In this paper, we propose a spatial propagation networks for learning affinity matrix. We show that by constructing a row/column linear propagation model, the spatially variant transformation matrix constitutes an affinity matrix that models dense, global pairwise similarities of an image. Specifically, we develop a three-way connection for the linear propagation model, which (a) formulates a sparse transformation matrix where all elements can be the output from a deep CNN, but (b) results in a dense affinity matrix that is effective to model any task-specific pairwise similarity.

In this paper, we propose a spatial propagation networks for learning affinity matrix. We show that by constructing a row/column linear propagation model, the spatially variant transformation matrix constitutes an affinity matrix that models dense, global pairwise similarities of an image. Specifically, we develop a three-way connection for the linear propagation model, which (a) formulates a sparse transformation matrix where all elements can be the output from a deep CNN, but (b) results in a dense affinity matrix that is effective to model any task-specific pairwise similarity.

In this paper, we propose spatial propagation networks for learning the affinity matrix for vision tasks.

The authors incorporate ideas from image processing into CNNs and show how nonlinear diffusion can be combined with deep learning. This allows to train more accurate post-processing modules for semantic segmentation, that are shown to outperform denseCRF-based post-processing, or recurrent alternatives that rely on more straightforward interpretations of recursive signal filtering, as introduced in [3,16]. The main practical contribution lies in extending the techniques of [3,16]: when these techniques apply recursive filtering, say in the horizontal direction of an image, they pass information along rows in isolation. Instead the method of the authors allows one to propagate information across rows, by rephrasing the originally scalar recursion in terms of vector-matrix products. This is shown to be much more effective than the baseline.

In this paper, we propose spatial propagation networks for learning the affinity matrix for vision tasks. We show that by constructing a row/column linear propagation model, the spatially varying transformation matrix exactly constitutes an affinity matrix that models dense, global pairwise relationships of an image. Specifically, we develop a three-way connection for the linear propagation model, which (a) formulates a sparse transformation matrix, where all elements can be outputs from a deep CNN, but (b) results in a dense affinity matrix that effectively models any task-specific pairwise similarity matrix.

Image guided depth completion aims to recover per-pixel dense depth maps from sparse depth measurements with the help of aligned color images, which has a wide range of applications from robotics to autonomous driving. However, the 3D nature of sparse-to-dense depth completion has not been fully explored by previous methods. In this work, we propose a Graph Convolution based Spatial Propagation Network (GraphCSPN) as a general approach for depth completion. First, unlike previous methods, we leverage convolution neural networks as well as graph neural networks in a complementary way for geometric representation learning. In addition, the proposed networks explicitly incorporate learnable geometric constraints to regularize the propagation process performed in three-dimensional space rather than in two-dimensional plane. Furthermore, we construct the graph utilizing sequences of feature patches, and update it dynamically with an edge attention module during propagation, so as to better capture both the local neighboring features and global relationships over long distance. Extensive experiments on both indoor NYU-Depth-v2 and outdoor KITTI datasets demonstrate that our method achieves the state-of-the-art performance, especially when compared in the case of using only a few propagation steps. Code and models are available at the project page.

In this paper, we propose a spatial propagation networks for learning affinity matrix. We show that by constructing a row/column linear propagation model, the spatially variant transformation matrix constitutes an affinity matrix that models dense, global pairwise similarities of an image. Specifically, we develop a three-way connection for the linear propagation model, which (a) formulates a sparse transformation matrix where all elements can be the output from a deep CNN, but (b) results in a dense affinity matrix that is effective to model any task-specific pairwise similarity. The spatial propagation network is a generic framework that can be applied to numerous tasks, which traditionally benefit from designed affinity, e.g., image matting, colorization, and guided filtering, to name a few. Furthermore, the model can also learn semantic-aware affinity for high-level vision tasks due to the learning capability of the deep model.

In this paper, we propose a spatial propagation networks for learning affinity matrix. We show that by constructing a row/column linear propagation model, the spatially variant transformation matrix constitutes an affinity matrix that models dense, global pairwise similarities of an image. Specifically, we develop a three-way connection for the linear propagation model, which (a) formulates a sparse transformation matrix where all elements can be the output from a deep CNN, but (b) results in a dense affinity matrix that is effective to model any task-specific pairwise similarity. Instead of designing the similarity kernels according to image features of two points, we can directly output all similarities in a pure data-driven manner. The spatial propagation network is a generic framework that can be applied to numerous tasks, which traditionally benefit from designed affinity, e.g., image matting, colorization, and guided filtering, to name a few. Furthermore, the model can also learn semantic-aware affinity for high-level vision tasks due to the learning capability of the deep model. We validate the proposed framework by refinement of object segmentation. Experiments on the HELEN face parsing and PASCAL VOC-2012 semantic segmentation tasks show that the spatial propagation network provides general, effective and efficient solutions for generating high-quality segmentation results.

In this paper, we propose spatial propagation networks for learning the affinity matrix for vision tasks. We show that by constructing a row/column linear propagation model, the spatially varying transformation matrix exactly constitutes an affinity matrix that models dense, global pairwise relationships of an image. Specifically, we develop a three-way connection for the linear propagation model, which (a) formulates a sparse transformation matrix, where all elements can be outputs from a deep CNN, but (b) results in a dense affinity matrix that effectively models any task-specific pairwise similarity matrix. The spatial propagation network is a generic framework that can be applied to many affinity-related tasks, such as image matting, segmentation and colorization, to name a few. Essentially, the model can learn semantically aware affinity values for high-level vision tasks due to the powerful learning capability of deep CNNs.