Pre-print of a paper to appear in the proceedings of the IEEE International Conference on Machine Learning Applications (ICMLA 2020), 10 pages, 9 figures, 1 table
This paper proposes to use Fast Fourier Transformation-based U-Net (a refined fully convolutional networks) and perform image convolution in neural networks. Leveraging the Fast Fourier Transformation, it reduces the image convolution costs involved in the Convolutional Neural Networks (CNNs) and thus reduces the overall computational costs. The proposed model identifies the object information from the images. We apply the Fast Fourier transform algorithm on an image data set to obtain more accessible information about the image data, before segmenting them through the U-Net architecture. More specifically, we implement the FFT-based convolutional neural network to improve the training time of the network. The proposed approach was applied to publicly available Broad Bioimage Benchmark Collection (BBBC) dataset. Our model demonstrated improvement in training time during convolution from $600-700$ ms/step to $400-500$ ms/step. We evaluated the accuracy of our model using Intersection over Union (IoU) metric showing significant improvements.
University of California, Santa Barbara（加州大学圣塔芭芭拉分校）；The Ohio State University（俄亥俄州立大学）
With the increasing popularity of deep learning, Convolutional Neural Networks (CNNs) have been widely applied in various domains, such as image classification and object detection, and achieve stunning success in terms of their high accuracy over the traditional statistical methods. To exploit the potential of CNN models, a huge amount of research and industry efforts have been devoted to optimizing CNNs. Among these endeavors, CNN architecture design has attracted tremendous attention because of its great potential of improving model accuracy or reducing model complexity. However, existing w…
Indian Institute of Technology Gandhinagar（印度理工学院甘地纳格尔分校）
In this paper, we propose a new convolutional layer called Depthwise-STFT Separable layer that can serve as an alternative to the standard depthwise separable convolutional layer. The construction of the proposed layer is inspired by the fact that the Fourier coefficients can accurately represent important features such as edges in an image. It utilizes the Fourier coefficients computed (channelwise) in the 2D local neighborhood (e.g., 3x3) of each position of the input map to obtain the feature maps. The Fourier coefficients are computed using 2D Short Term Fourier Transform (STFT) at multipl…
Data-agnostic quasi-imperceptible perturbations on inputs are known to degrade recognition accuracy of deep convolutional networks severely. This phenomenon is considered to be a potential security issue. Moreover, some results on statistical generalization guarantees indicate that the phenomenon can be a key to improve the networks' generalization. However, the characteristics of the shared directions of such harmful perturbations remain unknown. Our primal finding is that convolutional networks are sensitive to the directions of Fourier basis functions. We derived the property by specializin…
A Fast Fourier Convolutional Deep Neural Network For Accurate and Explainable Discrimination Of Wheat Yellow Rust And Nitrogen Deficiency From Sentinel-2 Time-Series Data
The University of Leeds（利兹大学）；Manchester Metropolitan University（曼彻斯特城市大学）；University of Córdoba（科尔多瓦大学）；The University of Manchester（曼彻斯特大学）；Beijing University of Technology（北京工业大学）；Yangzhou University（扬州大学）
Southeast University（东南大学）；The first affiliated hospital of Nanjing medical university（南京医科大学第一附属医院）；Centre de Recherche en Information Biomédicale Sino-Français (CRIBs)（中法生物医学信息研究中心（CRIBs））；University of Western Ontario（西安大略大学）
Reliable automatic classification of colonoscopy images is of great significance in assessing the stage of colonic lesions and formulating appropriate treatment plans. However, it is challenging due to uneven brightness, location variability, inter-class similarity, and intra-class dissimilarity, affecting the classification accuracy. To address the above issues, we propose a Fourier-based Frequency Complex Network (FFCNet) for colon disease classification in this study. Specifically, FFCNet is a novel complex network that enables the combination of complex convolutional networks with frequenc…
Recognizing facial action units (AUs) during spontaneous facial displays is a challenging problem. Most recently, Convolutional Neural Networks (CNNs) have shown promise for facial AU recognition, where predefined and fixed convolution filter sizes are employed. In order to achieve the best performance, the optimal filter size is often empirically found by conducting extensive experimental validation. Such a training process suffers from expensive training cost, especially as the network becomes deeper. This paper proposes a novel Optimized Filter Size CNN (OFS-CNN), where the filter sizes and…
