TACO-Net: Topological Signatures Triumph in 3D Object Classification

Conference: ECCV2026
Paper: ECCV paper page
Authors: Anirban Ghosh, Ayan Dutta; University of North Florida
Area: 3D Vision
Keywords: point cloud classification, topological data analysis, cubical persistent homology, directional filtrations, lightweight convolutional network

TL;DR

TACO-Net converts point clouds into fixed topological statistics from multiple grayscale voxel volumes and trains a lightweight 1D CNN to combine them, reaching 99.05% OA on ModelNet40, while the full pipeline including topological feature generation processes approximately 5.3 point clouds/second.

Background & Motivation

Point cloud classification identifies objects from unordered, unevenly sampled, and potentially incomplete geometric observations. PointNet aggregates pointwise features, PointNet++ introduces local neighborhoods, and DGCNN learns neighborhood relationships; these approaches primarily build shape representations from coordinates and local geometry. Other methods voxelize objects or render multiple views before applying deep networks. All must preserve category-discriminative shape information without becoming excessively sensitive to sample locations and noise.

Persistent homology offers a different perspective: instead of recording only where points occur, it tracks when connected components, loops, and cavities appear and disappear as a threshold changes. A topological descriptor alone, however, is not automatically a strong classifier. Scanning a shape from different directions or expanding around different centers reveals complementary structures, and useful combinations of their statistics still need to be learned. The paper therefore establishes a clear division: a fixed front end produces reusable shape descriptors, and a learned back end makes them discriminative.

Core Idea: use complementary grayscale filtrations to define different orders for observing a shape, compress their cubical persistent homology into fixed-length signatures, and learn higher-order combinations with a small 1D CNN without back-propagating through topology computation. The task is general 3D object classification; autonomous driving is an application mentioned in the motivation, not the exclusive experimental setting.

Method

Overall Architecture

The input is an object point cloud, and the output is a probability distribution over a closed set of categories. The cloud is converted into a binary voxel grid within its own axis-aligned bounding box, with a voxel occupied if it contains at least one point. Multi-filtration shape probing, cubical topological signatures, and signature convolutional classification then process it, following Figures 4 and 5 of the paper.

The first two stages have no learnable parameters and can be precomputed and cached. The final network processes a statistical vector with a fixed concatenation order, not the original point sequence or a three-dimensional convolution over the voxel grid.

%%{init: {'flowchart': {'rankSpacing': 24, 'nodeSpacing': 28, 'padding': 6, 'wrappingWidth': 400}}}%%
flowchart TD
    INPUT["Object point cloud"] --> VOXEL["Binary voxelization<br/>within its bounding box"]
    VOXEL --> FILTER["Multi-filtration shape probing<br/>Height, radial, and DEDS"]
    FILTER --> TOPO["Cubical topological signatures<br/>Persistence diagrams and statistics"]
    TOPO --> CNN["Signature convolutional classification<br/>Three-layer 1D CNN"]
    CNN --> OUTPUT["Object category probabilities"]

Key Designs

1. Multi-filtration shape probing: examine the same occupancy grid in different orders

A binary voxel grid records occupancy but does not directly describe how structures become connected. TACO-Net assigns grayscale values that determine when voxels enter a subsequent filtration. Height filtrations use 26 directions whose coordinates are drawn from -1, 0, and 1, excluding the zero vector. Occupied voxels receive distances to the corresponding hyperplane, while unoccupied voxels receive the maximum distance plus 1 and therefore enter later. Radial filtrations instead measure distance to a reference center, with up to 27 centers sampled from a regular three-dimensional grid inside the bounding box to probe structural organization around different locations.

Four additional filtrations are grouped as DEDS. Density counts occupied voxels within radius 1; dilation uses Manhattan distance to the nearest occupied voxel; erosion applies dilation after swapping occupied and unoccupied voxels. Signed distance assigns occupied voxels their Manhattan distance to the nearest unoccupied voxel minus 1, and assigns unoccupied voxels the negative distance to the nearest occupied voxel. These functions provide complementary information about local concentration, external distance, internal structure, and distances on both sides of a boundary.

These filtrations first produce grayscale volumes; they are not neural convolutional filters. Persistent homology subsequently thresholds each volume. The largest configuration contains 26 height, 27 radial, and 4 DEDS volumes. ModelNet10/40 retains only the first 18 radial centers: the first two slices grouped by x-coordinate, with centers ordered lexicographically within each slice. It therefore uses 48 volumes. The authors state that center count and voxel resolution are selected on training splits, so a fixed front end should not be interpreted as identical hyperparameters for every dataset.

2. Cubical topological signatures: compress variable-length structural events into fixed statistics

For each grayscale volume, voxels and their faces, edges, and vertices are added in increasing intensity order, producing nested cubical complexes. As the threshold increases, connected components merge, loops can emerge and become filled, and enclosed cavities can appear or disappear. Birth and death events are recorded separately for \(H_0,H_1,H_2\), corresponding to connected components, loops or tunnels, and enclosed cavities. This exploits the regular voxel structure without directly constructing a more complex point-set complex from every sample.

