Camera Model

Principle

The camera model defines the transformation between image space coordinate system and pixel coordinate system.

  • Image space coordinate system: The origin is projection center. The Z axis points towards the viewing direction, X axis points to the right, Y axis points down.
  • Pixel coordinate system: The origin is the top left corner of the top left pixel. In other words, the coordinates of the top left pixel's center is (0.5, 0.5). The X axis points to the right, Y axis points down.

The notations are described below:

(X, Y, Z)        - point coordinates in the image space coordinate system

(u, v)          - projected pixel coordinates

(cx, cy)         - principal point offset

(K1, K2, K3)      - radial distortion coefficients

(P1, P2)        - tangential distortion coefficients

(B1, B2)        - affinity and non-orthogonality (skew) coefficients

(w, h)         - image width and height in pixels

f            - focal length

Equations of the transformation are described below :

x = X / Z

y = Y / Z

r = sqrt(x2 + y2 )

x' = x(1 + K1r2 + K2r4 + K3r6) + P1(r2+2x2) + 2P2xy

y' = y(1 + K1r2 + K2r4 + K3r6 ) + P2(r2+2y2) + 2P1xy

u = w * 0.5 + cx + x'f + x'B1 + y'B2

v = h * 0.5 + cy + y'f

LiMapper Internal Parameters File(*.xml)

<?xml version="1.0" encoding="UTF-8"?>  
<calibration>  
    <width>8256</width>  
    <height>6450</height>  
    <f>6771.25</f>  
    <ps>0.00436047</ps>  <!-- pixel size -->
    <cx>4.57016999999996</cx> 
    <cy>3.04289000000017</cy>  
    <k1>-0.0778992</k1>  
    <k2>0.0695091</k2>  
    <k3>-0.0223276</k3>  
    <p1>-2.68206e-5</p1> 
    <p2>0.000617037</p2>  
    <b1>6.06111\</b1>      
    <b2>-0.816488\</b2>  
</calibration>

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