Fourier fractal dimension to predict the generalization of deep neural networks

Predicting the generalization performance of deep neural networks without relying on hold-out validation data is a fundamental challenge in machine learning. While Stochastic Gradient Descent (SGD) drives the optimization of these highly parameterized models, its heavy-tailed, non-Gaussian dynamics induce complex, scale-invariant trajectories in the parameter space. In this paper, we propose a novel generalization measure based on the Fourier fractal dimension of the network's weight variations. By analyzing the characteristic function of the Lévy-driven stochastic differential equations in the frequency domain, we extract a metric that robustly captures the geometric complexity of the learning process. Furthermore, we introduce a customized Fourier-based optimizer designed to actively regularize this fractal dimension during training. Extensive empirical evaluations on the CIFAR-10, SVHN, and MNIST datasets demonstrate that our proposed Fourier generalization measure exhibits a strong correlation with the actual generalization gap. Our method achieves state-of-the-art Kendall rank correlation coefficients, outperforming a wide array of existing norm-based, margin-based, and PAC-Bayesian measures. Ultimately, this work highlights the potential of frequency-domain fractal analysis as both a powerful predictor for model generalizability and a principled foundation for developing more stable optimization algorithms.

A self-supervised learning approach to deep filter banks for texture recognition

An important challenge in texture recognition is the limited amount of data for training frequently found in real-world applications. In computer vision in general, a successful strategy to mitigate this issue is the use of a pretraining stage where the neural network learns to identify relations between parts of the data in a self-supervised manner. A well-established framework in this direction is masked autoencoder. Nevertheless, these models usually rely on computationally intensive architectures, such as vision transformers. In the particular case of texture images, most of the relevant information is compacted within a delimited area around each pixel, which suggests that capturing long-range dependence via the attention mechanism may be unnecessary. Based on that assumption, here we propose a framework where the pretraining model is a convolutional autoencoder. To leverage the rich information conveyed by texture patterns, we employ deep filters coupled with Fisher vector pooling. In this way, we improve the performance of texture recognition without adding significant computational burden. Our approach is compared with several state-of-the-art methods in different texture databases, confirming its potential both in terms of classification accuracy and computational complexity.

Multilayer deep feature extraction for visual texture recognition

Convolutional neural networks have shown successful results in image classification achieving real-time results superior to the human level. However, texture images still pose some challenge to these models due, for example, to the limited availability of data for training in several problems where these images appear, high inter-class similarity, the absence of a global viewpoint of the object represented, and others. In this context, the present paper is focused on improving the accuracy of convolutional neural networks in texture classification. This is done by extracting features from multiple convolutional layers of a pretrained neural network and aggregating such features using Fisher vector. The reason for using features from earlier convolutional layers is obtaining information that is less domain specific. We verify the effectiveness of our method on texture classification of benchmark datasets, as well as on a practical task of Brazilian plant species identification. In both scenarios, Fisher vectors calculated on multiple layers outperform state-of-art methods, confirming that early convolutional layers provide important information about the texture image for classification.

Fractal measures of image local features: an application to texture recognition

Here we propose a new method for the classification of texture images combining fractal measures (fractal dimension, multifractal spectrum and lacunarity) with local binary patterns. More specifically we compute the box counting dimension of the local binary codes thresholded at different levels to compose the feature vector. The proposal is assessed in the classification of three benchmark databases: KTHTIPS-2b, UMD and UIUC as well as in a real-world problem, namely the identification of Brazilian plant species (database 1200Tex) using scanned images of their leaves. The proposed method demonstrated to be competitive with other state-of-the-art solutions reported in the literature. Such results confirmed the potential of combining a powerful local coding description with the multiscale information captured by the fractal dimension for texture classification.

VisGraphNet: a complex network interpretation of convolutional neural features

Here we propose and investigate the use of visibility graphs to model the feature map of a neural network. The model, initially devised for studies on complex networks, is employed here for the classification of texture images. The work is motivated by an alternative viewpoint provided by these graphs over the original data. The performance of the proposed method is verified in the classification of four benchmark databases, namely, KTHTIPS-2b, FMD, UIUC, and UMD and in a practical problem, which is the identification of plant species using scanned images of their leaves. Our method was competitive with other state-of-the-art approaches, confirming the potential of techniques used for data analysis in different contexts to give more meaningful interpretation to the use of neural networks in texture classification.

An application of a pseudo-parabolic modeling to texture image recognition

In this work, we present a novel methodology for texture image recognition using a partial differential equation modeling. More specifically, we employ the pseudo-parabolic Buckley-Leverett equation to provide a dynamics to the digital image representation and collect local descriptors from those images evolving in time. For the local descriptors we employ the magnitude and signal binary patterns and a simple histogram of these features was capable of achieving promising results in a classification task. We compare the accuracy over well established benchmark texture databases and the results demonstrate competitiveness, even with the most modern deep learning approaches. The achieved results open space for future investigation on this type of modeling for image analysis, especially when there is no large amount of data for training deep learning models and therefore model-based approaches arise as suitable alternatives.

Texture image classification based on a pseudo-parabolic diffusion model

This work proposes a novel method based on a pseudo-parabolic diffusion process to be employed for texture recognition. The proposed operator is applied over a range of time scales giving rise to a family of images transformed by nonlinear filters. Therefore each of those images are encoded by a local descriptor (we use local binary patterns for that purpose) and they are summarized by a simple histogram, yielding in this way the image feature vector. The proposed approach is tested on the classification of well established benchmark texture databases and on a practical task of plant species recognition. In both cases, it is compared with several state-of-the-art methodologies employed for texture recognition. Our proposal outperforms those methods in terms of classification accuracy, confirming its competitiveness. The good performance can be justified to a large extent by the ability of the pseudo-parabolic operator to smooth possibly noisy details inside homogeneous regions of the image at the same time that it preserves discontinuities that convey critical information for the object description. Such results also confirm that model-based approaches like the proposed one can still be competitive with the omnipresent learning-based approaches, especially when the user does not have access to a powerful computational structure and a large amount of labeled data for training.