In this paper we challenge the common assumption that convolutional layers in modern CNNs are translation invariant. We show that CNNs can and will exploit the absolute spatial location by learning filters that respond exclusively to particular absolute locations by exploiting image boundary effects. Because modern CNNs filters have a huge receptive field, these boundary effects operate even far from the image boundary, allowing the network to exploit absolute spatial location all over the image. We give a simple solution to remove spatial location encoding which improves translation invariance and thus gives a stronger visual inductive bias which particularly benefits small data sets. We broadly demonstrate these benefits on several architectures and various applications such as image classification, patch matching, and two video classification datasets.
This paper is focused on studying the view-manifold structure in the feature spaces implied by the different layers of Convolutional Neural Networks (CNN). There are several questions that this paper aims to answer: Does the learned CNN representation achieve viewpoint invariance? How does it achieve viewpoint invariance? Is it achieved by collapsing the view manifolds, or separating them while preserving them? At which layer is view invariance achieved? How can the structure of the view manifold at each layer of a deep convolutional neural network be quantified experimentally? How does fine-t…
Toshiba Infrastructure Systems & Solutions Corporation（东芝基础设施系统与解决方案公司）
This report deals with translation invariance of convolutional neural networks (CNNs) for automatic target recognition (ATR) from synthetic aperture radar (SAR) imagery. In particular, the translation invariance of CNNs for SAR ATR represents the robustness against misalignment of target chips extracted from SAR images. To understand the translation invariance of the CNNs, we trained CNNs which classify the target chips from the MSTAR into the ten classes under the condition of with and without data augmentation, and then visualized the translation invariance of the CNNs. According to our resu…
Being able to adequately process and combine data arising from different sites is crucial in neuroimaging, but is difficult, owing to site, sequence and acquisition-parameter dependent biases. It is important therefore to design algorithms that are not only robust to images of differing contrasts, but also be able to generalise well to unseen ones, with a quantifiable measure of uncertainty. In this paper we demonstrate the efficacy of a physics-informed, uncertainty-aware, segmentation network that employs augmentation-time MR simulations and homogeneous batch feature stratification to achiev…
When seeing a new object, humans can immediately recognize it across different retinal locations: we say that the internal object representation is invariant to translation. It is commonly believed that Convolutional Neural Networks (CNNs) are architecturally invariant to translation thanks to the convolution and/or pooling operations they are endowed with. In fact, several works have found that these networks systematically fail to recognise new objects on untrained locations. In this work we show how, even though CNNs are not 'architecturally invariant' to translation, they can indeed 'learn…
To tackle increasingly complex tasks, it has become an essential ability of neural networks to learn abstract representations. These task-specific representations and, particularly, the invariances they capture turn neural networks into black box models that lack interpretability. To open such a black box, it is, therefore, crucial to uncover the different semantic concepts a model has learned as well as those that it has learned to be invariant to. We present an approach based on INNs that (i) recovers the task-specific, learned invariances by disentangling the remaining factor of variation i…
University of Applied Sciences Western Switzerland (HES-SO)（瑞士西部应用科学大学）；Harvard School of Engineering and Applied Sciences（哈佛大学工程与应用科学学院）；Centre Hospitalier Universitaire Vaudois (CHUV)（沃州大学中心医院）；Hopitaux Universitaires de Genève (HUG)（日内瓦大学医院）
Locally Rotation Invariant (LRI) image analysis was shown to be fundamental in many applications and in particular in medical imaging where local structures of tissues occur at arbitrary rotations. LRI constituted the cornerstone of several breakthroughs in texture analysis, including Local Binary Patterns (LBP), Maximum Response 8 (MR8) and steerable filterbanks. Whereas globally rotation invariant Convolutional Neural Networks (CNN) were recently proposed, LRI was very little investigated in the context of deep learning. LRI designs allow learning filters accounting for all orientations, whi…
Convolution is an equivariant operation, and image position does not affect its result. A recent study shows that the zero-padding employed in convolutional layers of CNNs provides position information to the CNNs. The study further claims that the position information enables accurate inference for several tasks, such as object recognition, segmentation, etc. However, there is a technical issue with the design of the experiments of the study, and thus the correctness of the claim is yet to be verified. Moreover, the absolute image position may not be essential for the segmentation of natural …