Persistence diagrams vary in size across objects and must be vectorized. Each homology dimension first contributes persistent entropy, which measures how dispersed the normalized lifetime distribution is. For the finite lifetimes included in the calculation, the paper defines:

\[ p_i=\frac{d_i-b_i}{\sum_j(d_j-b_j)},\qquad \rho(X)=-\sum_i p_i\log p_i. \]

Here \(b_i,d_i\) are birth and death thresholds. The formula explains the statistic, but the cached main text does not fully specify implementation handling of infinite lifetimes or empty diagrams; these details still require checking the supplementary code. Beyond entropy, amplitudes measure distance to the empty diagram. Wasserstein uses orders 1 and 2, Bottleneck uses the limiting case, Betti curves count active intervals and use two norms, persistence landscapes use layers 1 and 2 with two norms, and the heat kernel uses standard deviation 0.15 with two norms.

Across the three homology dimensions, this produces 3 entropy values and 6 Wasserstein, 3 Bottleneck, 6 Betti, 12 landscape, and 6 heat amplitudes: 36 values per grayscale volume. Betti curves and landscapes use 100 threshold samples, while the heat kernel uses 20. The full and ModelNet configurations consequently have the following lengths:

\[ D_{\mathrm{full}}=(26+27+4)\times36=2052,\qquad D_{\mathrm{ModelNet}}=(26+18+4)\times36=1728. \]

These statistics summarize lifetime distributions, prominent persistent structures, and topological activity across thresholds instead of relying on a single aggregate. However, finitely sampled directions followed by statistical compression do not inherit the invertibility guarantees of the complete Persistent Homology Transform. The cited theory motivates the design; it does not establish that the 1728-dimensional vector uniquely determines every shape.

3. Signature convolutional classification: learn descriptor combinations without relearning topology

The network uses three Conv1D layers with kernel sizes 3, 5, and 7, each followed by batch normalization and ReLU. The first two layers have 128 and 64 channels. The third has the category count on ModelNet, 40 channels on ScanObjectNN, and 32 on the two medical datasets. A fully connected layer with one output per category and a softmax produce category probabilities. The ModelNet40 model contains 0.72M learnable parameters.

Convolution operates on neighborhoods in the fixed-order vector of topological statistics, not spatially neighboring points. Successive layers combine statistics into discriminative representations, while feature generation remains outside gradient optimization. Classifier replacements show that the descriptors alone do not explain the full improvement: the best ModelNet40 features yield 81.35% OA with XGBoost and 62.20% with the authors' tested 2.2M-parameter Transformer, both substantially below this CNN. These comparisons support the tested configuration, not a universal claim that convolution outperforms Transformers.

A Worked Example

Figure 2 shows a ModelNet40 car containing 2048 points. After voxelization at size 0.05, permuting the input points does not change which cells are occupied. Scanning from the front and from the side nevertheless introduces structures in different orders, producing different persistence diagrams.

With the ModelNet configuration, the car produces 48 grayscale volumes, each summarized into 36 values across three homology dimensions. Their concatenation forms a 1728-dimensional vector, which passes through three convolutional layers and a 40-category classification head. This example follows the input in Figure 2 to explain the pipeline; it does not invent sample-specific confidence scores or topology measurements.

Loss & Training

The topological front end uses Python and giotto-tda, while the 1D CNN is implemented in MATLAB. Experiments use an Intel i9-12900K, 32 GB RAM, and an NVIDIA RTX 3060. Training uses Adam with initial learning rate \(10^{-3}\), batch size 128, and at most 1000 epochs, stopping early once training loss falls below 0.005. Unless stated otherwise, each configuration is trained 5 times and results are averaged.

The main text specifies softmax classification and the stopping threshold but does not explicitly give the loss formula. No additional topological loss or regularizer is inferred here. Only the classifier is optimized, and a separate classifier is trained for each dataset; evaluation on multiple datasets is not zero-shot transfer of one model.

Key Experimental Results

Main Results

OA is overall accuracy across test samples, whereas mAcc averages classwise accuracies; all accuracy values below are percentages. ModelNet40 uses voxel size 0.05 and 1728-dimensional features, and ModelNet10 uses the same feature length. Table 2 restricts ScanObjectNN comparisons to from-scratch supervised methods and does not support superiority over all pretrained approaches.

Dataset / condition	Metric	TACO-Net	Comparator	Comparator value	Source location
ModelNet40, standard test	OA / mAcc	99.05 / 97.97	RotationNet	97.37 / 96.29	Table 1
ModelNet10	OA / mAcc	99.52 / 99.52	Baseline not reproduced here	Not listed	Section 3.1 prose; appendix table reference unresolved
ScanObjectNN, OBJ_BG	OA	95.08	Mamba3D	94.49	Table 2
ScanObjectNN, OBJ_ONLY	OA	94.01	Mamba3D	92.43	Table 2
ScanObjectNN, PB_T50_RS	OA	91.87	Mamba3D	92.64	Table 2

On ModelNet40, the OA gain over RotationNet is 1.68 percentage points. On the hardest PB_T50_RS variant, TACO-Net is 0.77 percentage points below Mamba3D and ranks second in the table, not first. The paper separately reports ModelNet40 five-fold cross-validation mean OA of 97.49% with standard deviation 0.32. This is a different evaluation from the standard-split 99.05%, not its repeated-run uncertainty.