University of California, Santa Barbara（加州大学圣巴巴拉分校）
As the key advancement of the convolutional neural networks (CNNs), depthwise separable convolutions (DSCs) are becoming one of the most popular techniques to reduce the computations and parameters size of CNNs meanwhile maintaining the model accuracy. It also brings profound impact to improve the applicability of the compute- and memory-intensive CNNs to a broad range of applications, such as mobile devices, which are generally short of computation power and memory. However, previous research in DSCs are largely focusing on compositing the limited existing DSC designs, thus, missing the oppor…
FMI for Biomedical Research（FMI生物医学研究所）；Fondazione Human Technopole（人类技术基金会）
Transformer architectures show spectacular performance on NLP tasks and have recently also been used for tasks such as image completion or image classification. Here we propose to use a sequential image representation, where each prefix of the complete sequence describes the whole image at reduced resolution. Using such Fourier Domain Encodings (FDEs), an auto-regressive image completion task is equivalent to predicting a higher resolution output given a low-resolution input. Additionally, we show that an encoder-decoder setup can be used to query arbitrary Fourier coefficients given a set of …
Fast Fourier Convolutional GAN for 30 m Clear-Sky Land Surface Temperature Gap-Free Reconstruction
Technical University of Munich（慕尼黑工业大学）；Helmholtz Centre for Polar and Marine Research, Alfred Wegener Institute（亥姆霍兹极地与海洋研究中心阿尔弗雷德·韦格纳研究所）；Swiss Federal Institute of Technology Zurich (ETH Zurich)（瑞士联邦理工学院苏黎世分校）
Deep Learning-based Computer Vision field has recently been trying to explore larger kernels for convolution to effectively scale up Convolutional Neural Networks. Simultaneously, new paradigm of models such as Vision Transformers find it difficult to scale up to larger higher resolution images due to their quadratic complexity in terms of input sequence. In this report, Fast Fourier Transform is utilised in various ways to provide some solutions to these issues.
Optimizing Convolutional Neural Networks for Chronic Obstructive Pulmonary Disease Detection in Clinical Computed Tomography Imaging
Technical University of Munich（慕尼黑工业大学）；Munich Institute of Biomedical Engineering（慕尼黑生物医学工程研究所）；Klinikum rechts der Isar（伊萨尔河右岸医院）；Institute for Advanced Study, Technical University of Munich（慕尼黑工业大学高等研究院）
Generative Adversarial Networks (GANs) have achieved remarkable results in the task of generating realistic natural images. In most successful applications, GAN models share two common aspects: solving a challenging saddle point optimization problem, interpreted as an adversarial game between a generator and a discriminator functions; and parameterizing the generator and the discriminator as deep convolutional neural networks. The goal of this paper is to disentangle the contribution of these two factors to the success of GANs. In particular, we introduce Generative Latent Optimization (GLO), …
Friedrich-Alexander University Erlangen-Nürnberg（埃尔朗根-纽伦堡弗里德里希-亚历山大大学）；Siemens Healthcare GmbH（西门子医疗有限公司）
Purpose: To develop an algorithm for robust partial Fourier (PF) reconstruction applicable to diffusion-weighted (DW) images with non-smooth phase variations. Methods: Based on an unrolled proximal splitting algorithm, a neural network architecture is derived which alternates between data consistency operations and regularization implemented by recurrent convolutions. In order to exploit correlations, multiple repetitions of the same slice are jointly reconstructed under consideration of permutation-equivariance. The algorithm is trained on DW liver data of 60 volunteers and evaluated on retro…
We propose Absum, which is a regularization method for improving adversarial robustness of convolutional neural networks (CNNs). Although CNNs can accurately recognize images, recent studies have shown that the convolution operations in CNNs commonly have structural sensitivity to specific noise composed of Fourier basis functions. By exploiting this sensitivity, they proposed a simple black-box adversarial attack: Single Fourier attack. To reduce structural sensitivity, we can use regularization of convolution filter weights since the sensitivity of linear transform can be assessed by the nor…
Austin Peay State University（奥斯汀佩伊州立大学）；Baidu Research（百度研究院）；University of Southern Mississippi（南密西西比大学）