Convolutional neural networks (CNN) are now being widely used for classifying and detecting pulmonary abnormalities in chest radiographs. Two complementary generalization properties of CNNs, translation invariance and equivariance, are particularly useful in detecting manifested abnormalities associated with pulmonary disease, regardless of their spatial locations within the image. However, these properties also come with the loss of exact spatial information and global relative positions of abnormalities detected in local regions. Global relative positions of such abnormalities may help disti…
Recently, self-attention (SA) structures became popular in computer vision fields. They have locally independent filters and can use large kernels, which contradicts the previously popular convolutional neural networks (CNNs). CNNs success was attributed to the hard-coded inductive biases of locality and spatial invariance. However, recent studies have shown that inductive biases in CNNs are too restrictive. On the other hand, the relative position encodings, similar to depthwise (DW) convolution, are necessary for the local SA networks, which indicates that the SA structures are not entirely …
Humans can identify objects following various spatial transformations such as scale and viewpoint. This extends to novel objects, after a single presentation at a single pose, sometimes referred to as online invariance. CNNs have been proposed as a compelling model of human vision, but their ability to identify objects across transformations is typically tested on held-out samples of trained categories after extensive data augmentation. This paper assesses whether standard CNNs can support human-like online invariance by training models to recognize images of synthetic 3D objects that undergo …
Many of our core assumptions about how neural networks operate remain empirically untested. One common assumption is that convolutional neural networks need to be stable to small translations and deformations to solve image recognition tasks. For many years, this stability was baked into CNN architectures by incorporating interleaved pooling layers. Recently, however, interleaved pooling has largely been abandoned. This raises a number of questions: Are our intuitions about deformation stability right at all? Is it important? Is pooling necessary for deformation invariance? If not, how is defo…
We address the problem that state-of-the-art Convolution Neural Networks (CNN) classifiers are not invariant to small shifts. The problem can be solved by the removal of sub-sampling operations such as stride and max pooling, but at a cost of severely degraded training and test efficiency. We present a novel usage of Gaussian-Hermite basis to efficiently approximate arbitrary filters within the CNN framework to obtain translation invariance. This is shown to be invariant to small shifts, and preserves the efficiency of training. Further, to improve efficiency in memory usage as well as computa…
Tolerance to image variations (e.g. translation, scale, pose, illumination) is an important desired property of any object recognition system, be it human or machine. Moving towards increasingly bigger datasets has been trending in computer vision specially with the emergence of highly popular deep learning models. While being very useful for learning invariance to object inter- and intra-class shape variability, these large-scale wild datasets are not very useful for learning invariance to other parameters forcing researchers to resort to other tricks for training a model. In this work, we in…
Beihang University（北京航空航天大学）；Shanghai Aerospace Control Technology Institute（上海航天控制技术研究所）；Peking Union Medical College Hospital（北京协和医院）；Chinese Academy of Medical Sciences and Peking Union Medical College（中国医学科学院北京协和医学院）
The computer-aided diagnosis (CAD) system can provide a reference basis for the clinical diagnosis of skin diseases. Convolutional neural networks (CNNs) can not only extract visual elements such as colors and shapes but also semantic features. As such they have made great improvements in many tasks of dermoscopy images. The imaging of dermoscopy has no principal orientation, indicating that there are a large number of skin lesion rotations in the datasets. However, CNNs lack rotation invariance, which is bound to affect the robustness of CNNs against rotations. To tackle this issue, we propos…
Macquarie University（麦考瑞大学）；University of Technology Sydney（悉尼科技大学）；The University of Sydney（悉尼大学）
Automatic tumor segmentation is a crucial step in medical image analysis for computer-aided diagnosis. Although the existing methods based on convolutional neural networks (CNNs) have achieved the state-of-the-art performance, many challenges still remain in medical tumor segmentation. This is because regular CNNs can only exploit translation invariance, ignoring further inherent symmetries existing in medical images such as rotations and reflections. To mitigate this shortcoming, we propose a novel group equivariant segmentation framework by encoding those inherent symmetries for learning mor…
