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
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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
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1.
Define Pixel Grid
- Camera
Placed at World Coordinate System Origin
- Image
Plane Assumed to be at Unit Distance from Origin in Y-Direction
- 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)
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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
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3.
Create Pixel Node Vectors
- Vectors
Created Between Focal Point of Camera and Pixel Grid Nodes
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Vectors Represented in Terms of Plücker Line Coordinates
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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
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5.
Determine Pixel Areas
- Each
Pixel Node Intersection Point Corresponds to the Corner of a Pixel
Area
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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
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This
method tells the physical ground area seen by each pixel in the
video.
Expanding
this concept to track a vehicle is relatively simple. Vehicle tracking
features must be added that are parallel to the ground plane. (Typically,
the roof of the vehicle.)
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In
the image to the right, the blue plane indicates the ground plane
and the red indicates the feature tracking plane. |
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Setting
Up Environment for Planar Positioning:
- Vehicle
Must Have Trackable Features
- Vehicle
Drive Path Must be Planar
- Cameras
Must Cover All Possible Drive Areas
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Vehicle
Tracking Features
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Example
Camera Placements in Warehouse
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Setup
for Planar Positioning
- Camera
Properties Must be Precisely Defined
- Environment
Must be Accurately Mapped
- Tracking
Plane Must be Defined as the Plane the Tracking Features are in
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Using
Planar Positioning
- Tracking
Information is Displayed for Allowed Areas
- Areas
with Obstacles are Blacked Out
- Gridlines
Display the World Coordinates in the X and Y directions
- Pixel
Location of the Tracking Features is Correlated to the Range Data
Lookup Table
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