A Joint Learning Approach to Face Detection in Wavelet Compressed Domain

Algorithm 1

The AdaBoost algorithm [22].

Input: sequence of 𝑁 labeled examples (𝑥₁,𝑦₁),…,(𝑥_𝑛,𝑦_𝑛)

   Distribution 𝐷 over 𝑁 examples

   Weak learning algorithm WeakLearn

   integer 𝑇 specifying number of iterations

Initialize the weight vector 𝑤¹_𝑖=𝐷(𝑖) for 𝑖=1,…,𝑁

Do for  𝑡=1,2,…,𝑇

  (1) Set 𝑝^𝑡=𝑤^𝑡/∑^𝑁_𝑖=1𝑤^𝑡_𝑖

  (2) Call WeakLearn, providing it with the distribution 𝑝^𝑡; get back a hypothesis ℎ_𝑡: 𝑋→[0,1]

  (3) Calculate the error of ℎ_𝑡∶𝜀_𝑡=∑^𝑁_𝑖=1𝑝^𝑡_𝑖ℎ_𝑡(𝑥_𝑖)−𝑦_𝑖

  (4) Set 𝛽_𝑡=𝜀_𝑡/(1−𝜀_𝑡)

  (5) Set the new weight 𝑠 vector to be 𝑤_𝑡^𝑡+1=𝑤^𝑡_𝑖𝛽^{1−|ℎ𝑡(𝑥𝑖)−𝑦𝑖|}_𝑡

Output the hypothesis

      ℎ_𝑓(𝑥)=1when^𝑇_𝑡=11log𝛽_𝑡ℎ_𝑡(𝑥)≥12^𝑇_𝑡=11log𝛽_𝑡0otherwise