Arizonas First University. Command and Control Wind Tunnel Simulated Camera Design Jacob Gulotta

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