Deep Roto-Translation Scattering for Object Classification (1412.8659v2)

Abstract: 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.

• The paper introduces a scattering convolution network leveraging Morlet wavelet filters to capture both translation and rotation invariances, significantly enhancing image representation.
• It employs a cascading architecture with dual wavelet transforms that extract stable, multi-scale features for robust image classification.
• Experimental evaluations on Caltech and CIFAR demonstrate competitive performance compared to state-of-the-art unsupervised methods.

Deep Roto-Translation Scattering for Object Classification

The research paper "Deep Roto-Translation Scattering for Object Classification" by Edouard Oyallon and Stéphan Mallat presents an intriguing approach to image classification using a deep scattering convolution network. This network utilizes complex wavelet filters designed for spatial and angular variables to enhance the accuracy of image representations. The authors explore the potency of incorporating geometric priors and the promise it holds in augmenting image classification tasks.

Methodology Overview

Scattering Networks

The scattering network introduced in this paper is characterized by its reliance on predefined wavelet filters, which are adept at capturing geometric invariances in images. These filters are tailored to the peculiarities of rigid movements and deformations observed in perspective projections, emphasizing the importance of building invariants to these transformations. The network extends prior work on translation-invariant scattering networks by incorporating additional complexity to handle both translation and rotation variabilities. This modification results in a rich feature representation incorporating interactions between scales and angles.

Architecture and Implementation

The network architecture is a cascade of wavelet transforms, implementing a multi-layer approach that mimics deep convolutional networks. A key innovation is the use of Morlet wavelets, providing a robust framework for generating invariants to translation and rotation. The scattering network outputs are propagated through a cascade of linear filtering, modulus non-linearities, and pooling operators, ultimately resulting in a hierarchical feature representation that maintains stability to small deformations—a critical property lacking in some deep learning architectures.

Throughout the network, a cascade of two wavelet transforms, $W_1$ and $W_2$, is employed. $W_1$ is a spatial wavelet transform capturing scale and orientation information, while $W_2$ addresses variability across angles, thus handling rotational transformations. This modularity contributes to a representation that gracefully adapts to the various geometric variabilities intrinsic to real-world images.

Evaluation and Results

The paper presents experimental results on two well-known datasets: Caltech and CIFAR, demonstrating robust performance relative to state-of-the-art methods. The reported accuracy significantly for both prior feature-based algorithms and unsupervised deep learning techniques. Notably, the roto-translation scattering representation competes effectively with unsupervised methods across different datasets, providing evidence of its versatility.

Implications and Future Directions

The introduction of geometric priors into image classification represents a promising frontier, potentially enriching model interpretability and robustness. The scattering approach offers a balance between learned features and those inherently defined by mathematical constructs, which could guide future developments in explainable deep learning.

This work raises pertinent questions about the capabilities of unsupervised learning paradigms and the extent of geometric transformations captured by existing models. The stability and nearly complete nature of the scattering representation imply that these networks can serve as a reliable computational building block for various image analysis tasks.

Future research could explore decomposing the scattering network into even more complex transformation groups, advancing the understanding of geometrical variations beyond simple rigid movements and small deformations. Another potential research trajectory lies in integrating these scattering networks into larger supervised learning systems, potentially revitalizing the field of hybrid models that marry the strength of geometric and learned features.

In summary, this paper elucidates the significance of embedding geometric properties in the feature representation of images, underscoring the potential for these methods to complement existing deep learning paradigms and advance the discipline of computer vision.