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