What's Next?

Improvements to the Curriculum

The students were successful in mastering the first day of material covering image transformations by solving for the matrix A which rotated, reflected, and translated the image to a new location in a single time step. The learning that occurred while working with the OSSLET gave the students a better understanding of how to build and solve systems of equations. We quantify the measurement of success by analyzing their test scores covering this objective.

In retrospect, the animation of the image covered in the second day of material was hard for all of the students to master. Most students were able to animate their image, but mostly because of experimentation rather than understanding the idea of parameterization; most did not understand how to use t to create an animation over multiple time steps. We could improve their understanding in this area by introducing another day of material to bridge the existing two lessons.

Possibly spending half of the new lesson understanding the new parameter would help our students. By the end of the new lesson, we could move back into the animation OSSLET, and continue our class as previously established, while extending this instruction into the third day of class. If all objectives are covered and we see an increase in the students mastery of the material, we could cover an array of image transformation applications.

Military Applications

Aerial photographs are often used to provide reconnaissance for forward troops to use for ground maneuvers. Given a perfect top down view, the image transformations we have studied here can be applied to translate between coordinates on the photograph and coordinates on the ground. The figure below is an aerial photograph taken approximately 500 feet above the ground, but at some distance away from Michie Stadium located at the United States Military Academy. This photograph does not provide a top down view. Translating from coordinates on photographs like this to ground coordinates is mathematically interesting and very useful.

This photograph identifies an actual military scenario which precludes the ability to take an aerial photo with a perpendicular view of the area of interest. Aerial photos are taken from traditional fixed wing aircraft, rotary wing aircraft, and from unmanned aerial vehicles (UAVs). In the event a no fly zone (NFZ) exists where an aircraft is forbidden to fly across, the photograph taken of the ground within the NFZ will not be a top down view. See the figure below.