Deep learning models learn to fit training data while they are highly expected to generalize well to testing data. Most works aim at finding such models by creatively designing architectures and fine-tuning parameters. To adapt to particular tasks, hand-crafted information such as image prior has also been incorporated into end-to-end learning. However, very little progress has been made on investigating how an individual training sample will influence the generalization ability of a model. In other words, to achieve high generalization accuracy, do we really need all the samples in a training…
This paper presents a significant improvement for the synthesis of texture images using convolutional neural networks (CNNs), making use of constraints on the Fourier spectrum of the results. More precisely, the texture synthesis is regarded as a constrained optimization problem, with constraints conditioning both the Fourier spectrum and statistical features learned by CNNs. In contrast with existing methods, the presented method inherits from previous CNN approaches the ability to depict local structures and fine scale details, and at the same time yields coherent large scale structures, eve…
Isfahan University of Technology（伊斯法罕理工大学）；McMaster University（麦克马斯特大学）
Convolutional neural networks (CNNs) have a large number of variables and hence suffer from a complexity problem for their implementation. Different methods and techniques have developed to alleviate the problem of CNN's complexity, such as quantization, pruning, etc. Among the different simplification methods, computation in the Fourier domain is regarded as a new paradigm for the acceleration of CNNs. Recent studies on Fast Fourier Transform (FFT) based CNN aiming at simplifying the computations required for FFT. However, there is a lot of space for working on the reduction of the computatio…
We propose an unsupervised superpixel segmentation method by optimizing a randomly-initialized convolutional neural network (CNN) in inference time. Our method generates superpixels via CNN from a single image without any labels by minimizing a proposed objective function for superpixel segmentation in inference time. There are three advantages to our method compared with many of existing methods: (i) leverages an image prior of CNN for superpixel segmentation, (ii) adaptively changes the number of superpixels according to the given images, and (iii) controls the property of superpixels by add…
Using Frame Theoretic Convolutional Gridding for Robust Synthetic Aperture Sonar Imaging
Department of Electrical Engineering, Pennsylvania State University, State College, PA（电气工程系，宾夕法尼亚州立大学，州立学院，PA）；Department of Mathematics, Dartmouth College, Hanover, NH（数学系，达特茅斯学院，汉诺威，NH）；U.S. Naval Research Laboratory, Washington, DC（美国海军研究实验室，华盛顿，DC）
Indian Institute of Technology Gandhinagar（印度理工学院甘地讷格尔分校）；Osaka University（大阪大学）
Conventional 3D convolutional neural networks (CNNs) are computationally expensive, memory intensive, prone to overfitting, and most importantly, there is a need to improve their feature learning capabilities. To address these issues, we propose spatio-temporal short term Fourier transform (STFT) blocks, a new class of convolutional blocks that can serve as an alternative to the 3D convolutional layer and its variants in 3D CNNs. An STFT block consists of non-trainable convolution layers that capture spatially and/or temporally local Fourier information using a STFT kernel at multiple low freq…
Carnegie Mellon University（卡内基梅隆大学）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Performance of neural networks can be significantly improved by encoding known invariance for particular tasks. Many image classification tasks, such as those related to cellular imaging, exhibit invariance to rotation. We present a novel scheme using the magnitude response of the 2D-discrete-Fourier transform (2D-DFT) to encode rotational invariance in neural networks, along with a new, efficient convolutional scheme for encoding rotational equivariance throughout convolutional layers. We implemented this scheme for several image classification tasks and demonstrated improved performance, in …
3D Fourier-based Global Feature Extraction for Hyperspectral Image Classification
SDAIA-KFUPM, Joint Research Center for Artificial Intelligence (JRCAI), King Fahd University of Petroleum and Minerals（SDAIA-KFUPM联合人工智能研究中心（JRCAI）、国王法赫德石油矿物大学）
University of Central Florida（中佛罗里达大学）；Center for Research in Computer Vision（计算机视觉研究中心）
In this work, we explain in detail how receptive fields, effective receptive fields, and projective fields of neurons in different layers, convolution or pooling, of a Convolutional Neural Network (CNN) are calculated. While our focus here is on CNNs, the same operations, but in the reverse order, can be used to calculate these quantities for deconvolutional neural networks. These are important concepts, not only for better understanding and analyzing convolutional and deconvolutional networks, but also for optimizing their performance in real-world applications.
