arizonas first university. command and control wind tunnel simulated camera design jacob gulotta
DESCRIPTION
Electrical and Computer Engineering Resolving Reference Frames Attitude and Euler Angles –roll (ψ) –pitch (θ) –yaw (Φ) Translation 3 3/4/2016TRANSCRIPT
Arizona’s First University.
Command and Control Wind TunnelSimulated 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
205/08/23
Electrical and Computer Engineering
Resolving Reference Frames
• Attitude and Euler Angles– roll (ψ)
– pitch (θ)
– yaw (Φ)
• Translation
305/08/23
Electrical and Computer Engineering
405/08/23
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
505/08/23
• Using homogenous coordinates
Electrical and Computer Engineering
Addressing the Camera
• Basic Imaging – Ideal Pinhole Camera
• Using the frontal imaging plane model and our notation
605/08/23
Electrical and Computer Engineering
Revision
• Rewriting the previous equations in homogenous coordinates
705/08/23
Electrical and Computer Engineering
Accounting for Camera Properties
• Intrinsic Properties
805/08/23
• 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
905/08/23
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
1005/08/23
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
1105/08/23