Calculating
the Range Data for a Camera Requires a Few Quantities be Known:
 Equation
of the Tracking Plane (Typically Parallel to the Ground
 Position
/ Orientation of Each Camera
 Resolution
of the Video Stream

Procedure
 Once
all Required Quantities are Known, Determining Range Data Can
be Solved
 Sequence
of Mathematical Manipulations Converts Viewing Volume (Shown Right)
into Individual Pixel Projection Areas




1.
Define Pixel Grid
 Camera
Placed at World Coordinate System Origin
 Image
Plane Assumed to be at Unit Distance from Origin in YDirection
 Image
Plane Boundaries Determined Trigonometrically Using Fields of
View in Horizontal and Vertical
 Plane
Area Divided Into Pixel Grid Corresponding to Capture Resolution
 Intersections
of Gridlines are Referred to as Pixel Grid Nodes
 Pixel
Grid Node Locations are Recorded in Homogenous Coordinate Format:
(w;x,y,z)




2.
Translate & Rotate Pixel Grid
 Pixel
Grid Points Translated to Camera XYZ Location By Multiplying Each
Point by Translation Matrix
 Pixel
Grid Points Rotated to Camera Orientation By Multiplying Each
Point by Three Rotation Matrices




3.
Create Pixel Node Vectors
 Vectors
Created Between Focal Point of Camera and Pixel Grid Nodes

Vectors Represented in Terms of Plücker Line Coordinates




4.
Create Planar Intersection Points
 Intersection
Between All Vectors and Plane Can be Found
 Using
Projective Geometry, the Intersection of a Plane and a Line Creates
a Point




5.
Determine Pixel Areas
 Each
Pixel Node Intersection Point Corresponds to the Corner of a Pixel
Area




6.
Calculate Pixel Centroids
 Pixel
Centroid is the Average of the Four Corners of Pixel Area
 The
Centroid Represents the Coordinates that the Pixel Represents
in Space
 Error
Represented by Maximum Distance from Centroid to Area Vertex


