Reinforced AdaBoost Learning for Object Detection with Local Pattern Representations

Algorithm 1

Proposed update procedure of a classifier based on a reinforced Adaboost learning.

𝑁_pos: Number of positive samples, 𝑁_neg: Number of negative samples

Γ^pos_𝑖: LPR of ith positive sample, Γ^neg_𝑖: LPR of ith negative sample

𝑦_𝑖∈{+1,−1}: labels (+1: positive, −1: negative)

(1) Initialize sample weights

           𝑤¹_𝑖=12𝑁_pos,12𝑁_neg

(2) For 𝑡=1∶𝑇 do

 (a) Generate histograms of LPR from positive samples and negative samples

     𝑔^pos_𝑡(𝐱,𝛾)=∑_𝑖𝑤^𝑡_𝑖𝐼Γ^pos_𝑖(𝐱)=𝛾𝐼(𝑦_𝑖=1)

     𝑔^neg_𝑡(𝐱,𝛾)=∑_𝑖𝑤^𝑡_𝑖𝐼Γ^neg_𝑖(𝐱)=𝛾𝐼(𝑦_𝑖=−1)

 𝐼(⋅): indicator function that takes 1 if the argument is true and 0 otherwise

  (b) Compute error rate

       𝜀(𝐱)=∑_𝛾min𝑔^pos_𝑡(𝐱,𝛾),𝑔^neg_𝑡(𝐱,𝛾)

  (c) Select the best pixel location with the smallest error rate

        𝐱_𝑡=argmin_𝐱𝜀_𝑡(𝐱),if𝑊_𝑡<𝑛argmin_{𝐱∈𝑊𝑡}𝜀_𝑡(𝐱),else

 𝑛: the maximum number of pixel locations allowed

 𝑊_𝑡: the set of pixel locations already chosen before, 𝑊_𝑡=𝑊_𝑡−1∪𝐱_𝑡

  (d) Create a lookup table for the weak classifier of pixel location 𝐱_𝑡

      ℎ_𝑡𝛾=𝑔^pos_𝑡𝐱_𝑡,𝛾⋅𝑃_pos−𝑔^neg_𝑡𝐱_𝑡,𝛾⋅𝑃_neg𝑔^pos_𝑡𝐱_𝑡,𝛾⋅𝑃_pos+𝑔^neg_𝑡𝐱_𝑡,𝛾⋅𝑃_neg,

         𝑃_pos=∑_𝑗∈pos𝑤^𝑡_𝑗∑_𝑖𝑤^𝑡_𝑖,𝑃_neg=∑_𝑗∈neg𝑤^𝑡_𝑗∑_𝑖𝑤^𝑡_𝑖

  (e) Update the sample weights & Normalization

        𝑤_𝑖^𝑡+1=𝑤^𝑡_𝑖exp−𝑦_𝑖ℎ_𝑡Γ_𝑖(𝐱)𝑍_𝑡,

        𝑍_𝑡=∑^𝑁_𝑖=1𝑤^𝑡_𝑖exp−𝑦_𝑖ℎ_𝑡Γ_𝑖(𝐱)

(3) Obtain pixel classifier of a single pixel location x

          𝑝_𝐱(𝛾)=∑^𝑇_𝑡=1ℎ_𝑡(𝛾)𝐼(𝐱=𝐱_𝑡)

Constructed strong classifier

         𝐻(Γ)=sign∑_𝐱𝑝_𝐱(Γ(𝐱))