Evaluation of an Optical Flow Method for Measuring 2D and 3D Corn Seedling Growth

Abstract

We propose the use of optical flow as a means of accurately measuring 2D and 3D growth of young corn seedlings. Our method is ultra-sensitive and operates in a non-intrusive, non-contact manner and can measure motions whose magnitude is as minuscule as 5 microns/second. Our 2D analysis, started in 1994 (Barron and Liptay, 1994), uses a least squares integration method to locally integrate spatio-temporal image derivatives into an optical flow field (Lucas and Kanade, 1981). Thus the work described here is an evaluation and verification of just one optical flow method for the use in (accurately) measuring young corn seedling growth. The 2D plant motion is displayed as a vector field of nearly uniform 2D velocities. A key assumption of the 2D growth analysis is that growth motion occurs locally in a 3D plane and its accuracy depends on this assumption being satisfied. We observed that the plant sways in 3D space as it grows, so this assumption does not hold over long time intervals. To capture this swaying over longer time intervals we extended our optical flow approach to 3D (Barron and Liptay, 1997). We use a single least squares calculation to integrate all spatio-temporal image derivatives into a single 3D velocity. Each image in the sequence consists of two views of the same seedling; one view of the corn seedling is front-on while the second view is an orthogonal view (at 90 degrees) of the seedling made by projecting the plant’s orthogonal image onto a mirror oriented at 45° with respect to the camera. We compute 3D optical flow at the corn seedling’s tip by using a simple extension of the 2D motion constraint equation. Both the 2D and 3D methods assume orthographic projection, which holds locally in the image plane. This allowed motions in pixels/frame to be directly scaled to meters/second. We conclude this chapter by showing the accuracy of optical flow as a means of measuring 2D and 3D corn seedling growth.