We show that existing upsampling operators can be unified with the notion of the index function. This notion is inspired by an observation in the decoding process of deep image matting where indices-guided unpooling can recover boundary details much better than other upsampling operators such as bilinear interpolation. By looking at the indices as a function of the feature map, we introduce the concept of learning to index, and present a novel index-guided encoder-decoder framework where indices are self-learned adaptively from data and are used to guide the pooling and upsampling operators, without the need of supervision. At the core of this framework is a flexible network module, termed IndexNet, which dynamically predicts indices given an input. Due to its flexibility, IndexNet can be used as a plug-in applying to any off-the-shelf convolutional networks that have coupled downsampling and upsampling stages. We demonstrate the effectiveness of IndexNet on the task of natural image matting where the quality of learned indices can be visually observed from predicted alpha mattes. Results on the Composition-1k matting dataset show that our model built on MobileNetv2 exhibits at least @math improvement over the seminal VGG-16 based deep matting baseline, with less training data and lower model capacity. Code and models has been made available at: this https URL
Our work is primarily inspired by the unpooling operator @cite_24 . We remark that, it is important to keep the spatial information before loss of such information occurred in feature map downsampling, and more importantly, to use stored information during upsampling. Unpooling shows a simple and effective case of doing this, but we argue there is much room to improve. In this paper, we illustrate that the unpooling operator is a special form of index function, and we can learn an index function beyond unpooling.
@cite_24
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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. To reduce the cost of storing, processing, and visualizing a large-scale point cloud, we propose a randomized resampling strategy that selects a representative subset of points while preserving application-dependent features. The strategy is based on graphs, which can represent underlying surfaces and lend themselves well to efficient computation. We use a general feature-extraction operator to represent application-dependent features and propose a general reconstruction error to evaluate the quality of resampling; by minimizing the error, we obtain a general form of optimal resampling distribution. The proposed resampling distribution is guaranteed to be shift-, rotation- and scale-invariant in the three-dimensional space. We then specify the feature-extraction operator to be a graph filter and study specific resampling strategies based on all-pass, low-pass, high-pass graph filtering and graph filter banks. We validate the proposed methods on three applications: Large-scale visualization, accurate registration, and robust shape modeling demonstrating the effectiveness and efficiency of the proposed resampling methods. For crowded scenes, the accuracy of object-based computer vision methods declines when the images are low-resolution and objects have severe occlusions. Taking counting methods for example, almost all the recent state-of-the-art counting methods bypass explicit detection and adopt regression-based methods to directly count the objects of interest. Among regression-based methods, density map estimation, where the number of objects inside a subregion is the integral of the density map over that subregion, is especially promising because it preserves spatial information, which makes it useful for both counting and localization (detection and tracking). With the power of deep convolutional neural networks (CNNs) the counting performance has improved steadily. The goal of this paper is to evaluate density maps generated by density estimation methods on a variety of crowd analysis tasks, including counting, detection, and tracking. Most existing CNN methods produce density maps with resolution that is smaller than the original images, due to the downsample strides in the convolution pooling operations. To produce an original-resolution density map, we also evaluate a classical CNN that uses a sliding window regressor to predict the density for every pixel in the image. We also consider a fully convolutional adaptation, with skip connections from lower convolutional layers to compensate for loss in spatial information during upsampling. In our experiments, we found that the lower-resolution density maps sometimes have better counting performance. In contrast, the original-resolution density maps improved localization tasks, such as detection and tracking, compared with bilinear upsampling the lower-resolution density maps. Finally, we also propose several metrics for measuring the quality of a density map, and relate them to experiment results on counting and localization. Most convolutional neural networks use some method for gradually downscaling the size of the hidden layers. This is commonly referred to as pooling, and is applied to reduce the number of parameters, improve invariance to certain distortions, and increase the receptive field size. Since pooling by nature is a lossy process, it is crucial that each such layer maintains the portion of the activations that is most important for the network's discriminability. Yet, simple maximization or averaging over blocks, max or average pooling, or plain downsampling in the form of strided convolutions are the standard. In this paper, we aim to leverage recent results on image downscaling for the purposes of deep learning. Inspired by the human visual system, which focuses on local spatial changes, we propose detail-preserving pooling (DPP), an adaptive pooling method that magnifies spatial changes and preserves important structural detail. Importantly, its parameters can be learned jointly with the rest of the network. We analyze some of its theoretical properties and show its empirical benefits on several datasets and networks, where DPP consistently outperforms previous pooling approaches.