Cityzen Data（Cityzen Data 公司）；Telecom Bretagne（布列塔尼电信学院）
Convolutional Neural Networks (CNNs) have become the state-of-the-art in supervised learning vision tasks. Their convolutional filters are of paramount importance for they allow to learn patterns while disregarding their locations in input images. When facing highly irregular domains, generalized convolutional operators based on an underlying graph structure have been proposed. However, these operators do not exactly match standard ones on grid graphs, and introduce unwanted additional invariance (e.g. with regards to rotations). We propose a novel approach to generalize CNNs to irregular doma…
Deep convolutional neural networks (CNNs) are broadly considered to be state-of-the-art generic end-to-end image classification systems. However, they are known to underperform when training data are limited and thus require data augmentation strategies that render the method computationally expensive and not always effective. Rather than using a data augmentation strategy to encode invariances as typically done in machine learning, here we propose to mathematically augment a nearest subspace classification model in sliced-Wasserstein space by exploiting certain mathematical properties of the …
Ryerson University（瑞尔森大学）；Vector Institute for Artificial Intelligence（向量人工智能研究所）
In contrast to fully connected networks, Convolutional Neural Networks (CNNs) achieve efficiency by learning weights associated with local filters with a finite spatial extent. An implication of this is that a filter may know what it is looking at, but not where it is positioned in the image. Information concerning absolute position is inherently useful, and it is reasonable to assume that deep CNNs may implicitly learn to encode this information if there is a means to do so. In this paper, we test this hypothesis revealing the surprising degree of absolute position information that is encoded…
As object recognition becomes an increasingly common ML task, and recent research demonstrating CNNs vulnerability to attacks and small image perturbations necessitate fully understanding the foundations of object recognition. We focus on understanding the mechanisms behind how neural networks generalize to spatial transformations of complex objects. While humans excel at discriminating between objects shown at new positions, orientations, and scales, past results demonstrate that this may be limited to familiar objects - humans demonstrate low tolerance of spatial-variances for purposefully c…
Macquarie University（麦考瑞大学）；University of Technology Sydney（悉尼科技大学）；Shanghai AI Laboratory（上海人工智能实验室）
Automatic tumor or lesion segmentation is a crucial step in medical image analysis for computer-aided diagnosis. Although the existing methods based on Convolutional Neural Networks (CNNs) have achieved the state-of-the-art performance, many challenges still remain in medical tumor segmentation. This is because, although the human visual system can detect symmetries in 2D images effectively, regular CNNs can only exploit translation invariance, overlooking further inherent symmetries existing in medical images such as rotations and reflections. To solve this problem, we propose a novel group e…
Regularization in convolutional neural networks (CNNs) is usually addressed with dropout layers. However, dropout is sometimes detrimental in the convolutional part of a CNN as it simply sets to zero a percentage of pixels in the feature maps, adding unrepresentative examples during training. Here, we propose a CNN layer that performs regularization by applying random rotations of reflections to a small percentage of feature maps after every convolutional layer. We prove how this concept is beneficial for images with orientational symmetries, such as in medical images, as it provides a certain…
Institute for Infocomm Research (A*STAR)（信息通信研究院（新加坡科技研究局））；Université Pierre et Marie Curie（皮埃尔和玛丽·居里大学）
With deep learning becoming the dominant approach in computer vision, the use of representations extracted from Convolutional Neural Nets (CNNs) is quickly gaining ground on Fisher Vectors (FVs) as favoured state-of-the-art global image descriptors for image instance retrieval. While the good performance of CNNs for image classification are unambiguously recognised, which of the two has the upper hand in the image retrieval context is not entirely clear yet. In this work, we propose a comprehensive study that systematically evaluates FVs and CNNs for image retrieval. The first part compares th…
DIKU University of Copenhagen（哥本哈根大学DIKU）；Biomediq A/S（Biomediq公司）；Cerebriu A/S（Cerebriu公司）；King’s College London（伦敦国王学院）；University College London（伦敦大学学院）
