We introduce a simple modification of local image descriptors, such as SIFT, based on pooling gradient orientations across different domain sizes, in addition to spatial locations. The resulting descriptor, which we call DSP-SIFT, outperforms other methods in wide-baseline matching benchmarks, including those based on convolutional neural networks, despite having the same dimension of SIFT and requiring no training.
In neural network architectures, there is evidence that abstracting spatial pooling hierarchically, aggregating nearby responses in feature maps, is beneficial @cite_15 . This process could be extended by aggregating across different neighborhood sizes in feature space. To the best of our knowledge, the only architecture that performs some kind of pooling across scales is @cite_38 , although the justification provided in @cite_26 only concerns translation within each scale. The same goes for @cite_33 , where pooling (low-pass filtering) is only performed within each scale, and not across scales. Other works learn the regions for spatial pooling, for instance @cite_19 @cite_5 , but still restrict pooling to within-scale, similar to @cite_24 , rather than across scales as we advocate.
@cite_38 @cite_26 @cite_33 @cite_24 @cite_19 @cite_5 @cite_15
2963544187 2559156603 2798598284 2962971773
Deep neural networks with alternating convolutional, max-pooling and decimation layers are widely used in state of the art architectures for computer vision. Max-pooling purposefully discards precise spatial information in order to create features that are more robust, and typically organized as lower resolution spatial feature maps. On some tasks, such as whole-image classification, max-pooling derived features are well suited, however, for tasks requiring precise localization, such as pixel level prediction and segmentation, max-pooling destroys exactly the information required to perform well. Precise localization may be preserved by shallow convnets without pooling but at the expense of robustness. Can we have our max-pooled multilayered cake and eat it too? Several papers have proposed summation and concatenation based methods for combining upsampled coarse, abstract features with finer features to produce robust pixel level predictions. Here we introduce another model — dubbed Recombinator Networks — where coarse features inform finer features early in their formation such that finer features can make use of several layers of computation in deciding how to use coarse features. The model is trained once, end-to-end and performs better than summation-based architectures, reducing the error from the previous state of the art on two facial keypoint datasets, AFW and AFLW, by 30 and beating the current state-of-the-art on 300W without using extra data. We improve performance even further by adding a denoising prediction model based on a novel convnet formulation. Feature pooling layers (e.g., max pooling) in convolutional neural networks (CNNs) serve the dual purpose of providing increasingly abstract representations as well as yielding computational savings in subsequent convolutional layers. We view the pooling operation in CNNs as a two step procedure: first, a pooling window (e.g., 2&#xd7; 2) slides over the feature map with stride one which leaves the spatial resolution intact, and second, downsampling is performed by selecting one pixel from each non-overlapping pooling window in an often uniform and deterministic (e.g., top-left) manner. Our starting point in this work is the observation that this regularly spaced downsampling arising from non-overlapping windows, although intuitive from a signal processing perspective (which has the goal of signal reconstruction), is not necessarily optimal for learning (where the goal is to generalize). We study this aspect and propose a novel pooling strategy with stochastic spatial sampling (S3Pool), where the regular downsampling is replaced by a more general stochastic version. We observe that this general stochasticity acts as a strong regularizer, and can also be seen as doing implicit data augmentation by introducing distortions in the feature maps. We further introduce a mechanism to control the amount of distortion to suit different datasets and architectures. To demonstrate the effectiveness of the proposed approach, we perform extensive experiments on several popular image classification benchmarks, observing excellent improvements over baseline models. Two architectures that generalize convolutional neural networks (CNNs) for the processing of signals supported on graphs are introduced. We start with the selection graph neural network (GNN), which replaces linear time invariant filters with linear shift invariant graph filters to generate convolutional features and reinterprets pooling as a possibly nonlinear subsampling stage where nearby nodes pool their information in a set of preselected sample nodes. A key component of the architecture is to remember the position of sampled nodes to permit computation of convolutional features at deeper layers. The second architecture, dubbed aggregation GNN, diffuses the signal through the graph and stores the sequence of diffused components observed by a designated node. This procedure effectively aggregates all components into a stream of information having temporal structure to which the convolution and pooling stages of regular CNNs can be applied. A multinode version of aggregation GNNs is further introduced for operation in large-scale graphs. An important property of selection and aggregation GNNs is that they reduce to conventional CNNs when particularized to time signals reinterpreted as graph signals in a circulant graph. Comparative numerical analyses are performed in a source localization application over synthetic and real-world networks. Performance is also evaluated for an authorship attribution problem and text category classification. Multinode aggregation GNNs are consistently the best-performing GNN architecture. Deep convolutional neural networks (DCNNs) have shown remarkable performance in image classification tasks in recent years. Generally, deep neural network architectures are stacks consisting of a large number of convolutional layers, and they perform downsampling along the spatial dimension via pooling to reduce memory usage. Concurrently, the feature map dimension (i.e., the number of channels) is sharply increased at downsampling locations, which is essential to ensure effective performance because it increases the diversity of high-level attributes. This also applies to residual networks and is very closely related to their performance. In this research, instead of sharply increasing the feature map dimension at units that perform downsampling, we gradually increase the feature map dimension at all units to involve as many locations as possible. This design, which is discussed in depth together with our new insights, has proven to be an effective means of improving generalization ability. Furthermore, we propose a novel residual unit capable of further improving the classification accuracy with our new network architecture. Experiments on benchmark CIFAR-10, CIFAR-100, and ImageNet datasets have shown that our network architecture has superior generalization ability compared to the original residual networks. Code is available at https: github.com jhkim89 PyramidNet.