Research map / Architectures and efficiency / CNN design

Selective Disk Bispectrum: A Complete and Rotation Invariant Image Descriptor

NeurIPS 2026 · Architectures and efficiency › CNN design · approach: Steerable rotation-equivariant CNNs · 0 citations (OpenAlex)

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 the selective disk bispectrum (SDB), a minimal, complete, rotation-invariant image descriptor obtained from disk harmonic coefficients, with an analytic inversion, complexity reductions, noise statistics, and classification/MRA experiments on rotated noisy MNIST and FashionMNIST.

Problem

Rotation-invariant image descriptors are either efficient but non-discriminative (hand-crafted) or discriminative but costly (learned); existing full disk bispectrum is expensive and lacks an inversion, so completeness is unproven.

Approach

Derives an analytic inversion of the disk bispectrum showing most coefficients are redundant, yielding a minimal subset (SDB) that is a complete rotation invariant with O(m) space and O(L^3+m) time, plus an approximate version with accuracy guarantees and closed-form noise expectation/variance.

Key results

• SDB outperforms pooled G-CNN descriptors on noisy rotated MNIST and FashionMNIST whenever noise is added, across image sizes and MLP budgets.
• On MNIST at low resolution with heavy noise, SDB outperforms frozen transformer features (DINOv3, EVA-02, OpenCLIP); the advantage narrows with larger MLPs and vanishes at 112x112 and on FashionMNIST.
• SDB multi-reference alignment on rotated 56x56 and 112x112 images recovers the ground truth up to rotation, with some instability reported.

Surprising findings

• Most disk bispectrum coefficients are redundant: a minimal subset suffices for complete reconstruction.
• The advantage over transformer features disappears at 112x112 resolution and on FashionMNIST.

Limitations

• SDB is invariant only to global planar rotation, not to local feature rotation, translation, or reflection, so it is best for centered single-object images.
• MRA reconstruction shows instability likely from recursive inversion amplifying errors.
• Classification gains do not hold for transformers with larger MLPs, higher resolution, or on FashionMNIST.

Experimental setup

Datasets: MNIST FashionMNIST

Benchmarks: rotated noisy MNIST rotated noisy FashionMNIST multi-reference alignment on rotated images

Metrics: classification accuracy relative reconstruction error training time

Baselines: max-pooled G-CNN average-pooled G-CNN Selective G-Bispectrum G-Triple Correlation DINOv3 EVA-02 OpenCLIP

Builds on: disk bispectrum classical bispectrum G-CNN selective G-bispectrum disk harmonic transform

Closest papers by meaning

• $\texttt{bispectrum}$: Selective $G$-Bispectra Made Practical (NeurIPS 2026 · similarity 0.85)
• Spectral State Space Model for Rotation-Invariant Visual Representation Learning (CVPR 2025 · similarity 0.85)
• R2Det: Exploring Relaxed Rotation Equivariance in 2D Object Detection (ICLR 2025 · similarity 0.84)
• ReDiffDet: Rotation-equivariant Diffusion Model for Oriented Object Detection (CVPR 2025 · similarity 0.84)
• Estimating Extreme 3D Image Rotations using Cascaded Attention (CVPR 2024 · similarity 0.84)
• Steerers: A Framework for Rotation Equivariant Keypoint Descriptors (CVPR 2024 · similarity 0.84)