasing the sampling frequency. Unfortunately, because a reciprocal relationship exists between resolution and refresh rate for current video hardware, a practical limit is imposed on the amount of resolution that can be achieved. Even very high-resolution display devices do not provide adequate resolution for sampling over arbitrarily small intervals. Therefore, increased resolution is not a complete solution to the problem of aliasing. It is also possible to reduce the effects of aliasing by applying anti-aliasing filters to the image that compensate for undersampling. These filters must be applied before or during the sampling process, because aliasing errors cannot be corrected by subsequent filtering. One such technique for reducing the effects of aliasing is to apply a low-pass filter to the image prior to sampling, so that the highest frequency present in the image is less than one half of the sampling frequency. An entirely different approach, which is utilized in this tutorial to construct the Anti-Aliased Image, is to interpolate brightness values over the sampling interval. Interpolation works by computing a weighted approximation of the pixel brightness values over a neighborhood that contains the sampling interval. This technique amounts to re-sampling the image to artificially increase resolution.

In the tutorial, the horizontal sampling interval is equal to the ratio of the original image width to the scaled image width, and the vertical sampling interval is equal to the ratio of the original image height to the scaled image height. The Undersampled Image is constructed from the original image by taking each sampled pixel brightness value from the pixel that is closest to the start of the sampling interval. This violates the Nyquist criterion, and the distortion that results is especially noticeable along feature boundaries where large or frequent brightness transitions occur. When the Image Scale Factor slider is dragged continuously, this distortion is often manifested as a shimmering effect that can be seen in the Undersampled Image as the image size changes. The Anti-Aliased Image suffers from very little distortion, preserves much more of the original image details, and has superior visual quality.

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