For proper generalization performance of convolutional neural networks (CNNs) in medical image segmentation, the learnt features should be invariant under particular non-linear shape variations of the input. To induce invariance in CNNs to such transformations, we propose Probabilistic Augmentation of Data using Diffeomorphic Image Transformation (PADDIT) -- a systematic framework for generating realistic transformations that can be used to augment data for training CNNs. We show that CNNs trained with PADDIT outperforms CNNs trained without augmentation and with generic augmentation in segmen…
Convolutional Neural Networks (CNNs) are commonly assumed to be invariant to small image transformations: either because of the convolutional architecture or because they were trained using data augmentation. Recently, several authors have shown that this is not the case: small translations or rescalings of the input image can drastically change the network's prediction. In this paper, we quantify this phenomena and ask why neither the convolutional architecture nor data augmentation are sufficient to achieve the desired invariance. Specifically, we show that the convolutional architecture doe…
Tracking and localizing objects is a central problem in computer-assisted surgery. Optical coherence tomography (OCT) can be employed as an optical tracking system, due to its high spatial and temporal resolution. Recently, 3D convolutional neural networks (CNNs) have shown promising performance for pose estimation of a marker object using single volumetric OCT images. While this approach relied on spatial information only, OCT allows for a temporal stream of OCT image volumes capturing the motion of an object at high volumes rates. In this work, we systematically extend 3D CNNs to 4D spatio-t…
Australian Institute for Machine Learning（澳大利亚机器学习研究所）；University of Adelaide（阿德莱德大学）
Although provably robust to translational perturbations, convolutional neural networks (CNNs) are known to suffer from extreme performance degradation when presented at test time with more general geometric transformations of inputs. Recently, this limitation has motivated a shift in focus from CNNs to Capsule Networks (CapsNets). However, CapsNets suffer from admitting relatively few theoretical guarantees of invariance. We introduce a rigourous mathematical framework to permit invariance to any Lie group of warps, exclusively using convolutions (over Lie groups), without the need for capsule…
University of Applied Sciences Western Switzerland (HES-SO)（瑞士西部应用科学大学）；CHUV（洛桑大学医院）；Harvard School of Engineering and Applied Sciences（哈佛工程与应用科学学院）
Locally Rotation Invariant (LRI) operators have shown great potential in biomedical texture analysis where patterns appear at random positions and orientations. LRI operators can be obtained by computing the responses to the discrete rotation of local descriptors, such as Local Binary Patterns (LBP) or the Scale Invariant Feature Transform (SIFT). Other strategies achieve this invariance using Laplacian of Gaussian or steerable wavelets for instance, preventing the introduction of sampling errors during the discretization of the rotations. In this work, we obtain LRI operators via the local pr…
A fundamental problem in object recognition is the development of image representations that are invariant to common transformations such as translation, rotation, and small deformations. There are multiple hypotheses regarding the source of translation invariance in CNNs. One idea is that translation invariance is due to the increasing receptive field size of neurons in successive convolution layers. Another possibility is that invariance is due to the pooling operation. We develop a simple a tool, the translation-sensitivity map, which we use to visualize and quantify the translation-invaria…
Cardiac left ventricle (LV) quantification provides a tool for diagnosing cardiac diseases. Automatic calculation of all relevant LV indices from cardiac MR images is an intricate task due to large variations among patients and deformation during the cardiac cycle. Typical methods are based on segmentation of the myocardium or direct regression from MR images. To consider cardiac motion and deformation, recurrent neural networks and spatio-temporal convolutional neural networks (CNNs) have been proposed. We study an approach combining state-of-the-art models and emphasizing transfer learning t…
University of Electronic Science and Technology of China（电子科技大学）
Convolutional Neural Networks (CNNs) perform very well in image classification and object detection in recent years, but even the most advanced models have limited rotation invariance. Known solutions include the enhancement of training data and the increase of rotation invariance by globally merging the rotation equivariant features. These methods either increase the workload of training or increase the number of model parameters. To address this problem, this paper proposes a module that can be inserted into the existing networks, and directly incorporates the rotation invariance into the fe…