Ablation Study

The following ModelNet40 feature and network ablations come from Table 6; the full-model reference is from Table 1. H denotes height, R radial, and DEDS density, erosion, dilation, and signed distance filtrations.

Config	OA (%)	mAcc (%)	Note
Full model	99.05	97.97	1728 dimensions, three Conv1D layers
DEDS only	96.52	93.76	No height or radial features
R only	95.47	91.52	Radial features only
H only	98.29	96.38	Strong standalone height features
DEDS + H	98.82	97.33	No radial features
Entropy only	96.16	92.79	No amplitudes
First two Conv1D layers	98.18	95.93	Best input features retained
First Conv1D layer only	94.76	90.70	Best input features retained

Key Findings

• Height is the strongest individual feature family. Adding radial features to DEDS + H improves OA by 0.23 percentage points. The H-only full pipeline is reportedly 3.5 times faster, whereas entropy-only feature generation is 2.2 times faster; these speedups cover different stages.
• Finer voxels are not always better: voxel size 0.03 gives OA/mAcc of 98.61/96.96, and 0.07 gives 98.30/96.16, both below the 0.05 setting. Finer grids also increase topological computation cost.
• Corruption evaluation follows ideas from ModelNet40-C but uses 2048 × 3 point clouds without normalization after corruption. It additionally tests uniform random removal of 10%/30% of points at low/high severity, so it is not an identical standard protocol.
• Low-severity impulse corruption reduces OA to 52.88%. Under high-severity rotation, the non-augmented model reaches 49.39%; adding corrupted copies of randomly selected 20% of training instances raises it to 96.11%. The former uses a clean-trained checkpoint selected by clean test accuracy, not the default five-run average condition.

Highlights & Insights

• The most reusable idea is separating shape description from discriminative learning. Cached topological vectors permit repeated classifier training and help distinguish a weak descriptor from an unsuitable classifier.
• Directional height filtrations encode the timing of structural events, not merely an object's total hole count. Their strong standalone performance illustrates how geometric information enters a representation through topology over a changing threshold.
• The feature budget is explicit: filtration count and statistic types directly control vector length. Table 6 supports reducing features while retaining high accuracy, although deployment must still measure front-end cost.

Limitations & Future Work

• The authors identify topological front-end acceleration as future work. At voxel size 0.05, feature generation and the full pipeline process approximately 5.3 point clouds/second; 16,454 point clouds/second is classifier-only throughput with features already available. The 2.50-minute training time likewise does not cover all preparation from raw clouds.
• Topological stability does not guarantee robustness to arbitrary rotations, outliers, or abrupt occupancy changes. Fixed directions, axis-aligned bounding boxes, and finite resolution introduce pose and discretization dependencies, with impulse corruption and severe rotation providing direct counterexamples.
• Filtration families and vectorization rules are reused across datasets, but radial center count, voxel resolution, and some network channel counts change. Claiming no dataset adaptation whatsoever would overstate the actual setup.
• The cache contains unresolved appendix references and lacks the corresponding tables and some preprocessing details. Standard-test averages across five training runs also differ notably from the five-fold result. Data splits, hyperparameter selection, feature normalization, and supplementary implementation should be checked before asserting either the presence or absence of leakage from the high accuracy alone.
• Separate evaluation on multiple datasets does not establish cross-domain zero-shot generalization or full-scene autonomous-driving capability. Faster persistent homology, pose augmentation, and fusion with local geometric features are plausible extensions.

Related Work & Insights

• vs PointNet / PointNet++ / DGCNN: These models learn from point coordinates or neighborhoods, whereas TACO-Net fixes the shape descriptor before learning classification. Its front end is interpretable and cacheable, but discretization and statistical compression can discard fine local information.
• vs RotationNet: RotationNet performs classification through multiple views and viewpoint estimation, while TACO-Net uses topological signatures of voxelized point clouds. Table 1 supports the benchmark accuracy difference, but their representations and computation pipelines differ.
• vs TopoRec: TopoRec targets large-scale point cloud recognition rather than the category-classification task here. The authors report approximately 36% ModelNet40 OA with its closest-vector approach and approximately 69% after replacing the classifier with their CNN, suggesting that both signature design and the learned back end matter.
• Persistent Homology Transform: Shape-identification theory for the complete transform motivates directional scanning. Understanding approximation errors after restricting directions and compressing diagrams into finite statistics remains an important research question.

Rating

• Novelty: 4/5. An effective combination of complementary cubical filtrations, rich topology statistics, and a lightweight CNN, with established precedents for the individual components.
• Experimental Thoroughness: 4/5. Multiple datasets, feature and network ablations, and corruption tests, but some protocol and appendix details are unavailable in the cache.
• Writing Quality: 3/5. The main pipeline is clear, while unresolved references and universality claims require careful reading against the actual hyperparameters.
• Value: 4/5. Strong evidence for fixed topological descriptors with a small learned classifier, although front-end throughput limits deployment value.