Microscopy Primer
Light and Color
Microscope Basics
Special Techniques
Digital Imaging
Confocal Microscopy
Live-Cell Imaging
Photomicrography
Microscopy Museum
Virtual Microscopy
Fluorescence
Web Resources
License Info
Image Use
Custom Photos
Partners
Site Info
Contact Us
Publications
Home

The Galleries:

Photo Gallery
Silicon Zoo
Pharmaceuticals
Chip Shots
Phytochemicals
DNA Gallery
Microscapes
Vitamins
Amino Acids
Birthstones
Religion Collection
Pesticides
BeerShots
Cocktail Collection
Screen Savers
Win Wallpaper
Mac Wallpaper
Movie Gallery

Interactive Java Tutorials

Undersampling Digital Images
and
Aliasing Artifacts

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.

Contributing Authors

Kenneth R. Spring - Scientific Consultant, Lusby, Maryland, 20657.

Matthew J. Parry-Hill and Michael W. Davidson - National High Magnetic Field Laboratory, 1800 East Paul Dirac Dr., The Florida State University, Tallahassee, Florida, 32310.


BACK TO DIGITAL IMAGE PROCESSING TUTORIALS

Questions or comments? Send us an email.
Text and graphics for this interactive tutorial are
© 2000-2022 by Kenneth R. Spring and Michael W. Davidson.
All Rights Reserved.
© 1998-2022 by Michael W. Davidson and The Florida State University. All Rights Reserved. No images, graphics, scripts, or applets may be reproduced or used in any manner without permission from the copyright holders. Use of this website means you agree to all of the Legal Terms and Conditions set forth by the owners.
This website is maintained by our
Graphics & Web Programming Team
in collaboration with Optical Microscopy at the
National High Magnetic Field Laboratory.
Last modification: Thursday, Jun 14, 2018 at 02:37 PM
Access Count Since March 1, 2001: 14991
Visit the websites of our partners in digital imaging education:
Visit the Olympus Microscopy Resource Center website. Visit the QImaging website.