# Mathematical methods in VidSync

The novel blend of mathematical methods used by VidSync enables excellent precision and accuracy as well as a more flexible range of applications than any other published method of fisheries videogrammetry. VidSync performs all the calculations for 3-D measurement automatically, and one can use it proficiently without understanding the details. However, basic familiarity with the mathematics helps to understand the reasoning behind our hardware and software guidelines, and to better interpret program output.

The mathematics are thoroughly described and evaluated for accuracy in a manuscript under revision at a fisheries journal, and in the author's Ph.D. dissertation:

*Neuswanger J. 2014. New 3-D video methods reveal novel territorial drift-feeding behaviors that help explain environmental correlates of Chena River Chinook salmon productivity. Ph.D. Dissertation, University of Alaska Fairbanks, 181 pp.*

## A brief summary

Each 3-D position is calculated from points on two or more video screens, which the user digitizes by clicking on the same object (e.g., a fishâ€™s snout) in each view. The input point is adjusted to compensate for non-linear (radial and decentering) distortion caused by optical imperfections in the lens and housing system. Then, a linear method projects the distortion-corrected 2-D coordinates of each point into a line of sight in 3-D space. When at least two lines of sight have been obtained from different camera views, their approximate intersection is triangulated to find the 3-D world coordinates (e.g., in meters) of the measured point.