Yike Gong Aims at Camera Study in Connection with Computer Vision, Graphics

 

  • Prof. Annalisa Crannell and Yike Gong partnered together for summer research. Prof. Annalisa Crannell and Yike Gong partnered together for summer research.

Equipped with a curiosity focused on computer vision and graphics, and a desire to study this technical area after graduating from F&M, Yike Gong ’19 was drawn to research on the two-slit camera, a specialization of the camera models.

 

“I wanted to do independent research simply because I wanted to see what a research process would be like. More specifically, I wanted to know how Math professors come up with ideas, what do they do when they get stuck, and how they get a paper published.”  

 

The student researcher says, "Our research on the two-slit camera is a mathematical approach to the study of camera models, and I believe that the research will support my future study of computer vision. The two-slit camera is a projection model that maps R3 to R2 (or P3 to P2) through two slits that are skew. We think that the images generated by this type of camera have interesting properties different from those generated by a regular pinhole camera."  Yike adds,  “The study of the images generated by the two-slit camera might be of interest to areas such as multi-view geometry, computer vision, and photogrammetry.”

Research advisor Prof. Annalisa Crannell explains that “two-slit cameras” are examples of what mathematicians call “generalized linear cameras”.  Instead of having a single pin hole that light rays pass through to make an image on a piece of film, two-slit cameras (as their name implies) have two slits, in different directions, separated by a bit of space.   Says the mathematician, “I wanted to look at the question, in what geometric ways are the pictures created by two-slit cameras different from the pictures generated by the familiar pinhole cameras?”

“The first task I asked Yike to undertake was to prove that the image of a real-world line in a two-slit camera would be another line.  But I was wrong!” Prof. Crannell exclaims.  “Generally, the image of a line is a hyperbola, something Yike managed to prove in her second week of work with me.”   

During the rest of the summer, Prof. Crannell explains that Yike’s work revealed beautiful structures that they hadn’t suspected would be part of the project.  The projection surface of a line--- the set of light rays from that line that pass through both slits and then pierce the film in the camera  -- form a lovely hyperbolic object called a “ruled surface”.  A video of Yike’s research is posted at:
https://drive.google.com/file/d/1uyYoiZHIJEE1NUFCsl65HlCaCyuPTLDO/view

 

“Sometimes when I start research with a student, I know pretty much where our work will lead us.   But in this research project, our early investigations revealed big surprises.”

 

Yike gained some experience in writing math and using graphing techniques. She frequently used Mathematica and Geogebra software to graph the images.

“Generally, I think the whole learning process is helpful for my future studies. From the feeling of going nowhere at the beginning to the frustration after getting unexpected results and to the happiness of discovering something new, I enjoy the self-guided learning experience that is so different from the experience I get in classrooms," describes the student researcher. “I am so glad to have worked with Professor Crannell. I learned not only some cool math but also lots of life skills, such as time management and presentation tips.”

Yike adds, “Always keep your notes. I used a lot of linear algebra and calculus in my research and it took me a long time to go back to the textbooks and learn something that I had already learned. It would have been much easier if I would have had my notes in hand.”

 

  • Yike Gong used Mathematica to create a computer visualization of a rotating cube as seen by a "Two-slit Camera." In this camera, the images of real-world lines become hyperbolas passing through vanishing points. Yike Gong used Mathematica to create a computer visualization of a rotating cube as seen by a "Two-slit Camera." In this camera, the images of real-world lines become hyperbolas passing through vanishing points.