A Real-Time Optical Tracking and Measurement Processing System for Flying Targets

Algorithm 1

Multiple interest points location based on 2D contour model.

Input: 2D shape model 𝐂^𝐵, real-time contour 𝐂^𝑅 with discrete sampling sets expression 𝐱_𝑏(𝑥_𝑏,𝑦_𝑏,1),𝐱_𝑟(𝑥_𝑟,𝑦_𝑟,1)

Input: model interest point sets 𝐗_𝑏

Output: interest point sets 𝐗_𝑟 in the real-time image

(1) // initial registration

(2) Decide whether 𝐂^𝐵 and 𝐂^𝑅 are mirrored or not. if mirrored, flip them. end if

(3) Compute the initial registration relationship 𝐻_𝑠(𝑠,𝜃,𝐭) on the hypothesis of similarity transformation, centroids

𝐜(𝐂^𝐵) and 𝐜(𝐂^𝑅), included angle between main axis with 𝑥 axis 𝛼(𝐂^𝐵) and 𝛼(𝐂^𝑅) by moment of inertia, and contour

perimeter 𝑝(𝐂^𝐵) and 𝑝(𝐂^𝑅), so

    scale 𝑠=𝑝(𝐂^𝑅)/𝑝(𝐂^𝐵); rotation angle 𝜃=𝛼(𝐂^𝑅)/𝛼(𝐂^𝐵); translation vector 𝐭𝟏=𝑥_𝑟−𝑠𝑅𝟎^𝑇𝑇𝐱_𝑏.

(4) // iterative optimization

(5) Iteration frequency 𝑘∶=0.

(6) Change 𝐱_𝑏 to 𝐱^𝑘_𝑏 according to initial registration relationship 𝐻_𝑠

(7) Find the nearest point pairs [4] by ass(𝑖, 𝑗) = FANN(𝐱_𝑟,𝐱^𝑘_𝑏) where 𝑖 and 𝑗 are the indexes of the contour sampling

points, and size is the function for capacity computing. The distance of the nearest point pairs 𝑑_𝑘 is computed by

(*), and the homograph 𝐻_𝑘 is estimated with RANSAC.

                  𝑑_𝑘=∑^{size(𝐱𝑟)}_{𝑖=1,ass𝑖,𝑗}𝐱_𝑟(𝑖)−𝐱^𝑘_𝑏(𝑗)²     (*)

(8) if   𝑘≥10 or Δ𝑑=𝑑_𝑘−𝑑_𝑘−1<𝜀

(9) Terminate the iteration, optimized 𝐻 is as (**), 𝐗_𝑟=𝐻𝐗_𝑏.

                    𝐻=∏^𝑘_𝑖=0𝐻_𝑖𝐻_𝑠    (**)

(10) else  𝑘∶=𝑘+1,𝐱^𝑘_𝑏=𝐻_𝑘−1𝐱_𝑏^𝑘−1, goto (7).

(11) end if