Learning Sparse High Dimensional Filters: Image Filtering, Dense CRFs and Bilateral Neural Networks

Bilateral filters have wide spread use due to their edge-preserving properties. The common use case is to manually choose a parametric filter type, usually a Gaussian filter. In this paper, we will generalize the parametrization and in particular derive a gradient descent algorithm so the filter parameters can be learned from data. This derivation allows to learn high dimensional linear filters that operate in sparsely populated feature spaces. We build on the permutohedral lattice construction for efficient filtering. The ability to learn more general forms of high-dimensional filters can be used in several diverse applications. First, we demonstrate the use in applications where single filter applications are desired for runtime reasons. Further, we show how this algorithm can be used to learn the pairwise potentials in densely connected conditional random fields and apply these to different image segmentation tasks. Finally, we introduce layers of bilateral filters in CNNs and propose bilateral neural networks for the use of high-dimensional sparse data. This view provides new ways to encode model structure into network architectures. A diverse set of experiments empirically validates the usage of general forms of filters

Superpixel Convolutional Networks using Bilateral Inceptions

In this paper we propose a CNN architecture for semantic image segmentation. We introduce a new 'bilateral inception' module that can be inserted in existing CNN architectures and performs bilateral filtering, at multiple feature-scales, between superpixels in an image. The feature spaces for bilateral filtering and other parameters of the module are learned end-to-end using standard backpropagation techniques. The bilateral inception module addresses two issues that arise with general CNN segmentation architectures. First, this module propagates information between (super) pixels while respecting image edges, thus using the structured information of the problem for improved results. Second, the layer recovers a full resolution segmentation result from the lower resolution solution of a CNN. In the experiments, we modify several existing CNN architectures by inserting our inception module between the last CNN (1x1 convolution) layers. Empirical results on three different datasets show reliable improvements not only in comparison to the baseline networks, but also in comparison to several dense-pixel prediction techniques such as CRFs, while being competitive in time.Comment: European Conference on Computer Vision (ECCV), 201

Segmentation-Aware Convolutional Networks Using Local Attention Masks

We introduce an approach to integrate segmentation information within a convolutional neural network (CNN). This counter-acts the tendency of CNNs to smooth information across regions and increases their spatial precision. To obtain segmentation information, we set up a CNN to provide an embedding space where region co-membership can be estimated based on Euclidean distance. We use these embeddings to compute a local attention mask relative to every neuron position. We incorporate such masks in CNNs and replace the convolution operation with a "segmentation-aware" variant that allows a neuron to selectively attend to inputs coming from its own region. We call the resulting network a segmentation-aware CNN because it adapts its filters at each image point according to local segmentation cues. We demonstrate the merit of our method on two widely different dense prediction tasks, that involve classification (semantic segmentation) and regression (optical flow). Our results show that in semantic segmentation we can match the performance of DenseCRFs while being faster and simpler, and in optical flow we obtain clearly sharper responses than networks that do not use local attention masks. In both cases, segmentation-aware convolution yields systematic improvements over strong baselines. Source code for this work is available online at http://cs.cmu.edu/~aharley/segaware

Bottom-Up and Top-Down Reasoning with Hierarchical Rectified Gaussians

Convolutional neural nets (CNNs) have demonstrated remarkable performance in recent history. Such approaches tend to work in a unidirectional bottom-up feed-forward fashion. However, practical experience and biological evidence tells us that feedback plays a crucial role, particularly for detailed spatial understanding tasks. This work explores bidirectional architectures that also reason with top-down feedback: neural units are influenced by both lower and higher-level units. We do so by treating units as rectified latent variables in a quadratic energy function, which can be seen as a hierarchical Rectified Gaussian model (RGs). We show that RGs can be optimized with a quadratic program (QP), that can in turn be optimized with a recurrent neural network (with rectified linear units). This allows RGs to be trained with GPU-optimized gradient descent. From a theoretical perspective, RGs help establish a connection between CNNs and hierarchical probabilistic models. From a practical perspective, RGs are well suited for detailed spatial tasks that can benefit from top-down reasoning. We illustrate them on the challenging task of keypoint localization under occlusions, where local bottom-up evidence may be misleading. We demonstrate state-of-the-art results on challenging benchmarks.Comment: To appear in CVPR 201

A Projected Gradient Descent Method for CRF Inference allowing End-To-End Training of Arbitrary Pairwise Potentials

Are we using the right potential functions in the Conditional Random Field models that are popular in the Vision community? Semantic segmentation and other pixel-level labelling tasks have made significant progress recently due to the deep learning paradigm. However, most state-of-the-art structured prediction methods also include a random field model with a hand-crafted Gaussian potential to model spatial priors, label consistencies and feature-based image conditioning. In this paper, we challenge this view by developing a new inference and learning framework which can learn pairwise CRF potentials restricted only by their dependence on the image pixel values and the size of the support. Both standard spatial and high-dimensional bilateral kernels are considered. Our framework is based on the observation that CRF inference can be achieved via projected gradient descent and consequently, can easily be integrated in deep neural networks to allow for end-to-end training. It is empirically demonstrated that such learned potentials can improve segmentation accuracy and that certain label class interactions are indeed better modelled by a non-Gaussian potential. In addition, we compare our inference method to the commonly used mean-field algorithm. Our framework is evaluated on several public benchmarks for semantic segmentation with improved performance compared to previous state-of-the-art CNN+CRF models.Comment: Presented at EMMCVPR 2017 conferenc

DeepLab: Semantic Image Segmentation with Deep Convolutional Nets, Atrous Convolution, and Fully Connected CRFs

In this work we address the task of semantic image segmentation with Deep Learning and make three main contributions that are experimentally shown to have substantial practical merit. First, we highlight convolution with upsampled filters, or 'atrous convolution', as a powerful tool in dense prediction tasks. Atrous convolution allows us to explicitly control the resolution at which feature responses are computed within Deep Convolutional Neural Networks. It also allows us to effectively enlarge the field of view of filters to incorporate larger context without increasing the number of parameters or the amount of computation. Second, we propose atrous spatial pyramid pooling (ASPP) to robustly segment objects at multiple scales. ASPP probes an incoming convolutional feature layer with filters at multiple sampling rates and effective fields-of-views, thus capturing objects as well as image context at multiple scales. Third, we improve the localization of object boundaries by combining methods from DCNNs and probabilistic graphical models. The commonly deployed combination of max-pooling and downsampling in DCNNs achieves invariance but has a toll on localization accuracy. We overcome this by combining the responses at the final DCNN layer with a fully connected Conditional Random Field (CRF), which is shown both qualitatively and quantitatively to improve localization performance. Our proposed "DeepLab" system sets the new state-of-art at the PASCAL VOC-2012 semantic image segmentation task, reaching 79.7% mIOU in the test set, and advances the results on three other datasets: PASCAL-Context, PASCAL-Person-Part, and Cityscapes. All of our code is made publicly available online.Comment: Accepted by TPAM