Topo-PCN / Projects

TOPO-PCN / 3D DEEP LEARNING

Mind
the Gap.

Complete the shape.
Keep the hole.

Reconstruct 3D geometry. Preserve structure.PyTorch / GUDHI · Learned topology fusion.

Explore the point cloud ↓Code ↗
BENCHMARK EXPLORER 01 / 03
Complete targetLoading sample…

DRAG TO ROTATE · SCROLL TO ZOOM · ARROW KEYS

Explore paired benchmark inputs and complete targets.

THE QUESTION

Can we reconstruct missing geometry
without erasing the topology?

↘

01 / WHY TOPOLOGY

What is missing
is part of the shape.

Geometric closeness alone does not tell the whole story. Controlled holes make structural errors visible, creating a testbed for completion models that need to preserve more than the surface.

Original presentation airplane point cloud with a hole marked by a magenta arrow and yellow circle
01 A controlled hole in an airplane point cloud.
Original presentation, slide 11.
Original H0 and H1 persistence diagram with birth and death axes and persistent H1 features away from the diagonal
02 Persistent homology describes structure across scales.
Original presentation, slide 12.

02 / THE APPROACH

Geometry meets
a topology descriptor.

Topo-PCN adds a small learned topology branch to a PCN-style network. The decoder receives geometric features together with a descriptor of the input’s persistent structure.

01 / ENCODE

Partial point cloud

PointNet-style layers encode the incomplete geometry into a global representation.

points → geometric code
02 / DESCRIBE

Topology vector

A three-value persistent-homology descriptor passes through a learned projection.

3 values → 32 features
03 / COMPLETE

Fuse & decode

Concatenate both representations, then reconstruct a coarse-to-fine point cloud.

joint code → completed points

03 / RESULTS

A better balance
around the hole.

In the presentation’s airplane experiment, Topo-PCN reduces hole-region error relative to the PCN-style baseline, with a small increase in global Chamfer distance.

TOPO-PCN vs. BASELINE19.9%

lower Hole CD

0.3699 → 0.2962
Computed from the reported values.
Lower is better for both metrics.
Airplane completion · validation metrics
ModelValidation CD ↓Hole CD ↓
Baseline-PCN0.0012370.3699
Topo-PCN OURS0.0012560.2962
PointAttention0.0045000.1648

Compare global Chamfer distance and local hole-region error across three completion models.

View the original results table ↗

Airplane experiment · 80/20 split · Adam · learning rate 10⁻⁴ · 20 epochs.

Original Topo-PCN completion visualization with input points, prediction points, and highlighted hole regions
Topo-PCN completion visualization from slide 21. Input, prediction, and hole-region annotations are retained from the original figure.

CODE / DATA

Look inside
the project.

Explore the benchmark and three PyTorch completion pipelines.

Code ↗
Benchmark data ↗