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Learning rotation invariant convolutional filters for texture classification

Diego Marcos, Michele Volpi, Devis Tuia

arXiv:1604.06720v2cs.CV

TL;DR

The paper addresses rotation-invariant texture classification when image orientations vary between training and testing. It learns tied groups of rotated filters in a shallow CNN, combining orientation pooling with discriminative training. The method achieves state-of-the-art-comparable benchmark accuracy, improves over standard shallow CNNs, and uses about an order of magnitude fewer learnable parameters.

  • Problem

    Texture classification requires descriptors that remain useful when images contain arbitrary rotations, especially with limited labeled training data.

  • Method

    A shallow CNN ties each rotation group to rotated versions of one learned canonical filter and pools across orientations to produce rotation-invariant features.

  • Results

    The method achieves accuracies comparable to the best published results on inca and tl84 and the best results on horizon, while improving performance with fewer parameters than standard shallow CNNs.

  • Takeaways & Limitations

    Explicitly learned rotatable filters provide discriminative rotation-invariant texture features with strong small-sample behavior and substantially reduced parameter requirements.

Abstract

from arXiv · show

We present a method for learning discriminative filters using a shallow Convolutional Neural Network (CNN). We encode rotation invariance directly in the model by tying the weights of groups of filters to several rotated versions of the canonical filter in the group. These filters can be used to extract rotation invariant features well-suited for image classification. We test this learning procedure on a texture classification benchmark, where the orientations of the training images differ from those of the test images. We obtain results comparable to the state-of-the-art. Compared to standard shallow CNNs, the proposed method obtains higher classification performance while reducing by an order of magnitude the number of parameters to be learned.

I. INTRODUCTION

Rotation-invariant texture descriptors matter because image orientation can vary across applications. The paper contrasts explicit rotatable filters with augmentation and related rotation-aware strategies.

  • I. INTRODUCTION: Rotation-invariant descriptors are useful for texture-based segmentation and classification when materials appear at arbitrary orientations.The motivation includes remote sensing and microscopy, where global image rotation should not change interpretation.
  • I. INTRODUCTION: Rotatable filters treat all explicitly sampled orientations as equivalent, providing rotation equivariance while allowing data-driven learning.Unlike strictly steerable filters, the approach uses interpolation and learns the filters from data.
  • I. INTRODUCTION: Rotation augmentation can learn invariance without explicit enforcement but independently learns redundant parameters for different rotation angles.Alternative approaches share filters across transformed inputs or pool over rotations, but do not necessarily enforce invariance directly.
  • I. INTRODUCTION: A rotated input produces feature responses whose maximal values remain similar while their orientation positions shift.The figure illustrates invariance through maximal activation across rotated filter responses.
  • I. INTRODUCTION: The proposed strategy uses tied rotated filters in a shallow CNN, while related filter-rotation methods commonly provide covariance through shifts across feature outputs.The paper’s approach is positioned against both input-rotation strategies and prior orientation-group CNNs.

C. Contribution

The paper learns rotation-invariant texture features by tying rotated versions of filters during shallow CNN training. It targets discriminative learning and generalization when labeled training data are limited.

  • C. Contribution: The contribution is a shallow-CNN method that learns tied, rotatable filters as part of standard training.The method ties weights across rotated filter versions rather than imposing a fixed symmetric filter family.
  • C. Contribution: The learned filters extract rotation-invariant features for texture classification while the study examines learned filters and small-sample generalization.The small-sample setting is emphasized because CNN performance depends on labeled data availability.

II. LEARNING ROTATABLE FILTERBANKS WITH CNNS

The model learns canonical filters and generates rotated group members, then pools across orientations and spatial locations to obtain rotation-invariant features. Training uses standard CNN optimization and regularization.

  • II. LEARNING ROTATABLE FILTERBANKS WITH CNNS: The network contains one convolutional layer, pooling blocks, a fully connected layer, and a softmax classifier, while its learned filters can also serve as an independent texture filterbank.The shallow architecture supports either downstream classification from CNN features or direct softmax prediction.
  • II. LEARNING ROTATABLE FILTERBANKS WITH CNNS: Each rotation group is generated from one canonical filter by rotating it across R discrete angles using bicubic interpolation.The tied filters share weights through the canonical filter rather than being learned independently.
  • II. LEARNING ROTATABLE FILTERBANKS WITH CNNS: Orientation max-pooling selects the largest activation across each rotation group, producing local rotation invariance and routing gradients through the winning angle.The winning orientation is recorded during the forward pass to update the canonical filter during backpropagation.
  • II. LEARNING ROTATABLE FILTERBANKS WITH CNNS: ReLU followed by spatial max-pooling and average-pooling extends the model from local orientation invariance to full rotation invariance across image locations.M denotes canonical filters, R sampled orientations per group, and C classification classes.
  • II. LEARNING ROTATABLE FILTERBANKS WITH CNNS: Training uses stochastic gradient descent with momentum, dropout, and convolution-filter weight decay to improve generalization and convergence.Dropout omits randomly selected filters during updates, while weight decay favors smaller filter parameters.

A. Dataset

The evaluation uses three Outex texture-classification benchmarks designed to test rotation-invariant methods. Training and test conditions differ in orientation and, for two settings, illumination.

