Region_Growing_and_Region_Merging_Segmentation

Region Growing Segmentation

• PROBLEM

  • 𝑓(𝑥,𝑦) : input image (shape 𝑚 𝑥 𝑛)
  • 𝑆(𝑥,𝑦) : 1s at seed point and 0s elsewhere (shape 𝑚 𝑥 𝑛)
  • 𝑄 : predicate to apply at each location (𝑥,𝑦)

• SOLUTION

  • Find all connected components in 𝑆(𝑥,𝑦) and reduce each connected component to one pixel; label all such pixels found as 1. All other pixels in 𝑆 are labeled 0
  • Form an image 𝑓_𝑄 such that at each point (𝑥,𝑦), 𝑓_𝑄(𝑥,𝑦)=1 if the input image satisfies a given predicate,𝑄, at those coordinates, and 𝑓_𝑄(𝑥,𝑦)=0 otherwise.
  • Let 𝑔 be an image formed by appending to each seed point in 𝑆 all the 1-valued points in 𝑓_𝑄 that are 8-connected to that seed point.
  • Label each connected component in 𝑔 with a different region label (e.g.,integers or letters). This is the segmented image obtained by region growing.

• 8-connected neighbors

  

Region Spliting and Merging Segmentation

• PROBLEM

  • 𝑓(𝑥,𝑦) : input image (shape 𝑚 𝑥 𝑛)
  • 𝑄 : predicate to apply at each location (𝑥,𝑦)

• SOLUTION

  • Split into four disjoint quadrants any region Ri for which Q(R_i) = FALSE.
  • When no further splitting is possible, merge any adjacent regions Rj and Rk for which Q(R_j U R_k) = TRUE.

• Quadtree