Particle System Based Adaptive Sampling on Spherical Parameter Space to Improve the MDL Method for Construction of Statistical Shape Models

Algorithm 1

An iterative gradient descent based method to minimize the energy of the particle system defined in (3).

Initialization:  𝐱⁰_𝑖  (𝑖=1,2,…𝑁),  𝜆_𝑖=𝜆_Max  (𝑖=1,2,…𝑁),  𝜆_Min,  𝑇.

𝐸_old=𝐸(𝐱⁰₁,𝐱⁰₂,…𝐱⁰_𝑁)

FOR 𝑡=0→𝑇  DO

 FOR   𝑖=1→𝑁  DO

    LOOP

    𝐲^′←𝐱^𝑡_𝑖−𝜆_𝑖𝜕𝐸𝜕𝐱_𝑖

    𝐲←𝐲^′=1

    𝐸_new=𝐸…,𝐱^𝑡_𝑖−1,𝐲,𝐱^𝑡_𝑖+1,…

    IF  𝐸_new<𝐸_old  THEN

      𝐱^𝑡_𝑖←𝐲

      𝐸_old←𝐸_new

      BREAK LOOP

    ELSE

      𝜆_𝑖←𝜆_𝑖/2

    END IF

    IF  𝜆_𝑖<𝜆_Min  THEN

      𝜆_𝑖←𝜆_Min

      BREAK LOOP

    END IF

    END LOOP

  END FOR

END FOR