The state-of-the-art in semantic segmentation is currently represented by fully convolutional networks (FCNs). However, FCNs use large receptive fields and many pooling layers, both of which cause blurring and low spatial resolution in the deep layers. As a result FCNs tend to produce segmentations that are poorly localized around object boundaries. Prior work has attempted to address this issue in post-processing steps, for example using a color-based CRF on top of the FCN predictions. However, these approaches require additional parameters and low-level features that are difficult to tune and integrate into the original network architecture. Additionally, most CRFs use color-based pixel affinities, which are not well suited for semantic segmentation and lead to spatially disjoint predictions. To overcome these problems, we introduce a Boundary Neural Field (BNF), which is a global energy model integrating FCN predictions with boundary cues. The boundary information is used to enhance semantic segment coherence and to improve object localization. Specifically, we first show that the convolutional filters of semantic FCNs provide good features for boundary detection. We then employ the predicted boundaries to define pairwise potentials in our energy. Finally, we show that our energy decomposes semantic segmentation into multiple binary problems, which can be relaxed for efficient global optimization. We report extensive experiments demonstrating that minimization of our global boundary-based energy yields results superior to prior globalization methods, both quantitatively as well as qualitatively.
Spectral methods comprise one of the most prominent categories for boundary detection. In a typical spectral framework, one formulates a generalized eigenvalue system to solve a low-level pixel grouping problem. The resulting eigenvectors are then used to predict the boundaries. Some of the most notable approaches in this genre are MCG @cite_6 , gPb @cite_2 , PMI @cite_34 , and Normalized Cuts @cite_21 . A weakness of spectral approaches is that they tend to be slow as they perform a global inference over the entire image.
@cite_34 @cite_21 @cite_6 @cite_2
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Spectral algorithms are classic approaches to clustering and community detection in networks. However, for sparse networks the standard versions of these algorithms are suboptimal, in some cases completely failing to detect communities even when other algorithms such as belief propagation can do so. Here, we present a class of spectral algorithms based on a nonbacktracking walk on the directed edges of the graph. The spectrum of this operator is much better-behaved than that of the adjacency matrix or other commonly used matrices, maintaining a strong separation between the bulk eigenvalues and the eigenvalues relevant to community structure even in the sparse case. We show that our algorithm is optimal for graphs generated by the stochastic block model, detecting communities all of the way down to the theoretical limit. We also show the spectrum of the nonbacktracking operator for some real-world networks, illustrating its advantages over traditional spectral clustering. Most of the current boundary detection systems rely exclusively on low-level features, such as color and texture. However, perception studies suggest that humans employ object-level reasoning when judging if a particular pixel is a boundary. Inspired by this observation, in this work we show how to predict boundaries by exploiting object-level features from a pretrained object-classification network. Our method can be viewed as a "High-for-Low" approach where high-level object features inform the low-level boundary detection process. Our model achieves state-of-the-art performance on an established boundary detection benchmark and it is efficient to run. Additionally, we show that due to the semantic nature of our boundaries we can use them to aid a number of high-level vision tasks. We demonstrate that using our boundaries we improve the performance of state-of-the-art methods on the problems of semantic boundary labeling, semantic segmentation and object proposal generation. We can view this process as a "Low-for-High'" scheme, where low-level boundaries aid high-level vision tasks. Thus, our contributions include a boundary detection system that is accurate, efficient, generalizes well to multiple datasets, and is also shown to improve existing state-of-the-art high-level vision methods on three distinct tasks. We consider the change-point detection problem of deciding, based on noisy measurements, whether an unknown signal over a given graph is constant or is instead piecewise constant over two connected induced subgraphs of relatively low cut size. We analyze the corresponding generalized likelihood ratio (GLR) statistics and relate it to the problem of finding a sparsest cut in a graph. We develop a tractable relaxation of the GLR statistic based on the combinatorial Laplacian of the graph, which we call the spectral scan statistic, and analyze its properties. We show how its performance as a testing procedure depends directly on the spectrum of the graph, and use this result to explicitly derive its asymptotic properties on few significant graph topologies. Finally, we demonstrate both theoretically and by simulations that the spectral scan statistic can outperform naive testing procedures based on edge thresholding and @math testing. We study a spectral initialization method that serves a key role in recent work on estimating signals in nonconvex settings. Previous analysis of this method focuses on the phase retrieval problem and provides only performance bounds. In this paper, we consider arbitrary generalized linear sensing models and present a precise asymptotic characterization of the performance of the method in the high-dimensional limit. Our analysis also reveals a phase transition phenomenon that depends on the ratio between the number of samples and the signal dimension. When the ratio is below a minimum threshold, the estimates given by the spectral method are no better than random guesses drawn from a uniform distribution on the hypersphere, thus carrying no information; above a maximum threshold, the estimates become increasingly aligned with the target signal. The computational complexity of the method, as measured by the spectral gap, is also markedly different in the two phases. Worked examples and numerical results are provided to illustrate and verify the analytical predictions. In particular, simulations show that our asymptotic formulas provide accurate predictions for the actual performance of the spectral method even at moderate signal dimensions.