The human visual system is able to recognize objects despite transformations that can drastically alter their appearance. To this end, much effort has been devoted to the invariance properties of recognition systems. Invariance can be engineered (e.g. convolutional nets), or learned from data explicitly (e.g. temporal coherence) or implicitly (e.g. by data augmentation). One idea that has not, to date, been explored is the integration of latent variables which permit a search over a learned space of transformations. Motivated by evidence that people mentally simulate transformations in space w…
Malaria, a life-threatening disease, infects millions of people every year throughout the world demanding faster diagnosis for proper treatment before any damages occur. In this paper, an end-to-end deep learning-based approach is proposed for faster diagnosis of malaria from thin blood smear images by making efficient optimizations of features extracted from diversified receptive fields. Firstly, an efficient, highly scalable deep neural network, named as DilationNet, is proposed that incorporates features from a large spectrum by varying dilation rates of convolutions to extract features fro…
Filters in a Convolutional Neural Network (CNN) contain model parameters learned from enormous amounts of data. In this paper, we suggest to decompose convolutional filters in CNN as a truncated expansion with pre-fixed bases, namely the Decomposed Convolutional Filters network (DCFNet), where the expansion coefficients remain learned from data. Such a structure not only reduces the number of trainable parameters and computation, but also imposes filter regularity by bases truncation. Through extensive experiments, we consistently observe that DCFNet maintains accuracy for image classification…
In the current research of neural networks, the activation function is manually specified by human and not able to change themselves during training. This paper focus on how to make the activation function trainable for deep neural networks. We use series and linear combination of different activation functions make activation functions continuously variable. Also, we test the performance of CNNs with Fourier series simulated activation(Fourier-CNN) and CNNs with linear combined activation function (LC-CNN) on Cifar-10 dataset. The result shows our trainable activation function reveals better …
Johns Hopkins University（约翰斯·霍普金斯大学）；Technion Israel Institute of Technology（以色列理工学院）
The Convolutional Sparse Coding (CSC) model has recently gained considerable traction in the signal and image processing communities. By providing a global, yet tractable, model that operates on the whole image, the CSC was shown to overcome several limitations of the patch-based sparse model while achieving superior performance in various applications. Contemporary methods for pursuit and learning the CSC dictionary often rely on the Alternating Direction Method of Multipliers (ADMM) in the Fourier domain for the computational convenience of convolutions, while ignoring the local characteriza…
Pruning By Explaining Revisited: Optimizing Attribution Methods to Prune CNNs and Transformers
Fraunhofer Heinrich-Hertz-Institute（弗劳恩霍夫海因茨·赫兹研究所）；Technische Universität Berlin（柏林工业大学）；BIFOLD – Berlin Institute for the Foundations of Learning and Data（柏林学习与数据基础研究所（BIFOLD））
Courant Institute of Mathematical Sciences（库朗数学科学研究所）；New York University（纽约大学）
Convolutional networks are one of the most widely employed architectures in computer vision and machine learning. In order to leverage their ability to learn complex functions, large amounts of data are required for training. Training a large convolutional network to produce state-of-the-art results can take weeks, even when using modern GPUs. Producing labels using a trained network can also be costly when dealing with web-scale datasets. In this work, we present a simple algorithm which accelerates training and inference by a significant factor, and can yield improvements of over an order of…
We introduce a unified framework for group equivariant networks on homogeneous spaces derived from a Fourier perspective. We consider tensor-valued feature fields, before and after a convolutional layer. We present a unified derivation of kernels via the Fourier domain by leveraging the sparsity of Fourier coefficients of the lifted feature fields. The sparsity emerges when the stabilizer subgroup of the homogeneous space is a compact Lie group. We further introduce a nonlinear activation, via an elementwise nonlinearity on the regular representation after lifting and projecting back to the fi…
Inria（法国国家信息与自动化研究所）；Laboratoire Jean Kuntzmann（让·昆茨曼实验室）；CNRS（法国国家科学研究中心）；Univ. Grenoble Alpes（格勒诺布尔阿尔卑斯大学）
In this paper, we introduce a new image representation based on a multilayer kernel machine. Unlike traditional kernel methods where data representation is decoupled from the prediction task, we learn how to shape the kernel with supervision. We proceed by first proposing improvements of the recently-introduced convolutional kernel networks (CKNs) in the context of unsupervised learning; then, we derive backpropagation rules to take advantage of labeled training data. The resulting model is a new type of convolutional neural network, where optimizing the filters at each layer is equivalent to …
Convolutional networks have been widely applied for computer vision system. Encouraged by these results, a U-Net convolutional network was applied to recognition of vessels and materials in chemistry lab using the recent Vector-LabPics dataset, which contains 2187 images of materials within mostly transparent vessels in a chemistry lab and other general settings, labeled with 13 classes. By optimizing hyperparameters including learning rates and learning rate decays, 87% accuracy in vessel recognition was achieved. In the case of relatively small training and test sets (relatively rare materia…