Image based localization is one of the important problems in computer vision due to its wide applicability in robotics, augmented reality, and autonomous systems. There is a rich set of methods described in the literature how to geometrically register a 2D image w.r.t.\ a 3D model. Recently, methods based on deep (and convolutional) feedforward networks (CNNs) became popular for pose regression. However, these CNN-based methods are still less accurate than geometry based methods despite being fast and memory efficient. In this work we design a deep neural network architecture based on sparse f…
CentraleSupelec（巴黎中央理工-高等电力学院）；Université Paris-Saclay（巴黎萨克雷大学）；MILA（蒙特利尔学习算法研究所）；University of Montreal（蒙特利尔大学）；Inria Paris（法国国家信息与自动化研究所巴黎分部）；Inria Lille（法国国家信息与自动化研究所里尔分部）；Inria Saclay（法国国家信息与自动化研究所萨克雷分部）
We study the first-order scattering transform as a candidate for reducing the signal processed by a convolutional neural network (CNN). We show theoretical and empirical evidence that in the case of natural images and sufficiently small translation invariance, this transform preserves most of the signal information needed for classification while substantially reducing the spatial resolution and total signal size. We demonstrate that cascading a CNN with this representation performs on par with ImageNet classification models, commonly used in downstream tasks, such as the ResNet-50. We subsequ…
University of Science and Technology of China（中国科学技术大学）；University of Technology Sydney（悉尼科技大学）
Convolutional Neural Networks (CNNs) have demonstrated state-of-the-art performance on many visual recognition tasks. However, the combination of convolution and pooling operations only shows invariance to small local location changes in meaningful objects in input. Sometimes, such networks are trained using data augmentation to encode this invariance into the parameters, which restricts the capacity of the model to learn the content of these objects. A more efficient use of the parameter budget is to encode rotation or translation invariance into the model architecture, which relieves the mod…
Convolutional Neural Networks (CNNs) define an exceptionally powerful class of models for image classification, but the theoretical background and the understanding of how invariances to certain transformations are learned is limited. In a large scale screening with images modified by different affine and nonaffine transformations of varying magnitude, we analyzed the behavior of the CNN architectures AlexNet and ResNet. If the magnitude of different transformations does not exceed a class- and transformation dependent threshold, both architectures show invariant behavior. In this work we furt…
Taras Shevchenko National University of Kyiv（基辅塔拉斯·舍甫琴科国立大学）
At this work we introduce horizontally symmetric convolutional kernels for CNNs which make the network output invariant to horizontal flips of the image. We also study other types of symmetric kernels which lead to vertical flip invariance, and approximate rotational invariance. We show that usage of such kernels acts as regularizer, and improves generalization of the convolutional neural networks at the cost of more complicated training process.
Efficient Rotation Invariance in Deep Neural Networks through Artificial Mental Rotation
ZHAW Centre for Artificial Intelligence（苏黎世应用科学大学人工智能中心）；University of Lugano（卢加诺大学）；European Centre for Living Technology（欧洲生命技术中心）；The Swiss AI Lab IDSIA（瑞士人工智能实验室 IDSIA）；King Abdullah University of Science and Technology (KAUST)（阿卜杜拉国王科技大学）
Within the world of machine learning there exists a wide range of different methods with respective advantages and applications. This paper seeks to present and discuss one such method, namely Convolutional Neural Networks (CNNs). CNNs are deep neural networks that use a special linear operation called convolution. This operation represents a key and distinctive element of CNNs, and will therefore be the focus of this method paper. The discussion starts with the theoretical foundations that underlie convolutions and CNNs. Then, the discussion proceeds to discuss some improvements and augmentat…
Convolutional Neural Networks (CNNs) are extremely efficient, since they exploit the inherent translation-invariance of natural images. However, translation is just one of a myriad of useful spatial transformations. Can the same efficiency be attained when considering other spatial invariances? Such generalized convolutions have been considered in the past, but at a high computational cost. We present a construction that is simple and exact, yet has the same computational complexity that standard convolutions enjoy. It consists of a constant image warp followed by a simple convolution, which a…
Finding local correspondences between images with different viewpoints requires local descriptors that are robust against geometric transformations. An approach for transformation invariance is to integrate out the transformations by pooling the features extracted from transformed versions of an image. However, the feature pooling may sacrifice the distinctiveness of the resulting descriptors. In this paper, we introduce a novel visual descriptor named Group Invariant Feature Transform (GIFT), which is both discriminative and robust to geometric transformations. The key idea is that the featur…