  • A. Dataset: Outex TC 00012 is more challenging because its test images include illumination conditions absent from training.The two evaluated settings use tl84 and horizon test illuminations, while training uses inca.
  • A. Dataset: The dataset visualization shows one inca-illuminated training image for each of the 24 Outex texture classes.The figure provides a class-level view of the training samples rather than a quantitative result.

B. Texture classification pipeline

The pipeline extracts local response statistics and global frequency descriptors from rotation-pooled CNN features, using Fourier-domain computations at negligible additional cost.

  • B. Texture classification pipeline: The CNN generates rotation-invariant features that are classified with LDA after removing its average-pooling and fully connected layers.The extracted features are based on outputs of spatial max pooling across filters within each rotation group.
  • B. Texture classification pipeline: Four local descriptors—average, standard deviation, maximum, and minimum—summarize filter responses within each pooling window.Together they produce 4 · M local features representing the distribution of local responses.
  • B. Texture classification pipeline: Four global descriptors summarize the total cross power spectral density across orientations for each filter, capturing global texture frequency information.The descriptors are computed from the mean, standard deviation, maximum, and minimum values of the spectral measure.
  • B. Texture classification pipeline: Because image and rotated-filter Fourier transforms are already computed for convolution, adding the global descriptors has negligible computational cost.The global descriptors comprise another 4 · M features.
  • B. Texture classification pipeline: Using 35 × 35 filters at a single image scale captures texture information across a broad range of frequencies.The larger filters compensate for the shallow, single-scale CNN design.

C. Standard data augmented CNN

The study compares a rotatable CNN with standard CNNs trained using randomized input rotations, across model sizes and training-set sizes in two classification configurations.

  • C. Standard data augmented CNN: The data-augmented CNN sees randomly rotated input images in the range [0, 2π] at every training epoch, while its filters are learned independently.This setup tests whether augmentation produces filters equivalent to tied rotation groups.
  • C. Standard data augmented CNN: The comparison uses rotatable filters with M = 16 and R = 32 against standard CNNs containing 16, 128, or 512 filters.Each model is trained with datasets ranging from one to 20 images per class.
  • C. Standard data augmented CNN: Results are reported both from the jointly trained softmax classifier and from the full pipeline combining local and global features.The standard CNN supplies only one global spectral feature per filter.
  • C. Standard data augmented CNN: Table I reports classification accuracies on three Outex benchmarks, all trained under inca illumination.The table provides the benchmark context for the comparison.
  • C. Standard data augmented CNN: With as little as one training image per class, the comparison uses 1-nearest-neighbor classification with cityblock distance because LDA covariance matrices become singular.The training procedure otherwise varies sample counts up to the full set of 20 images per class.

A. Comparison with state-of-the-art methods

The proposed rotatable-filter method reaches state-of-the-art-level texture classification while benefiting especially from its compact parameterization and extended feature representation.

  • A. Comparison with state-of-the-art methods: The method achieves accuracies comparable to the best published results on inca and tl84, and the best results on horizon.These results are reported in Table I across the three benchmarks.
  • A. Comparison with state-of-the-art methods: The learned rotatable filters are highly directional, whereas standard augmented CNNs learn non-directional filters associated with spatial frequencies.The comparison uses M = 16 rotatable filters with R = 32 and standard CNNs with M = 16 and M = 128.
  • A. Comparison with state-of-the-art methods: The advantage of rotatable filters is more pronounced as the number of training images decreases in both evaluated settings.The reported explanation combines fewer learned parameters with the expressive power of multiple rotated filter versions.
  • A. Comparison with state-of-the-art methods: Standard augmented CNNs with M = 128 and M = 512 surpass the rotatable CNN with M = 16 only when all 20 training images per class are used.Larger parameter counts begin helping standard CNNs when training data are sufficiently abundant and patterns recur often enough.
  • A. Comparison with state-of-the-art methods: Extending the feature space beyond averaged local maxima makes rotatable features substantially outperform the other standard CNN filterbanks in the full pipeline.For M = 16, performance rises from an average of 87% to 94% with 20 training images, whereas M = 128 and M = 512 decline from 97% to 95%.

V. CONCLUSION

The paper learns rotation-invariant filter groups by tying rotated copies of canonical filters in a shallow CNN, improving texture classification with fewer parameters.

  • V. CONCLUSION: Tying first-layer filter weights so group members are rotated versions of one another explicitly learns rotation-invariant rotatable filters.The method uses standard shallow CNN formulations.
  • V. CONCLUSION: Higher filter expressiveness and fewer learned parameters improve performance to state-of-the-art levels on rotation-invariant texture classification benchmarks.The conclusion also reports significant advantages over standard data-augmented CNNs in small-training-set scenarios.

CNN softmax classification

Figure 5 compares different CNNs across three benchmarks using 1–20 training images per class, with results shown for direct CNN classification and an extended-feature 1-NN classifier.

  • Results span three benchmarks and use between 1 and 20 training images per class.
  • The top row reports results when the CNN is used directly as the classifier.
  • The bottom row reports results from the extended feature space with a 1-NN classifier, where rotatable filters have a larger advantage with fewer training images.
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