Research map / 3D vision / Face and shape

Training-free Spatially Grounded Geometric Shape Encoding

NeurIPS 2026 · 3D vision › Face and shape · approach: Primitive-based shape abstraction

Read the paperCheck your idea against 108,967 papers

AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.

Proposes XShapeEnc, a training-free encoding of spatially grounded 2D shapes that projects normalized geometry and a harmonic pose field onto Zernike bases, with frequency propagation and a joint phase-modulation scheme.

Problem

Encoding arbitrary spatially grounded 2D geometric shapes into compact, invertible, task-agnostic representations; existing encodings are task-specific, shape-type restricted, or require training.

Approach

Decompose a shape into unit-disk geometry (projected onto orthogonal Zernike basis with a radial/angular frequency propagation) and a pose (encoded as a harmonic pose field projected onto Zernike modes), then fuse geometry and pose via phase modulation with a tunable emphasis parameter beta.

Key results

• On Mendeley shape retrieval, XShapeEnc (Mag.) achieves mAP 0.91 vs 0.73 for the best training-required baseline ShapeEmbed.
• On Singapore topological relation classification, XShapeEnc reaches 0.760 accuracy vs 0.706 for Space2Vec and 0.702 for Poly2Vec.
• On target region control, XShapeEnc reports SDR 17.62, STOI 0.98, PESQ 4.38, above ShapeEmbed (15.37 SDR).

Surprising findings

• On MPEG-7, non-pretrained baselines drop while pretrained models (ResNet18, ViT, CLIP) gain, attributed to semantic correlation with ImageNet.

Limitations

• Pose encoding invertibility requires encoding length at least the number of pose parameters; geometry reconstruction error grows with shape complexity.
• Joint geometry-pose encoding cannot recover geometry or pose from the joint code alone.
• Rotation-variant features are not ideal for retrieval; magnitude features needed for rotation invariance.

Experimental setup

Datasets: XShapeCorpus Mendeley 2D shape dataset MPEG-7 CE-Shape-1 Part B OpenStreetMap New York and Singapore

Benchmarks: Mendeley 2D shape dataset MPEG-7 CE-Shape-1 Part B OpenStreetMap Singapore/New York topological relation synthetic indoor target region control audio

Metrics: mAP accuracy SDR STOI PESQ MSE

Baselines: AngularSweep 2DPE ShapeDist ShapeContexts PointSet ShapeEmbed Space2Vec Poly2Vec ResNet18 ViT CLIP SoundTRC

Builds on: Zernike polynomials Poly2Vec ShapeEmbed SoundTRC Space2Vec

Closest papers by meaning

• Matryoshka Networks: Predicting 3D Geometry via Nested Shape Layers (CVPR 2018 · similarity 0.87)
• ZeroShape: Regression-based Zero-shot Shape Reconstruction (CVPR 2024 · similarity 0.85)
• Frame Averaging for Equivariant Shape Space Learning (CVPR 2022 · similarity 0.85)
• Less Decoder is More Encoder: Geometric Representation Learning from Novel View Synthesis (NeurIPS 2026 · similarity 0.85)
• ESCAPE: Equivariant Shape Completion via Anchor Point Encoding (CVPR 2025 · similarity 0.85)
• Learning Shape-Independent Transformation via Spherical Representations for Category-Level Object Pose Estimation (ICLR 2025 · similarity 0.84)