Source-linked AI summary
Deep Roto-Translation Scattering for Object Classification
Edouard Oyallon, Stéphane Mallat
TL;DR
Image classification has benefited from learned representations, but it remains unclear whether their advantage reflects dataset adaptation or stronger geometric modeling. This paper introduces a predefined-wavelet scattering representation over spatial and angular variables, achieving strong Caltech and CIFAR results. The findings support geometric priors as a promising direction for image representation.
Problem
Learned and unsupervised representations outperform engineered features, but it is unclear whether their gains reflect dataset adaptation or refined geometric image properties.
Method
The paper constructs a translation-invariant roto-translation scattering representation with predefined spatial and angular wavelets that captures interactions across scales and angles.
Results
The representation improves on prior non-learning descriptors and achieves results comparable to state-of-the-art unsupervised and dictionary-learning methods on Caltech and CIFAR.
Takeaways & Limitations
Refining image representations with geometric priors remains promising for image classification and understanding.
Takeaways & Limitations
The architecture focuses on translations and rotations and does not recombine variability across color channels or scales; identifying the most important variability groups remains difficult.
Abstract
from arXiv · showhide
Dictionary learning algorithms or supervised deep convolution networks have considerably improved the efficiency of predefined feature representations such as SIFT. We introduce a deep scattering convolution network, with predefined wavelet filters over spatial and angular variables. This representation brings an important improvement to results previously obtained with predefined features over object image databases such as Caltech and CIFAR. The resulting accuracy is comparable to results obtained with unsupervised deep learning and dictionary based representations. This shows that refining image representations by using geometric priors is a promising direction to improve image classification and its understanding.
1. Introduction
The paper argues that geometric image properties can define competitive representations, challenging the view that learned representations are necessarily more promising for image classification. Its roto-translation scattering representation uses predefined wavelets to capture geometric variability and performs competitively with unsupervised learning methods.
- Learning-based representations have improved classification over engineered features such as SIFT and HOG, raising questions about the value of further geometric refinement.
- Unsupervised representations improve recognition but are tailored to individual databases, leaving unclear whether their gains reflect dataset adaptation or refined geometric properties.
- The proposed scattering network uses predefined complex wavelets adapted to geometric image variability rather than learned filters.
- Its representation is translation invariant, efficiently represents rotation variability without enforcing full rotation invariance, and combines information across scales and angles.
- The architecture delays information loss until supervised classification, using orthogonal least-square feature selection followed by a linear or Gaussian-kernel SVM.
- On Caltech and CIFAR, scattering outperforms non-learning representations and is competitive with database-adapted unsupervised learning procedures.
2. Roto-Translation Scattering Networks
Roto-translation scattering uses predefined wavelets and modulus nonlinearities to build translation-invariant, deformation-stable features while retaining rotation variability for classification.
- 2.1. Convolution Network Cascade: Each layer applies a linear operator followed by a modulus nonlinearity, progressively propagating features across increasing spatial supports and scales.The layer depth indexes the scale of the nonlinear features, and a classifier operates on the final layer.
- 2.2. Scattering Network: Scattering networks replace learned convolution filters with predefined wavelets adapted to desired geometric invariants and deformation linearization.The architecture is designed to produce locally translation-invariant features while retaining deformation information for final supervised classification.
- 2.2. Scattering Network: Cascaded wavelet transforms and modulus operations yield coefficients nearly invariant to translations below scale 2^j, with subsampling chosen to avoid aliasing.Wavelets separate image information across multiple scales and orientations; the factor-of-two oversampling avoids aliasing.
- 2.4. Roto-Translation Wavelet Transform W2: The second-order transform combines spatial and angular convolutions, linearizing rotation variability rather than imposing full rotation invariance.W2 uses separable spatial and one-dimensional angular wavelets, while the output is spatially averaged at scale 2^J.
