We study the effect of injecting local scale equivariance into Convolutional Neural Networks. This is done by applying each convolutional filter at multiple scales. The output is a vector field encoding for the maximally activating scale and the scale itself, which is further processed by the following convolutional layers. This allows all the intermediate representations to be locally scale equivariant. We show that this improves the performance of the model by over 20 in the scale equivariant task of regressing the scaling factor applied to randomly scaled MNIST digits. Furthermore, we find it also useful for scale invariant tasks, such as the actual classification of randomly scaled digits. This highlights the usefulness of allowing for a compact representation that can also learn relationships between different local scales by keeping internal scale equivariance.
The modified convolution operator presented by @cite_11 is locally scale invariant and consists of all the elements shown in Fig. , except that the output consists only of the magnitude map. If we apply it to an image and look at the value at a single location of the output, small variations in scale of the underlying local object will have no effect on this value (see Fig. middle). This is precisely the sought behavior. However, if these scale variations contained information useful for the task at hand but were discarded, we would be hampering the model's performance. For instance, in histology and cytology, the sizes of cells and organelles can provide hints about their functionality, while in scene understanding, apparent object sizes implicitly encode distance from the camera and can be valuable information for scene segmentation @cite_3 .
@cite_3 @cite_11
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Many existing scene parsing methods adopt Convolutional Neural Networks with fixed-size receptive fields, which frequently result in inconsistent predictions of large objects and invisibility of small objects. To tackle this issue, we propose a scale-adaptive convolution to acquire flexiblesize receptive fields during scene parsing. Through adding a new scale regression layer, we can dynamically infer the position-adaptive scale coefficients which are adopted to resize the convolutional patches. Consequently, the receptive fields can be adjusted automatically according to the various sizes of the objects in scene images. Thus, the problems of invisible small objects and inconsistent large-object predictions can be alleviated. Furthermore, our proposed scale-adaptive convolutions are not only differentiable to learn the convolutional parameters and scale coefficients in an end-to-end way, but also of high parallelizability for the convenience of GPU implementation. Additionally, since the new scale regression layers are learned implicitly, any extra training supervision of object sizes is unnecessary. Extensive experiments on Cityscapes and ADE20K datasets well demonstrate the effectiveness of the proposed scaleadaptive convolutions. Convolutional neural networks (CNNs) have recently achieved remarkable successes in various image classification and understanding tasks. The deep features obtained at the top fully connected layer of the CNN (FC-features) exhibit rich global semantic information and are extremely effective in image classification. On the other hand, the convolutional features in the middle layers of the CNN also contain meaningful local information, but are not fully explored for image representation. In this paper, we propose a novel locally supervised deep hybrid model (LS-DHM) that effectively enhances and explores the convolutional features for scene recognition. First, we notice that the convolutional features capture local objects and fine structures of scene images, which yield important cues for discriminating ambiguous scenes, whereas these features are significantly eliminated in the highly compressed FC representation. Second, we propose a new local convolutional supervision layer to enhance the local structure of the image by directly propagating the label information to the convolutional layers. Third, we propose an efficient Fisher convolutional vector (FCV) that successfully rescues the orderless mid-level semantic information (e.g., objects and textures) of scene image. The FCV encodes the large-sized convolutional maps into a fixed-length mid-level representation, and is demonstrated to be strongly complementary to the high-level FC-features. Finally, both the FCV and FC-features are collaboratively employed in the LS-DHM representation, which achieves outstanding performance in our experiments. It obtains 83.75 and 67.56 accuracies, respectively, on the heavily benchmarked MIT Indoor67 and SUN397 data sets, advancing the state-of-the-art substantially. In this correspondence, a completed modeling of the local binary pattern (LBP) operator is proposed and an associated completed LBP (CLBP) scheme is developed for texture classification. A local region is represented by its center pixel and a local difference sign-magnitude transform (LDSMT). The center pixels represent the image gray level and they are converted into a binary code, namely CLBP-Center (CLBP_C), by global thresholding. LDSMT decomposes the image local differences into two complementary components: the signs and the magnitudes, and two operators, namely CLBP-Sign (CLBP_S) and CLBP-Magnitude (CLBP_M), are proposed to code them. The traditional LBP is equivalent to the CLBP_S part of CLBP, and we show that CLBP_S preserves more information of the local structure than CLBP_M, which explains why the simple LBP operator can extract the texture features reasonably well. By combining CLBP_S, CLBP_M, and CLBP_C features into joint or hybrid distributions, significant improvement can be made for rotation invariant texture classification. Abstract Convolutional Neural Networks (CNNs) require large image corpora to be trained on classification tasks. The variation in image resolutions, sizes of objects and patterns depicted, and image scales, hampers CNN training and performance, because the task-relevant information varies over spatial scales. Previous work attempting to deal with such scale variations focused on encouraging scale-invariant CNN representations. However, scale-invariant representations are incomplete representations of images, because images contain scale-variant information as well. This paper addresses the combined development of scale-invariant and scale-variant representations. We propose a multi-scale CNN method to encourage the recognition of both types of features and evaluate it on a challenging image classification task involving task-relevant characteristics at multiple scales. The results show that our multi-scale CNN outperforms single-scale CNN. This leads to the conclusion that encouraging the combined development of a scale-invariant and scale-variant representation in CNNs is beneficial to image recognition performance.