smrfeld / chamfer-viz

Visualization of Chamfer distance between point clouds using Dash app

Chamfer distance visualization

Visualization of the Chamfer distance between two point clouds using dash app in both Python and Javascript.

https://www.oliver-ernst.com/chamfer-viz/

Running

Javascript

Navigate to the js directory and run using VSCode's Live Server extension or any other web server of your choice. For example:

cd js
python -m http.server

Python

Navigate to the python directory and install the requirements:

pip install -r requirements.txt

Then run the app:

python app.py

Optionally: specify the port with --port flag or debug mode with --debug flag.

Explanation

1. Given two sets of points or shapes, usually referred to as Set A and Set B.
2. For each point in Set A, find the closest point in Set B and calculate the distance between them.
3. For each point in Set B, find the closest point in Set A and calculate the distance between them.
4. Sum up all these distances from steps 2 and 3 to obtain the Chamfer distance.

Mathematically, the Chamfer distance can be expressed as:

$$Chamfer distance = Σ(min(dist(A_i, B_j)) + Σ(min(dist(B_i, A_j)))$$

Where:

A_i represents a point in Set A. B_j represents a point in Set B. dist(A_i, B_j) is the distance between point A_i and its closest point in Set B. dist(B_i, A_j) is the distance between point B_i and its closest point in Set A.

Implementation

Chamfer distance uses a KDTree. A KDTree is a data structure that organizes points in a way that enables fast nearest-neighbor queries. Computing the structure for Set B makes it faster to find the nearest neighbors in Set B for each point in Set A (and vice versa).

The use of the KDTree data structure significantly speeds up the computation of nearest neighbors for each point in Sets A and B. Without KDTree, you would need to perform a brute-force search, which can be computationally expensive, especially for large point sets. KDTree organizes the points in a way that allows for efficient nearest-neighbor queries and is commonly used in computational geometry and various data science tasks.

It's important to note that while KD-Trees offer efficient nearest neighbor and range search capabilities, their performance can degrade for very high-dimensional data (often referred to as the "curse of dimensionality"). In such cases, other data structures like ball trees or approximate nearest neighbor algorithms may be more suitable. Nevertheless, KD-Trees remain a valuable tool for solving a wide range of problems involving multi-dimensional data.

References

• KDtree in JS

• Basic Chamfer distance implementation

  import numpy as np
  from scipy.spatial import KDTree
  
  def chamfer_distance(A, B):
      """
      Computes the chamfer distance between two sets of points A and B.
      """
      tree = KDTree(B)
      dist_A = tree.query(A)[0]
      tree = KDTree(A)
      dist_B = tree.query(B)[0]
      return np.mean(dist_A) + np.mean(dist_B)