title: Condition to check if two planes form the boundary of the same object
body: <p><a href="https://i.stack.imgur.com/2DUfO.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/2DUfO.png" alt="enter image description here"></a>I am trying to figure out an algorithm to determine if the planes detected by a depth sensor can be said to be part of the same 3d object.</p>
  
  <p>I was reading a paper "Plane-Based Optimization of Geometry and Texture for RGB-D Reconstruction of Indoor Scenes" by C. Wang and X. Guo where they where they present a novel approach of adaptive planes. They essentially use 3 conditions:
  1. Angle between two plane normals are small:
  2. Average distance between two planes is small:
  3. Angle between the ray connecting two plane centers and each plane normal is as close as possible to 90◦</p>
  
  <p>I have com up with the following two conditions:
  1. The normals for the two planes should be perpendicular to each other. (I am making an assumption here that the 3D object is a cuboid).
  2. Average distance between two planes is small. (from the paper)</p>
  
  <p>What other conditions could be necessary and sufficient to conclude this? Any other research papers or documentation for this would greatly help.</p>