MiCADangelo: Fine-Grained Reconstruction of Constrained CAD Models from 3D Scans

Conference: NeurIPS 2025 arXiv: 2510.23429 Code: None Area: Other Keywords: CAD reverse engineering, sketch constraints, cross-sectional slicing, differentiable extrusion optimization, parametric modeling

TL;DR

MiCADangelo emulates the reverse engineering workflow of human CAD designers: it extracts 2D patterns via multi-plane cross-section analysis, predicts constrained parametric sketches, and optimizes extrusion parameters, achieving for the first time complete parametric model reconstruction with sketch constraints in 3D CAD reverse engineering.

Background & Motivation

CAD reverse engineering—converting 3D scans (meshes) into parametric CAD models—is a critical step in manufacturing and product development. Existing deep learning methods fall into two categories, each with notable shortcomings:

Bottom-up methods (e.g., Point2Cyl): Starting from geometry to predict individual extrusion solids, preserving local detail, but producing outputs that are not fully parametric and cannot be seamlessly integrated into CAD software.

Top-down methods (e.g., CAD-SIGNet): Directly predicting sketch-extrusion sequence parameters from point clouds, yielding fully parametric outputs, but often dominated by large-scale structures at the expense of fine-grained geometric detail.

More critically, existing methods entirely ignore sketch constraints (e.g., parallel, perpendicular, tangent), which are central to CAD modeling—they encode design intent and govern how a model responds to edits.

The authors observe that human designers perform reverse engineering by: extracting 2D cross-sections → reconstructing profiles with parametric curves and applying constraints → extruding into 3D solids. MiCADangelo automates this process.

Method

Overall Architecture

Given an input 3D mesh \(\mathbf{M}\), MiCADangelo executes three sequential stages: 1. Sketch plane detection: Uniformly sampled cross-sectional planes along the x/y/z axes to identify key cross-sections. 2. Constrained sketch parametrization: Predicting parametric sketch primitives and constraints for closed loops within key cross-sections. 3. Differentiable extrusion optimization: Optimizing extrusion parameters per sketch to best fit the input mesh.

Key Designs

1. Sketch plane detection network: \(N\) equally spaced planes are sampled along each of the three axes (default: 40 per axis), yielding cross-sectional slices \(\{\mathcal{S}_i\}_{i=1}^N\). Each slice is projected into a binary image \(\mathbf{X}_i \in \{0,1\}^{128 \times 128}\), encoded via a ResNet34 backbone, augmented with three context embeddings (position index, axis identity, normalized parameters), and passed through a 4-layer 4-head Transformer encoder for global interaction. A binary classifier then predicts whether each slice constitutes a key sketch plane.

2. Constrained sketch parametrization network: Each closed loop in a key cross-section is rendered as a binary image, encoded by ResNet34, and passed into a Transformer encoder-decoder that predicts embeddings for \(n_p\) sketch primitives. Two prediction heads follow:

3. Parametrization head: Predicts primitive type (line segment / circle / arc) and geometric parameters (endpoints, center, radius, etc.).

4. Constraint prediction head: Predicts 13 constraint types between primitive pairs (coincident, concentric, equal, horizontal, vertical, parallel, perpendicular, tangent, etc.).

The network operates in a quantized space, pre-trained on the SketchGraphs dataset and fine-tuned on synthetic noisy closed-loop images.

1. Differentiable extrusion optimization: For each sketch \(\mathcal{K}_j\), anchor points \(\{\mathbf{r}_k\}\) are sampled along the loop boundary, and a shared learnable extrusion length \(h_j\) generates extrusion vectors \(\rho_k = \mathbf{r}_k + h_j \mathbf{v}_j\). Points \(\mathcal{Q}\) sampled on the mesh minimize the distance to the nearest extrusion vector: $\(\mathcal{L}_{extr} = \frac{1}{n_M} \sum_{l=1}^{n_M} d(\mathbf{q}_l, \rho_{min})^2 + \lambda \sum_{i,j} h_j^2\)$ Extrusion type (add/cut) is determined by the nesting level of the loop (outermost = add, alternating thereafter).

Loss & Training

• Sketch plane detection: Binary cross-entropy loss, trained for 20 epochs on the DeepCAD training set, learning rate \(10^{-4}\).
• Sketch parametrization: Pre-trained on SketchGraphs, fine-tuned for 50 epochs on synthetic noisy closed-loop images.
• Extrusion optimization: 200 gradient descent iterations, learning rate \(2 \times 10^{-4}\).
• Both networks share a ResNet34 encoder, first trained with the parametrization network, then fine-tuned during plane detection training.
• Optimizer: AdamW.

