PaperlayerView exact revision on arXiv

Source-linked AI summary

Wavelet Convolutional Neural Networks for Texture Classification

Shin Fujieda, Kohei Takayama, Toshiya Hachisuka

arXiv:1707.07394v1cs.CVcs.LG

TL;DR

Texture classification is difficult because textures vary and often lack object-shape cues that help image classification. Wavelet CNNs integrate wavelet spectral analysis into CNN layers, and the paper reports better texture-classification accuracy with fewer trainable parameters than existing models.

  • Problem

    Texture classification remains challenging because textures vary within classes and often lack the shape information useful for distinguishing objects in image classification.

    Source: §1 · p. 1

  • Method

    Wavelet CNNs integrate wavelet-based multiresolution spectral analysis into convolution and pooling layers.

    Source: §1 · p. 1

  • Results

    Wavelet CNNs achieve better texture-classification accuracy with fewer trainable parameters than existing models, and outperform existing models with significantly more parameters when trained from scratch.

    Source: §6 · p. 8

  • Takeaways & Limitations

    The paper concludes that wavelet CNNs are a general learning model that can also be applied to problems beyond texture classification.

    Source: §6 · p. 8

    The maximum decomposition level is five, and decomposition level cannot be adjusted independently of network depth and its number of trainable parameters.

    Source: §5 · p. 8

Abstract

from arXiv · show

Texture classification is an important and challenging problem in many image processing applications. While convolutional neural networks (CNNs) achieved significant successes for image classification, texture classification remains a difficult problem since textures usually do not contain enough information regarding the shape of object. In image processing, texture classification has been traditionally studied well with spectral analyses which exploit repeated structures in many textures. Since CNNs process images as-is in the spatial domain whereas spectral analyses process images in the frequency domain, these models have different characteristics in terms of performance. We propose a novel CNN architecture, wavelet CNNs, which integrates a spectral analysis into CNNs. Our insight is that the pooling layer and the convolution layer can be viewed as a limited form of a spectral analysis. Based on this insight, we generalize both layers to perform a spectral analysis with wavelet transform. Wavelet CNNs allow us to utilize spectral information which is lost in conventional CNNs but useful in texture classification. The experiments demonstrate that our model achieves better accuracy in texture classification than existing models. We also show that our model has significantly fewer parameters than CNNs, making our model easier to train with less memory.

1. Introduction

Texture classification is challenging because textures vary within a class and often lack object-shape information; the paper proposes wavelet CNNs to combine CNNs with spectral analysis for this task.

1. Introduction

  • Texture classification supports applications such as inspection, segmentation, and texture-database generation, but textures vary with viewpoint, scale, and lighting and often lack object-shape cues.These properties make texture classification challenging compared with image classification.Source: §1 · p. 1
  • Wavelet CNNs combine CNN spatial features with spectral frequency information by generalizing pooling and convolution to perform wavelet-based multiresolution analysis.The approach aims to capture spatial and scale-invariant features within one model.Source: §1 · pp. 1–2
  • Wavelet CNNs achieve better or competitive classification accuracy with fewer trainable parameters than conventional CNNs, making them easier to train and less memory-intensive.The paper also reports experiments in which the model classified cases where existing models failed.Source: §1 · pp. 1–2
  • The model decomposes the input through multiresolution analysis, concatenates the decomposed images, and sends convolution outputs through average pooling and three fully connected layers.The output size equals the number of classes in the dataset.Source: Figure 1 · p. 2
  • The paper identifies accurate and efficient texture classification as a contribution of the proposed model.This contribution is stated alongside the combination of CNNs and spectral analysis and the generalization of pooling and convolution.Source: §1 · p. 2

2. Related Work

Prior texture methods use domain-specific descriptors or statistical spectral features, while CNNs have achieved only moderate results on texture classification; this work positions wavelet CNNs as a way to integrate spectral analysis into CNNs.

2. Related Work

  • Conventional structural and statistical descriptors can compactly represent texture, but only under the assumptions built into each approach.More general probability-model and basis-function methods make selecting a suitable model for a given texture difficult.Source: §2 · p. 2
  • CNNs achieve strong results across tasks but only moderate accuracy on texture classification, while FV-CNN improves accuracy using a pretrained CNN and Fisher Vectors [8].FV-CNN's CNN is not trained on texture datasets and inherits a large parameter count that makes general training difficult.Source: §2 · p. 2
  • T-CNN uses an energy layer that averages each feature map, reducing parameters through a simple architecture without improving classification accuracy.The proposed model is not restricted to texture classification and achieves competitive performance to AlexNet on image classification.Source: §2 · p. 2
  • Spectral approaches define texture features from statistics across frequency scales and orientations, and can selectively emphasize frequencies or represent periodic structure.Explicit frequency selection is difficult to control in CNNs.Source: §2 · p. 3
  • Wavelet CNNs integrate multiresolution analysis directly because whether CNNs can learn spectral analyses in practice with available datasets is unclear.Some layers use fixed wavelet-defined parameters rather than trainable parameters; experiments support that more CNN parameters do not make the models equivalent in practice.Source: §2 · p. 3

3. Wavelet Convolutional Neural Networks

The section recasts convolution and average pooling as filtering and downsampling, then uses wavelet multiresolution analysis to retain both low- and high-frequency components within a CNN. It also describes the network structure and training setup.

