Analysing rotation-invariance of a log-polar transformation in convolutional neural networks

Amorim, Marta; Bortoloti, Frederico Damasceno; Ciarelli, Patrick Marques; Oliveira, Elias; Souza, Alberto F. De

doi:10.1109/ijcnn.2018.8489295

Cited by 7 publications

(8 citation statements)

References 11 publications

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“…However, PTN only recognized global deformation. In [37], the results show that several angles are better fitted to CNNs with log-polar operations for all tested datasets. However, only rotation transformation is performed and experiments are carried out under different rotations.…”

Section: Introductionmentioning

confidence: 94%

“…If the target in the cartesian coordinates changes in proportion, then it is equivalent to the target in the log-polar coordinates being displaced along the radius axis [37]. The rotation change in the target in cartesian coordinates is equivalent to the displacement change in the target in the log-polar coordinate space along the angular axis.…”

Section: Log-polar Transformationmentioning

confidence: 99%

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LPNet: Retina Inspired Neural Network for Object Detection and Recognition

et al. 2021

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The detection of rotated objects is a meaningful and challenging research work. Although the state-of-the-art deep learning models have feature invariance, especially convolutional neural networks (CNNs), their architectures did not specifically design for rotation invariance. They only slightly compensate for this feature through pooling layers. In this study, we propose a novel network, named LPNet, to solve the problem of object rotation. LPNet improves the detection accuracy by combining retina-like log-polar transformation. Furthermore, LPNet is a plug-and-play architecture for object detection and recognition. It consists of two parts, which we name as encoder and decoder. An encoder extracts images which feature in log-polar coordinates while a decoder eliminates image noise in cartesian coordinates. Moreover, according to the movement of center points, LPNet has stable and sliding modes. LPNet takes the single-shot multibox detector (SSD) network as the baseline network and the visual geometry group (VGG16) as the feature extraction backbone network. The experiment results show that, compared with conventional SSD networks, the mean average precision (mAP) of LPNet increased by 3.4% for regular objects and by 17.6% for rotated objects.

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Section: Introductionmentioning

confidence: 94%

Section: Log-polar Transformationmentioning

confidence: 99%

LPNet: Retina Inspired Neural Network for Object Detection and Recognition

et al. 2021

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“…(Esteves et al, 2017) extend spatial transformer networks (Jaderberg et al, 2015) to use the log-polar transform allowing them to fixate the high-resolution region on objects of interest. (Amorim et al, 2018) evaluate the rotation invariance of log-polar image representations in conjunction with CNNs. (Kim et al, 2020) similarly evaluate scale and rotation in- (Balasuriya, 2006), resampled to a uniform grid.…”

Section: Deep Learning On Foveated Imagesmentioning

confidence: 99%

Monte-Carlo Convolutions on Foveated Images

Killick

Aragon-Camarasa

Siebert

2022

Proceedings of the 17th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Application

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Foveated vision captures a visual scene at space-variant resolution. This makes the application of parameterized convolutions to foveated images difficult as they do not have a dense-grid representation in cartesian space. Log-polar space is frequently used to create a dense grid representation of foveated images, however this image representation may not be appropriate for all applications. In this paper we rephrase the convolution operation as the Monte-Carlo estimation of the filter response of the foveated image and a continuous filter kernel, an idea that has seen frequent use for deep learning on point clouds. We subsume our convolution operation into a simple CNN architecture that processes foveated images in cartesian space. We evaluate our system in the context of image classification and show that our approach significantly outperforms an equivalent CNN processing a foveated image in log-polar space.

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“…In [147], Chen et al proposed two different polar transformation modules, Full Polar Convolution (FPolarConv) and Local Polar Fig. 11 Strategies for encoding scale invariance include using different filter sizes in each convolution layer (a), employing independent sub-networks for learning different scales and then aggregating their output predictions (b), using multi-scale ftlters with competitive pooling to select best option (c), and exploiting image and/or feature pyramids (d) Another type of domain conversion is based on log-radial harmonics or log-polar representation [65, [150][151][152][153], which renders the rotation of an image in the Cartesian coordinate system as a plane translation in one axis and scale change as a translation along the other main axes of the logarithmicpolar plane. A key advantage of the polar-log transformations lies in the fact that both rotation and scale are encoded as opposed to rotation-only invariance in the case of the polar transform approach.…”

Section: Rotation Invariancementioning

confidence: 99%

CNN Architectures for Geometric Transformation-Invariant Feature Representation in Computer Vision: A Review

Mumuni

2021

SN COMPUT. SCI.

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One of the main challenges in machine vision relates to the problem of obtaining robust representation of visual features that remain unaffected by geometric transformations. This challenge arises naturally in many practical machine vision tasks. For example, in mobile robot applications like simultaneous localization and mapping (SLAM) and visual tracking, object shapes change depending on their orientation in the 3D world, camera proximity, viewpoint, or perspective. In addition, natural phenomena such as occlusion, deformation, and clutter can cause geometric appearance changes of the underlying objects, leading to geometric transformations of the resulting images. Recently, deep learning techniques have proven very successful in visual recognition tasks but they typically perform poorly with small data or when deployed in environments that deviate from training conditions. While convolutional neural networks (CNNs) have inherent representation power that provides a high degree of invariance to geometric image transformations, they are unable to satisfactorily handle nontrivial transformations. In view of this limitation, several techniques have been devised to extend CNNs to handle these situations. This article reviews some of the most promising approaches to extend CNN architectures to handle nontrivial geometric transformations. Key strengths and weaknesses, as well as the application domains of the various approaches are also highlighted. The review shows that although an adequate model for generalized geometric transformations has not yet been formulated, several techniques exist for solving specific problems. Using these methods, it is possible to develop task-oriented solutions to deal with nontrivial transformations.

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Analysing rotation-invariance of a log-polar transformation in convolutional neural networks

Cited by 7 publications

References 11 publications

LPNet: Retina Inspired Neural Network for Object Detection and Recognition

LPNet: Retina Inspired Neural Network for Object Detection and Recognition

Monte-Carlo Convolutions on Foveated Images

CNN Architectures for Geometric Transformation-Invariant Feature Representation in Computer Vision: A Review

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