A Reliable Event-Driven Strategy for Real-Time Multiple Object Tracking Using Static Cameras

Algorithm 3

Transformation grid (TG) algorithm.

Input data:

  The image coordinates of point P(x_i,y_i).

  The TG-Cell point P laid in Cellⁱ = {P₁₁, P₂₁, P₂₂, P₁₂}.

  The real x-coordinate of point P₁₁ is called P_11-xr.

Calculated parameters:

  R_n: the iterated value of R after n tries.

  R₀: the initial value of R which equals 0.5.

  P_x1, P_x2: are calculated with equation (4) and by Cellⁱ

  points' image coordinates.

  x_th: the perpendicular distance in pixels from point

  P(x_i,y_i) to line P_x1, P_x2.

  P_xr: the real x-coordinate of Point P; it is the goal of

  this algorithm.

Algorithm:

  Start:

    for n = 0; R₀ = 0.5;

    if x_th for R₀ <= 1 pixel then R = R₀, and go to OUT

  Calculate R_n:

    n = n + 1

     R_n1 = R_n−1 + |R_n−1−R_n−2|* 0.5   // for n = 1;

     R_n1 = 0.75

     R_n2 = R_n−1 − |R_n−1−R_n−2| * 0.5    // for n = 1;

    R_n2 = 0.25

    if x_th for R_n1 > x_th for R_n2 then

        R_n = R_n1, and x_th = x_th for R_n1

    else

        R_n = R_n2, and x_th = x_th for R_n2

    if x_th <= 1 pixel then

        R = R_n, and go to OUT

    else

        go to Calculating R_n

  OUT:

    P_xr = P_11-xr + (P_12-xr – P_11-xr) * R