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

Figure 4

Iterative procedure to manipulate 1000 particles on the unit sphere according to Algorithm 1, where the weight terms of 𝜔(𝐱_𝑖,𝐱_𝑗) in (3) are set to be (5). The probability distribution for vertices of parameterized meshes is shown with colors on the unit sphere. Red parts show where the probability is high, and blue parts show where the probability is low. The figure (𝑡=0) shows initialized particles which are uniformly distributed on the unit sphere. Particles’ positions are shown after the 1st (𝑡=1), 2nd (𝑡=2), and 5th (𝑡=5) iterations are finished, respectively. Final positions of particles are shown by the most right figure from which it can be seen that more particles are located in red regions and less particles are located in blue regions.