- 2.4. Roto-Translation Wavelet Transform W2: The resulting representation is stable to additive perturbations and small deformations, while remaining nearly complete for image reconstruction.For L = 8, the stated near-completeness condition is valid when J ≥ 5.
3. Supervised Feature Selection
The paper uses supervised orthogonal least square regression to select scattering features adapted to each class, reduce representation variance, and form a compact dictionary for Gaussian SVM classification.
- Feature selection: Supervised orthogonal least square regression greedily selects scattering coefficients before SVM classification.The selected coefficients are adapted to one-versus-all class regression.
- Feature representation: A logarithm non-linearity separates low-frequency multiplicative illumination variations and linearizes scattering-coefficient decay across scales.The resulting additive offsets can be removed by a suitable linear projector in the final classifier.
- Feature selection: The regression selects and computes K scattering features for each class, then linearly transforms them into K decorrelated and normalized features.Selection minimizes training-set mean-square regression error.
- Feature representation: For nC classes, the union of class-specific features forms a dictionary of size M = K nC.M controls the bias-versus-variance trade-off and can be adjusted from regression-error decay or fixed beforehand.
- Classification: The selected features are classified with a Gaussian SVM whose kernel variance equals the training-set average scattering-vector norm.The passage reports that this relatively large variance reduces classification errors in Table 1.
4. Image Classification Results
The scattering classifier is evaluated across Caltech and CIFAR datasets using fixed scattering configurations and comparisons with predefined, unsupervised, and supervised representations. It performs strongly against predefined and unsupervised methods, while supervised deep networks remain the best-performing category in several settings.
- Second-order translated scattering reduces classification error by 10%, while rotation filtering adds 4.5% on Caltech-101 and 1.2% on CIFAR-10.These results show gains from adding second-order and angular information to first-order or translation-only scattering.
- Orthogonal least-square feature reduction further reduces error by 5.4% on Caltech-101 and 0.7% on CIFAR-10.Its larger effect on Caltech-101 is attributed to the smaller number of training examples per class.
- The experiments compare scattering with predefined features, unsupervised methods, and supervised deep networks across Caltech and CIFAR datasets.The evaluation covers Caltech-101, Caltech-256, CIFAR-10, and CIFAR-100, with different representation categories defined for the comparisons.
- Scattering outperforms all prior-feature classifiers on Caltech-101 and performs at least as well as unsupervised deep architectures without data augmentation on Caltech-101 and CIFAR-10.Random-filter convolutional networks remain below scattering accuracy on mono-CIFAR-10, even though color improves results by at most 10%.
- The same scattering representation, aside from image-size adaptation, is used across Caltech and CIFAR, whereas unsupervised methods vary in their relative performance across databases.The scattering classifier is comparable with unsupervised algorithms on CIFAR-10 and CIFAR-100, while RFL is slightly better on CIFAR-10 but worse on Caltech and CIFAR-100.
- Supervised deep networks achieve the best classification results, improving non-supervised accuracy by about 10% on CIFAR-10 or Caltech-101, 20% on Caltech-256, and 5% on CIFAR-100.The smaller CIFAR-100 improvement is associated with 500 training samples per class rather than 5000, and Caltech lacks enough data to train a supervised deep network directly.
5. Conclusion
The work demonstrates that geometric image properties can produce competitive classification features, while supervised deep networks still achieve higher average accuracy. Understanding the geometric properties captured by supervised networks remains an open challenge for improving scattering representations.
- A roto-translation scattering transform constructs classification features from geometric image properties rather than learned representations.
- It combines information across multiple scales and angles for complex object classification.
- The transform improves performance over prior image descriptors and yields results comparable to unsupervised deep learning and dictionary learning algorithms.
- Supervised deep convolutional networks provide a clear improvement in average classification accuracy over unsupervised learning and roto-translation scattering.
- Identifying the refined geometric image properties captured by supervised networks is an open challenge for improving scattering representations.