Arizona’s First University. Command and Control Wind Tunnel Simulated Camera Design Jacob Gulotta

Electrical and Computer Engineering Problem Statement Objective –To “see” desired object with camera and report its absolute location Main Issues –Two reference frames: world and camera –2D image, 3D world –In simulation, cannot analyze image Assumptions –Pixel perfection –X-ray vision 2 3/4/2016

Electrical and Computer Engineering Resolving Reference Frames Attitude and Euler Angles –roll (ψ) –pitch (θ) –yaw (Φ) Translation 3 3/4/2016

Electrical and Computer Engineering 4 3/4/2016 The Math Rotation Matrix Translation vector Coordinates relative to world

Electrical and Computer Engineering More Math Homogenous Coordinates Position vectors Transformation matrix –Camera to world –World to camera 5 3/4/2016 Using homogenous coordinates

Electrical and Computer Engineering Addressing the Camera Basic Imaging – Ideal Pinhole Camera Using the frontal imaging plane model and our notation 6 3/4/2016

Electrical and Computer Engineering Revision Rewriting the previous equations in homogenous coordinates 7 3/4/2016

Electrical and Computer Engineering Accounting for Camera Properties Intrinsic Properties 8 3/4/2016 The end result, omitting the scaling factor

Electrical and Computer Engineering About Time We can use the last result to calculate the actual pixel coordinates These values are on the imaging plane in pixel coordinates 9 3/4/2016

Electrical and Computer Engineering In Simulation No way for computer to “see” the target through the actual image But it’s a simulation! Assumptions come into play here 10 3/4/2016

Electrical and Computer Engineering Going Backwards We know where it is in the picture We need to report where it is in the world Recall Using the pixel locations in homogenous coordinates Reported world location is mostly given by Actual reported location is 11 3/4/2016