Fast Regristration for Cross-Source Point Clouds by Using Weak Regional Affinity and Pixel-wise Refinement

Paper

• Fast Regristration for Cross-Source Point Clouds by Using Weak Regional Affinity and Pixel-wise Refinement
• PhD thesis - Cross-source point cloud matching by exploring structure property

Motivation

• fusion of cross-source point clouds are challenging since they contain mixture of various differences (density, noise, outliers, viewpoint changing…)

• existing regristration methods assume two point clouds being regristered are in strong structure consistency

Keypoints

point cloud regristration problem → tensor optimization problem

• the weak regional affinity and pixel-wise refinement
  • are used to maintain the global and local information of 3D point clouds, respectively
    • assemble weak regional affinity into three-order tensor (3D array)
    • assemble pixel-wise refinement into first-order tensor (1D array)
  • are intergrated into an interative tensor-based regristration algorithm
    • three-order tensor and first-order tensor are integrated into a tensor optimization framework
• two iterative process: Expectation-maximization (EM)
  • optimization for the correspondence X (E step)
  • optimizations for geometric transmoration T (M step)
  • iteratively update X and T until convergence

Proposed method (Geometric Constraint Tensor-based registration, GCTR)

Pixel-wise refinement & weak regional affinity are used to store the information of point cloud. Different to previous separated streams, coaffinity search and pixel-wise refinement are unified together and jointly considering both local and global information in one unified process.

• pixel-wise refinement is the potential point-to-point correspondence
  • in the representation of H_ii’
  • point cloud C₁ has N₁ points and point cloud C₂ has N₂ points
  • H_ii’ is a N₁xN₂ correspondent point similarity matrix
  • H_ii’ = exp(-dist(f_i, f_i’)); dist is Euclidean distance
  • H_ii’ is the similarity of point i in C₁ and point i’ in C₂
  • each descriptor f_i is in 3D point coordinate representation
  • store into first-order tensor (H_ii’ → H_{(i + i’x N1)})
  • store local information
    
• weak regional affinity is the potential triplet-to-triplet correspondence
  • triplet points are used to represent weak salient structure of cross-source point cloud
  • triplet points are selected as large triangles
  • selection of triplet point: satisfy wide baseline strategy
  • three edges of the triangle are large than 50% of the overlapping 3D containing voxel’s the diameter
  • randomly select N₁N₂ triangles in C₁ (for implementation)
  • H_{ii’jj’kk’} is in the size of (N₁N₂)³
  • point (i, j, k) and point (i’, j’, k’) are triplet points with correspondent relations
  • H_{ii’jj’kk’} = exp(-dist(f_ijk, f_i’j’k’))
  • each descriptor f_ijk contains three cosine value of three inner angles in the triangle (cosine similarity)
  • store into three-order tensor
  • store global information
    
• Power iteration solution
  • for cross-source point cloud registration
  • two iterative process: optimizations for the correspondence X and geometric transmoration T
  • iteratively update X and T until convergence

Observation from experiments

• ICP shows some ability in aligning the cross-source point clouds when there is no scale variation and the initialization is very well and no large disorganized outliers.

I have some questions about this paper

• what does wide baseline strategy means?
• how H_{ii’jj’kk’} actually works?
• definition of the large traiangle