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Region Adjacency

This repository implements region adjacency matrix calculation using NumPy, PyTorch, and CUDA.

A region adjacency matrix indicates which regions are adjacent to each other.

For example, let's consider a 4x4 labeled image (typically from segmentation):

[[0, 0, 1, 1],
 [0, 1, 1, 1],
 [2, 2, 1, 3],
 [2, 2, 3, 4]]

This image has 5 classes (ranging from 0 to 4), so the shape of the region adjacency matrix is 5x5. Using 4-connectivity (immediate neighbors up, down, left, and right), the resulting matrix is:

[[0, 1, 1, 0, 0],
 [1, 0, 1, 1, 0],
 [1, 1, 0, 1, 0],
 [0, 1, 1, 0, 1],
 [0, 0, 0, 1, 0]]

Note that all diagonal elements are zero, and adjacent regions are marked as one.

Usage

There are 4 functions in region_adjacency.py.

  • region_adjacency_numpy_loop: A Simple loop-based NumPy version which is very slow.
  • region_adjacency_numpy: A vectorized NumPy version.
  • region_adjacency_torch: A vectorized PyTorch version, similar to the NumPy version.
  • region_adjacency_torch_cpp: A CUDA version which is very fast.

For detailed usage, please refer to the docstrings of the functions.

Benchmark

The following table shows the average time used by different functions.

Experimental Setup

Inputs

  • Batch size = 8
  • Height = Width = 512
  • Number of labels = 256
  • connectivity = 4-connectivity

Software

  • PyTorch version: 2.3.0
  • NumPy version: 1.26.1
  • CUDA version: 12.1

Hardware

  • CPU: Intel Core i9-13900K
  • GPU: NVIDIA GeForce RTX 4090
Function Device Avg Time (ms) Speedup
region_adjacency_numpy_loop CPU 309.36 1
region_adjacency_numpy CPU 10.03 30.84
region_adjacency_torch CPU 2.05 150.9
region_adjacency_torch GPU 7.15 43.27
region_adjacency_torch_cpp GPU 0.153 2022

License

This project is licensed under the MIT License.