This paper introduces a new approach to automatically quantify the severity of knee OA using X-ray images. Automatically quantifying knee OA severity involves two steps: first, automatically localizing the knee joints; next, classifying the localized knee joint images. We introduce a new approach to automatically detect the knee joints using a fully convolutional neural network (FCN). We train convolutional neural networks (CNN) from scratch to automatically quantify the knee OA severity optimizing a weighted ratio of two loss functions: categorical cross-entropy and mean-squared loss. This jo…
This paper aims to accelerate the test-time computation of convolutional neural networks (CNNs), especially very deep CNNs that have substantially impacted the computer vision community. Unlike previous methods that are designed for approximating linear filters or linear responses, our method takes the nonlinear units into account. We develop an effective solution to the resulting nonlinear optimization problem without the need of stochastic gradient descent (SGD). More importantly, while previous methods mainly focus on optimizing one or two layers, our nonlinear method enables an asymmetric …
It is challenging to bridge the performance gap between Binary CNN (BCNN) and Floating point CNN (FCNN). We observe that, this performance gap leads to substantial residuals between intermediate feature maps of BCNN and FCNN. To minimize the performance gap, we enforce BCNN to produce similar intermediate feature maps with the ones of FCNN. This training strategy, i.e., optimizing each binary convolutional block with block-wise distillation loss derived from FCNN, leads to a more effective optimization to BCNN. It also motivates us to update the binary convolutional block architecture to facil…
Hefei Institute of Physical Science, Chinese Academy of Sciences（中国科学院合肥物质科学研究院）；University of Science and Technology of China（中国科学技术大学）；SenseBrain Technology (SenseTime Research USA)（商汤美国研究院思脑科技）；Nanyang Technological University（南洋理工大学）；Xi’an Jiaotong University（西安交通大学）；Pazhou Laboratory (Huangpu)（琶洲实验室（黄埔））
Existing convolutional neural networks widely adopt spatial down-/up-sampling for multi-scale modeling. However, spatial up-sampling operators (\emph{e.g.}, interpolation, transposed convolution, and un-pooling) heavily depend on local pixel attention, incapably exploring the global dependency. In contrast, the Fourier domain obeys the nature of global modeling according to the spectral convolution theorem. Unlike the spatial domain that performs up-sampling with the property of local similarity, up-sampling in the Fourier domain is more challenging as it does not follow such a local property.…
School of mathematics and statistics, Nanjing University of Information Science and Technology（南京信息工程大学数学与统计学院）
With the development of the super-resolution convolutional neural network (SRCNN), deep learning technique has been widely applied in the field of image super-resolution. Previous works mainly focus on optimizing the structure of SRCNN, which have been achieved well performance in speed and restoration quality for image super-resolution. However, most of these approaches only consider a specific scale image during the training process, while ignoring the relationship between different scales of images. Motivated by this concern, in this paper, we propose a cascaded convolution neural network f…
Michigan State University（密歇根州立大学）；Department of Biosystems and Agricultural Engineering（生物系统与农业工程系）
Food image recognition is one of the promising applications of visual object recognition in computer vision. In this study, a small-scale dataset consisting of 5822 images of ten categories and a five-layer CNN was constructed to recognize these images. The bag-of-features (BoF) model coupled with support vector machine (SVM) was first evaluated for image classification, resulting in an overall accuracy of 56%; while the CNN model performed much better with an overall accuracy of 74%. Data augmentation techniques based on geometric transformation were applied to increase the size of training i…
UC San Diego（加州大学圣迭戈分校）；IBM T. J. Watson Research（IBM T. J. Watson 研究院）
A unified deep neural network, denoted the multi-scale CNN (MS-CNN), is proposed for fast multi-scale object detection. The MS-CNN consists of a proposal sub-network and a detection sub-network. In the proposal sub-network, detection is performed at multiple output layers, so that receptive fields match objects of different scales. These complementary scale-specific detectors are combined to produce a strong multi-scale object detector. The unified network is learned end-to-end, by optimizing a multi-task loss. Feature upsampling by deconvolution is also explored, as an alternative to input up…
Fraunhofer ITWM（弗劳恩霍夫工业数学研究所）；University of Kaiserslautern（凯泽斯劳滕大学）；Fraunhofer Center Machine Learning（弗劳恩霍夫机器学习中心）；University of Mannheim（曼海姆大学）；Offenburg University（奥芬堡大学）
Despite the success of convolutional neural networks (CNNs) in many computer vision and image analysis tasks, they remain vulnerable against so-called adversarial attacks: Small, crafted perturbations in the input images can lead to false predictions. A possible defense is to detect adversarial examples. In this work, we show how analysis in the Fourier domain of input images and feature maps can be used to distinguish benign test samples from adversarial images. We propose two novel detection methods: Our first method employs the magnitude spectrum of the input images to detect an adversarial…
Current research in convolutional neural networks (CNN) focuses mainly on changing the architecture of the networks, optimizing the hyper-parameters and improving the gradient descent. However, most work use only 3 standard families of operations inside the CNN, the convolution, the activation function, and the pooling. In this work, we propose a new family of operations based on the Green's function of the Laplacian, which allows the network to solve the Laplacian, to integrate any vector field and to regularize the field by forcing it to be conservative. Hence, the Green's function (GF) is t…