3.1. Convolutional Neural Networks

  • Convolution computes weighted sums over local neighborhoods, while average pooling applies an averaging filter followed by downsampling.The section frames convolution and pooling as filtering and downsampling, connecting them to multiresolution analysis.Source: §3 · p. 3, §3.1 · pp. 3–4, Figure 2 · p. 3

3.2. Generalized Convolution and Pooling

  • Multiresolution analysis repeatedly decomposes the low-frequency component into low- and high-frequency parts using generalized convolution and pooling.The number of applications is the level of multiresolution analysis.Source: §3.2 · p. 4
  • Wavelet CNNs use both low- and high-frequency components, whereas conventional CNNs retain only low-frequency components; avoiding information loss requires filters satisfying the quadrature mirror relationship.The experiments use Haar wavelets, though the model is not restricted to Haar.Source: §3.2 · p. 4

3.3. Implementation

  • The network follows a VGG-19 design with nine convolution layers, wavelet layers at decomposition levels, an energy layer, and three fully connected layers.Inputs are fixed at 224 × 224; training uses random crops and flips, batch normalization, Adam, and ReLU.Source: §3.3 · pp. 4–5

4. Results

With ImageNet pre-training, the wavelet CNN performs best on kth-tips2-b and is outperformed only by FV-CNN on DTD. The results also report stronger from-scratch accuracy than AlexNet and T-CNN, alongside substantially fewer parameters than competing models.

Datasets

  • The experiments average results over four splits for kth-tips2-b and ten splits for DTD, whose images were collected in uncontrolled conditions.Each DTD split has 40 training, 40 validation, and 40 testing images per class.Source: §4 · p. 5

Training from scratch

  • From scratch, wavelet CNN models outperform AlexNet and T-CNN on both texture datasets.Figure 4 compares the models on kth-tips2-b and DTD; Table 1 reports accuracy (%).Source: §4 · p. 5, Figure 4 · p. 5, Table 1 · p. 6
  • Four-level decomposition performs best; five levels achieve almost the same accuracy but require more trainable parameters.The decomposition level is a tunable hyper-parameter for different problems.Source: §4 · p. 5

Training with fine-tuning

  • The 4-level wavelet CNN performs best on kth-tips2-b and is outperformed only by FV-CNN on DTD after ImageNet pre-training.Figure 5 compares the 4-level model with shearlet transform, VGG-M, T-CNN, and FC+FV-CNN; Table 2 reports accuracy (%).Source: Figure 5 · p. 6, Table 2 · p. 6, §4 · p. 6

Number of parameters

  • Even with 5-level analysis, the model has fewer parameters than every tested competitor; the 4-level model has less than half as many as T-CNN.Its Caffemodel uses 43.8 MB, compared with 89.1 MB for T-CNN, 232 MB for AlexNet, and 392 MB for VGG-M.Source: Figure 6 · p. 6, §4 · p. 6

Visual comparisons of classified images

  • Shearlet transform handles the scale variation in wrinkled aluminium foil, while VGG-M classifies distorted lines in Banded correctly; the combined model labels both variations correctly.Figure 7 marks incorrectly classified images with red squares.Source: §4 · pp. 6, 8, Figure 7 · p. 7

5. Discussion

The discussion reports an image-classification result and examines wavelet CNNs’ pooling choices, decomposition-depth constraint, fine-tuning performance, and texture-classification accuracy.

Application to image classification

  • 59.8% accuracy for the wavelet CNN versus 57.1% for AlexNet on ImageNet 2012, with about five times fewer parameters.The model was trained from scratch.Source: §5 · p. 8

Lp pooling

  • Replacing downsampling with Lp-norm computation supports Lp pooling, but no longer retains all input frequency information.The paper focuses on average pooling because of its clear connection to multiresolution analysis.Source: §5 · p. 8

Limitations

  • The architecture’s four feature-map-reduction layers restrict its maximum decomposition level to five, coupling decomposition depth to network depth and trainable parameters.A different network design might separate these hyperparameters.Source: §5 · p. 8
  • Fine-tuning on ImageNet 2012 yields performance comparable to FV-CNN, and the authors say neural-network failure cases are generally difficult to explain.They note they could not find a publicly available texture dataset at ImageNet 2012 scale.Source: §5 · p. 8
  • Texture-only training improves accuracy, but results remain around 60% for kth-tips2-b and 32% for DTD, potentially insufficient for some applications.The authors note room for improvement relative to image classification.Source: §5 · p. 8

6. Conclusion

The conclusion presents wavelet CNNs as a single model combining CNN layers with spectral analysis through multiresolution analysis, reporting better texture-classification accuracy with fewer trainable parameters.

6. Conclusion

  • Wavelet CNNs achieve better texture-classification accuracy with fewer trainable parameters than existing models, and outperform all existing models with significantly more trainable parameters when trained from scratch.The conclusion describes the architecture as integrating spectral analysis into CNNs through generalized filtering and downsampling.Source: §6 · p. 8
Loading 1707.07394v1…