Key Experimental Results

Main Results (DeepCAD & Fusion360)

Method	DeepCAD CD↓	DeepCAD IoU↑	DeepCAD IR↓	DeepCAD ECD↓	Fusion360 CD↓	Fusion360 IoU↑	Fusion360 IR↓	Fusion360 ECD↓
DeepCAD	9.64	46.7	7.1	—	89.2	39.9	25.2	—
Point2Cyl	4.27	73.8	3.9	—	4.18	67.5	3.2	—
CAD-Diffuser	3.02	74.3	1.5	—	3.85	63.2	1.7	—
CAD-SIGNet	0.28	77.6	0.9	0.74	0.56	65.6	1.6	4.14
MiCADangelo	0.20	80.6	2.6	0.46	0.48	68.7	3.2	2.66

Complex Models and Constraint Robustness

Test Scenario	Method	CD↓	IoU↑	IR↓	ECD↓
Models with ≥4 loops	CAD-SIGNet	1.34	49.2	3.2	4.75
Models with ≥4 loops	MiCADangelo	0.37	68.3	4.1	2.04
Models with >2 extrusions	CAD-SIGNet	3.95	40.6	5.4	9.81
Models with >2 extrusions	MiCADangelo	0.46	64.8	3.0	2.27
Constraint deformation robustness	CAD-SIGNet	2.89	57.4	3.5	20.43
Constraint deformation robustness	MiCADangelo	0.38	81.1	4.3	1.29
CC3D real scans	CAD-SIGNet	2.90	42.6	4.4	8.68
CC3D real scans	MiCADangelo	1.69	50.8	2.2	5.93

Ablation Study

Experiment	Key Result	Remarks
Context embeddings for plane detection	F1: 0.296→0.870	Position/axis/normalization embeddings are critical
Cross-dataset plane detection	DeepCAD F1=0.870, Fusion360=0.820, CC3D=0.777	Good generalization
Sketch parametrization (SCD)	Davinci: 0.827, MiCADangelo: 0.283	Attributed to noisy closed-loop fine-tuning
Number of extrusion vectors	Performance saturates at 8 vectors	Minimal impact on inference time

Key Findings

1. Comprehensively surpasses SOTA on core metrics: MiCADangelo achieves a median CD of 0.20 on DeepCAD (vs. 0.28 for CAD-SIGNet) and IoU of 80.6% (vs. 77.6%).
2. Advantage is more pronounced on complex models: IoU improves by 19.1 percentage points on models with 4+ loops (68.3 vs. 49.2) and by 24.2 points on multi-extrusion models.
3. Core value of constraints: Constrained models maintain structural consistency after sketch editing (ECD 1.29 vs. 20.43), demonstrating that constraints are essential for editability.
4. Robustness to real scans: MiCADangelo outperforms CAD-SIGNet on CC3D real-world scans, improving IoU by 8.2 percentage points.

Highlights & Insights

• Human-inspired design workflow: Rather than pursuing end-to-end black-box reconstruction, MiCADangelo emulates the cross-section analysis → sketch reconstruction → extrusion workflow of human CAD designers, achieving both fine-grained accuracy and full parametrization.
• First introduction of sketch constraints into 3D CAD reverse engineering: Constraints not only enhance editability but also implicitly restrict the solution space, facilitating more accurate geometric reconstruction.
• Effective exploitation of cross-section views: By extracting geometric information from 2D cross-sections, the complex 3D problem is decomposed into multiple 2D image understanding tasks.
• Differentiable extrusion optimization: Casting extrusion parameter inference as a continuous optimization problem avoids the difficulty of discrete search.

Limitations & Future Work

• Only extrusion operations are supported (consistent with prior work); more complex CAD operations such as revolve and sweep are not handled.
• Extrusion direction is based on the sketch plane normal, limiting performance on models with non-axis-aligned extrusions.
• Complex sketch primitives such as B-splines are not supported.
• The invalid rate (IR) metric is slightly higher than that of CAD-SIGNet, as the latter benefits from test-time sampling of multiple candidates and selecting the best.
• Plane detection relies on uniform sampling (40 per axis), which may miss key cross-sections that are not axis-aligned.

Related Work & Insights

• Compared to CAD-SIGNet (top-down) and Point2Cyl (bottom-up), MiCADangelo combines the strengths of both paradigms.
• Sketch constraint prediction builds on Davinci (2D sketch parametrization) and improves robustness through noisy fine-tuning.
• The SketchGraphs dataset is leveraged to compensate for the absence of constraint annotations in DeepCAD and Fusion360.
• Insight: Decomposing complex 3D reconstruction into multiple 2D subproblems reduces learning difficulty and enables independent optimization of each module.

Rating

• Novelty: ⭐⭐⭐⭐⭐ (First constrained CAD reverse engineering; cross-section analysis is a novel perspective)
• Experimental Thoroughness: ⭐⭐⭐⭐⭐ (Multiple datasets, diverse scenarios, constraint robustness, real scans, comprehensive ablations)
• Writing Quality: ⭐⭐⭐⭐⭐ (Clear structure, rigorous formal definitions, intuitive comparison with human workflow)
• Value: ⭐⭐⭐⭐⭐ (A breakthrough contribution to the CAD reverse engineering field)

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