abspy 0.1.0

A Python tool for 3D adaptive binary space partitioning and beyond

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Introduction

abspy is a Python tool for 3D adaptive binary space partitioning and beyond: an ambient 3D space is adaptively partitioned to form a linear cell complex with pre-detected planar primitives in a point cloud, where an adjacency graph is dynamically obtained. The tool is implemented to support compact surface reconstruction initially, but can be extrapolated to other applications as well.

Key features

• Manipulation of planar primitives detected from point clouds
• Linear cell complex creation with adaptive binary space partitioning (a-BSP)
• Dynamic BSP-tree (NetworkX graph) updated locally upon insertion of primitives
• Support of polygonal surface reconstruction from graph cuts
• Compatible data structure with Easy3D on point clouds, primitives, cell complexes and surfaces
• Robust Boolean spatial operations underpinned by the rational ring from SageMath's exact kernel

Installation

Install requirements

All dependencies except for SageMath can be easily installed with PyPI:

pip install -r requirements.txt

Optionally, install trimesh and pyglet for benchmarking and visualisation, respectively:

pip install trimesh pyglet

Install SageMath

For Linux and macOS users, the easiest is to install from conda-forge:

conda config --add channels conda-forge
conda install sage

Alternatively, you can use mamba for faster parsing and package installation:

conda config --add channels conda-forge
conda install mamba
mamba install sage

For Windows users, you may have to build SageMath from source or install all other dependencies into a pre-built SageMath environment.

Install abspy

abspy can be found and installed via PyPI:

pip install abspy

Quick start

Here is an example of loading a point cloud in VertexGroup (.vg), partitioning the ambient space into candidate convexes, creating the adjacency graph and extracting the outer surface of the object. For the data structure of a .vg file, please refer to VertexGroup.

import numpy as np
from abspy import VertexGroup, AdjacencyGraph, CellComplex

# load a point cloud in VertexGroup 
vertex_group = VertexGroup(filepath='points.vg')

# normalise the point cloud
vertex_group.normalise_to_centroid_and_scale()

# retrieve planes, bounds and points from VertexGroup
planes, bounds, points = np.array(vertex_group.planes), np.array(vertex_group.bounds), np.array(vertex_group.points_grouped, dtype=object)

# additional planes to append (e.g., the bounding planes)
additional_planes = [[0, 0, 1, -bounds[:, 0, 2].min()]]

# initialise CellComplex from planar prititives
cell_complex = CellComplex(planes, bounds, points, build_graph=True, additional_planes=additional_planes)

# refine planar primitives
cell_complex.refine_planes()

# prioritise certain planes
cell_complex.prioritise_planes()

# construct CellComplex 
cell_complex.construct()

# print info on the cell complex
cell_complex.print_info()

# visualise the cell complex (only if trimesh installation is found)
cell_complex.visualise()

# build adjacency graph of the cell complex
graph = AdjacencyGraph(cell_complex.graph)

# apply random weights
# could instead be the predicted probability for each convex being inside the object
weights_list = np.array([random.random() for _ in range(cell_complex.num_cells)])
weights_list *= cell_complex.volumes(multiplier=10e5)
weights_dict = graph.to_dict(weights_list)

# assign weights to n-links and st-links to the graph
graph.assign_weights_to_n_links(cell_complex.cells, attribute='area_overlap', factor=0.1, cache_interfaces=True)
graph.assign_weights_to_st_links(weights_dict)

# perform graph-cut
_, _ = graph.cut()

# save surface model to an obj file
graph.save_surface_obj('surface.obj', engine='rendering')

Misc

• Why adaptive?

To avoid redundant partitioning, the adaptive strategy only allows intersecting spatially correlated primitives. This spatial correlation is described by intersection tests between the axis-aligned bounding box (AABB) of a primitive and the cells in the leaf nodes of the BSP tree.

Adaptive space partitioning can significantly reduce computations for cell complex creation, compared to an exhaustive partitioning strategy. The excessive number of cells from the latter not only hinders computation but also inclines to defective surfaces (if any) on subtle structures where inaccurate labels are more likely to be assigned.

• How can abspy be used for surface reconstruction?

With the cell complex constructed and its adjacency maintained, surface reconstruction can be addressed by solving a binary labelling problem that classifies each cell as being inside or outside the object. The surface, therefore, exists in between adjacent cells where one is inside and the other is outside --- exactly where the graph cut is performed. Points2Poly wraps abspy for building surface reconstruction. For more information on this Markov random field formulation, read this paper.

License

MIT

Citation

If you use abspy in a scientific work, please cite:

@article{chen2021reconstructing,
  title={Reconstructing Compact Building Models from Point Clouds Using Deep Implicit Fields},
  author={Chen, Zhaiyu and Khademi, Seyran and Ledoux, Hugo and Nan, Liangliang},
  journal={arXiv preprint arXiv:2112.13142},
  year={2021}
}