Sketch-based image retrieval (SBIR) is the task of retrieving natural images (photos) that match the semantics and the spatial configuration of hand-drawn sketch queries. The universality of sketches extends the scope of possible applications and increases the demand for efficient SBIR solutions. In this paper, we study classic triplet-based SBIR solutions and show that a persistent invariance to horizontal flip (even after model finetuning) is harming performance. To overcome this limitation, we propose several approaches and evaluate in depth each of them to check their effectiveness. Our ma…
State-of-the-art deep learning systems often require large amounts of data and computation. For this reason, leveraging known or unknown structure of the data is paramount. Convolutional neural networks (CNNs) are successful examples of this principle, their defining characteristic being the shift-equivariance. By sliding a filter over the input, when the input shifts, the response shifts by the same amount, exploiting the structure of natural images where semantic content is independent of absolute pixel positions. This property is essential to the success of CNNs in audio, image and video re…
Indian Institute of Technology Hyderabad（印度理工学院海得拉巴分校）；Indian Institute of Information Technology Vadodara（印度信息技术学院瓦多达拉分校）
With the substantial performance of neural networks in sensitive fields increases the need for interpretable deep learning models. Major challenge is to uncover the multiscale and distributed representation hidden inside the basket mappings of the deep neural networks. Researchers have been trying to comprehend it through visual analysis of features, mathematical structures, or other data-driven approaches. Here, we work on implementation invariances of CNN-based representations and present an analytical binary prototype that provides useful insights for large scale real-life applications. We …
Image representations, from SIFT and Bag of Visual Words to Convolutional Neural Networks (CNNs), are a crucial component of almost any image understanding system. Nevertheless, our understanding of them remains limited. In this paper we conduct a direct analysis of the visual information contained in representations by asking the following question: given an encoding of an image, to which extent is it possible to reconstruct the image itself? To answer this question we contribute a general framework to invert representations. We show that this method can invert representations such as HOG and…
Accurate Shift Invariant Convolutional Neural Networks Using Gaussian-Hermite Moments
organization= School of Computing, Engineering \& Digital Technologies, Teesside University , city= London , country= UK；organization= Department of Advanced Computing Sciences, Maastricht University , city= Maastricht , country= The Netherlands；organization= School of Agri-food Technology；Manufacturing, University of Lincoln , city= Lincoln , country= UK
The convolutional layers of standard convolutional neural networks (CNNs) are equivariant to translation. However, the convolution and fully-connected layers are not equivariant or invariant to other affine geometric transformations. Recently, a new class of CNNs is proposed in which the conventional layers of CNNs are replaced with equivariant convolution, pooling, and batch-normalization layers. The final classification layer in equivariant neural networks is invariant to different affine geometric transformations such as rotation, reflection and translation, and the scalar value is obtained…
Despite the importance of image representations such as histograms of oriented gradients and deep Convolutional Neural Networks (CNN), our theoretical understanding of them remains limited. Aiming at filling this gap, we investigate three key mathematical properties of representations: equivariance, invariance, and equivalence. Equivariance studies how transformations of the input image are encoded by the representation, invariance being a special case where a transformation has no effect. Equivalence studies whether two representations, for example two different parametrisations of a CNN, cap…
Revisiting Data Augmentation for Rotational Invariance in Convolutional Neural Networks
Instituto de Investigación en Informática LIDI, Facultad de Informática, Universidad Nacional de La Plata（拉普拉塔国立大学信息学院LIDI信息学研究所）；Universitat Rovira i Virgili（罗维拉-依维尔基里大学）
Ryerson University（瑞尔森大学）；Vector Institute for AI（向量人工智能研究所）；York University（约克大学）；Toronto AI Lab, LG Electronics（LG电子多伦多人工智能实验室）；Samsung AI Centre Toronto（三星多伦多人工智能中心）；University of Guelph（圭尔夫大学）
In this paper, we challenge the common assumption that collapsing the spatial dimensions of a 3D (spatial-channel) tensor in a convolutional neural network (CNN) into a vector via global pooling removes all spatial information. Specifically, we demonstrate that positional information is encoded based on the ordering of the channel dimensions, while semantic information is largely not. Following this demonstration, we show the real world impact of these findings by applying them to two applications. First, we propose a simple yet effective data augmentation strategy and loss function which impr…
