Humans take advantage of real world symmetries for various tasks, yet capturing their superb symmetry perception mechanism into a computational model remains elusive. Encouraged by a new discovery (CVPR 2016) demonstrating extremely high inter-person accuracy of human perceived symmetries in the wild, we have created the first deep-learning neural network for reflection and rotation symmetry detection (Sym-NET), trained on photos from MS-COCO (Common Object in COntext) dataset with nearly 11K symmetry-labels from more than 400 human observers. We employ novel methods to convert discrete human labels into symmetry heatmaps, capture symmetry densely in an image and quantitatively evaluate Sym-NET against multiple existing computer vision algorithms. Using the symmetry competition testsets from CVPR 2013 and unseen MS-COCO photos, Sym-NET comes out as the winner with significantly superior performance over all other competitors. Beyond mathematically well-defined symmetries on a plane, Sym-NET demonstrates abilities to identify viewpoint-varied 3D symmetries, partially occluded symmetrical objects and symmetries at a semantic level.
Different from recent efforts in the deep learning CNN community where researchers are seeking networks that are rotation reflection or affine invariant to input images @cite_23 @cite_68 @cite_16 @cite_24 , our work explicitly acknowledges (near) reflection and rotation symmetries in the raw data regardless of the transformations applied on the input images. To the best of our knowledge, there have been no deep learning networks trained on human symmetry labels for automated reflection and rotation symmetry detections.
@cite_24 @cite_68 @cite_23 @cite_16
2775143585 2461725797 2951320766 2576915720
In recent years, convolutional neural networks (CNN) have played an important role in the field of deep learning. Variants of CNN's have proven to be very successful in classification tasks across different domains. However, there are two big drawbacks to CNN's: their failure to take into account of important spatial hierarchies between features, and their lack of rotational invariance. As long as certain key features of an object are present in the test data, CNN's classify the test data as the object, disregarding features' relative spatial orientation to each other. This causes false positives. The lack of rotational invariance in CNN's would cause the network to incorrectly assign the object another label, causing false negatives. To address this concern, propose a novel type of neural network using the concept of capsules in a recent paper. With the use of dynamic routing and reconstruction regularization, the capsule network model would be both rotation invariant and spatially aware. The capsule network has shown its potential by achieving a state-of-the-art result of 0.25 test error on MNIST without data augmentation such as rotation and scaling, better than the previous baseline of 0.39 . To further test out the application of capsule networks on data with higher dimensionality, we attempt to find the best set of configurations that yield the optimal test error on CIFAR10 dataset. Thanks to the powerful feature representations obtained through deep convolutional neural network (CNN), the performance of object detection has recently been substantially boosted. Despite the remarkable success, the problems of object rotation, within-class variability, and between-class similarity remain several major challenges. To address these problems, this paper proposes a novel and effective method to learn a rotation-invariant and Fisher discriminative CNN (RIFD-CNN) model. This is achieved by introducing and learning a rotation-invariant layer and a Fisher discriminative layer, respectively, on the basis of the existing high-capacity CNN architectures. Specifically, the rotation-invariant layer is trained by imposing an explicit regularization constraint on the objective function that enforces invariance on the CNN features before and after rotating. The Fisher discriminative layer is trained by imposing the Fisher discrimination criterion on the CNN features so that they have small within-class scatter but large between-class separation. In the experiments, we comprehensively evaluate the proposed method for object detection task on a public available aerial image dataset and the PASCAL VOC 2007 dataset. State-of-the-art results are achieved compared with the existing baseline methods. Translating or rotating an input image should not affect the results of many computer vision tasks. Convolutional neural networks (CNNs) are already translation equivariant: input image translations produce proportionate feature map translations. This is not the case for rotations. Global rotation equivariance is typically sought through data augmentation, but patch-wise equivariance is more difficult. We present Harmonic Networks or H-Nets, a CNN exhibiting equivariance to patch-wise translation and 360-rotation. We achieve this by replacing regular CNN filters with circular harmonics, returning a maximal response and orientation for every receptive field patch. H-Nets use a rich, parameter-efficient and low computational complexity representation, and we show that deep feature maps within the network encode complicated rotational invariants. We demonstrate that our layers are general enough to be used in conjunction with the latest architectures and techniques, such as deep supervision and batch normalization. We also achieve state-of-the-art classification on rotated-MNIST, and competitive results on other benchmark challenges. Translating or rotating an input image should not affect the results of many computer vision tasks. Convolutional neural networks (CNNs) are already translation equivariant: input image translations produce proportionate feature map translations. This is not the case for rotations. Global rotation equivariance is typically sought through data augmentation, but patch-wise equivariance is more difficult. We present Harmonic Networks or H-Nets, a CNN exhibiting equivariance to patch-wise translation and 360-rotation. We achieve this by replacing regular CNN filters with circular harmonics, returning a maximal response and orientation for every receptive field patch. H-Nets use a rich, parameter-efficient and fixed computational complexity representation, and we show that deep feature maps within the network encode complicated rotational invariants. We demonstrate that our layers are general enough to be used in conjunction with the latest architectures and techniques, such as deep supervision and batch normalization. We also achieve state-of-the-art classification on rotated-MNIST, and competitive results on other benchmark challenges.