Case Study: Image Processing

A working draft of resources and reports from an NSF-sponsored project intended to strengthen the role of mathematics in Advanced Technological Education (ATE) programs. Intended as a resource for ATE faculty and members of the mathematical community. Comments are welcome by e-mail to the project directors: Susan L. Forman or Lynn A. Steen.

Image processing in its broadest sense is an umbrella term for representing and analyzing of data in visual form. More narrowly, image processing is the manipulation of numeric data contained in a digital image for the purpose of enhancing its visual appearance. Through image processing, faded pictures can be enhanced, medical images clarified, and satellite photographs calibrated. Image processing software can also translate numeric information into visual images that can be edited, enhanced, filtered, or animated in order to reveal relationships previously not apparent. Image analysis, in contrast, involves collecting data from digital images in the form of measurements that can then be analyzed and transformed. Image analysis provides an accurate digital substitute for rulers and calipers.

Originally developed for space exploration and biomedicine, digital image processing and analysis are now used in a wide range of industrial, artistic, and educational applications. Software for image processing and analysis is widely available on all major computer platforms. This software supports the modern adage that "a picture is worth a thousand words, but an image is worth a thousand pictures."

Uses of Image Processing:

In biotechnology:

Automated DNA sequencing.
Analysis of electrophoretic gels.
Analysis of Polymerase chain reaction (PCR).
Automatic analysis of petri dish colonies.
Representing proteins visually.
Designing drugs.

In Medicine:

Analysing the morphology of tissue sections.
Clarifying mammograms, MRI, PET, and XRay images.
Representing human anatomy (Visible Human).
Digital dissection.
Comparing DNA images for clinical or forensic research.

In Environmental Science:

Monitoring weather patterns.
Enhancing images from underwater photography.
Determining water flow from satellite photography.

In Art:

Creating digital images for films.
Modifying photographs for advertising.
Enhancing architectural drawings.

Examples of Instructional Use

Since satellite photographs of developing storms are readily available on the Internet, these images provide excellent source material for learning the potential uses of image processing. By taking measurements from a sequence of satellite images of a developing hurricane and combining these data with other meterological data (for example, position of the jet stream and position and barometric strength of high and low pressure cells), students can track hurricanes as they develop in order to predict the time and location of landfall. It is not uncommon for student predictions to be almost as accurate as those of professional forecasters.

In order to properly interpret electrocardiogram (EKG) graphs, emergency medical technicians (EMT) need to understand the relation between the electrical and mechanical actions of the heart. Image analysis software offers students training for EMT certification an invaluable link between the physiology of the heart and the abstract graphs associated with the heart's electrical activity. By displaying graphical information alongside slow motion images of a beating heart, students can learn to "read" the graphs--a skill they will need when dealing with a patient on the way to the hospital.

Image processing software provides a natural context for students in the middle grades to learn about measurement, geometry, ratio, slopes, percentages, histograms, and simple equations. Images of the United States with state outlines overlaid on satellite images provide a rich resource for exercises in measurement and area. A CAT scan of an emphysema patient's lungs provides a realistic context to learn about ratios, percents, and decimals. And the process of image processing itself provides opportunities for students to "see" the impact of different histograms--which can represent scaling changes used to improve visualization of image data.

Other instructional uses include:

Displaying the significance of small units of measurement (e.g., millimeters, microns) by using magnified images of small bugs, mites, and cells.
Creating a "typical" face by averaging the pixels from a number of scanned pictures.
Morphing one picture into another using linear transitions between corresponding pixels.
Measuring angles and distances in handwriting samples to detect forgeries.
Measuring key sports data from video images of baseball hitters , tennis servers, and free throw shooters.

Supporting Mathematics

A digital image is a matrix of measurements (of light, temperature, altitude, or some other quantity) sampled at regular intervals, rounded off to integers, and displayed according to a scale that translates integer values into pixels of specific colors or shades of gray. In a computer, a digital image is a long string of numbers representing rows of pixels of different colors (or brightness). Indeed, the data that create a digital image can be exported to (or imported from) a spreadsheet, where they can be manipulated with standard mathematical tools.

Digital image processing is an inherently mathematical process. Every action embodied in the image processing software corresponds to one or more mathematical transformations of the digital data. These include resizing, density slicing, measuring (distances and angles), scaling, and stacking. Many of these transformations are linear, but some (e.g., enhancing edge effects) are nonlinear. Image processing software enables an investigator to work in many different modes--entirely visually, or with graphs of the associated mathematical transformations, or with the actual underlying data.

Resources

The principal computer tools used for image processing are NIH Image for Macintosh and Scion Image for Windows.

The Center for Image Processing in Education (CIPE) is supported by the ATE program to provide professional development opportunities for educators of students studying for careers in such fields as bio-, environmental, and agricultural technology. Director: Melanie Magisos Curriculum Director: Don Adams.

References

Center for Image Processing in Education (CIPE).

ESRI: Environmental Systems Research Institute.

BASIS: Spatial Information Systems. (Berry & Assoc.)

Supported by the Advanced Technological Educaiton (ATE) program at the National Science Foundation. Opinions and information on this site are those of the authors and do not represent the views of either the ATE program or the National Science Foundation.