Pushing the Boundaries of Boundary Detection using Deep Learning

In this work we show that adapting Deep Convolutional Neural Network training to the task of boundary detection can result in substantial improvements over the current state-of-the-art in boundary detection. Our contributions consist firstly in combining a careful design of the loss for boundary detection training, a multi-resolution architecture and training with external data to improve the detection accuracy of the current state of the art. When measured on the standard Berkeley Segmentation Dataset, we improve theoptimal dataset scale F-measure from 0.780 to 0.808 - while human performance is at 0.803. We further improve performance to 0.813 by combining deep learning with grouping, integrating the Normalized Cuts technique within a deep network. We also examine the potential of our boundary detector in conjunction with the task of semantic segmentation and demonstrate clear improvements over state-of-the-art systems. Our detector is fully integrated in the popular Caffe framework and processes a 320x420 image in less than a second.Comment: The previous version reported large improvements w.r.t. the LPO region proposal baseline, which turned out to be due to a wrong computation for the baseline. The improvements are currently less important, and are omitted. We are sorry if the reported results caused any confusion. We have also integrated reviewer feedback regarding human performance on the BSD benchmar

The use of singular functions for the approximate conformal mapping of doubly-connected domains

Let f be the function which maps conformally a given doubly- connected domain onto a circular annulus. We consider the use of two closely related methods for determining approximations to f of the form fn (z) = z exp, ⎪⎩⎪⎨⎧⎭⎬⎫Σ−(z)uan1jjj where {uj} is a set of basis functions. The two methods are respectively a variational method, based on an extremum property of the function H(z) = f′(z)/f(z) - 1/z, and an orthononnalization method, based on approximating the function H by a finite Fourier series sum. The main purpose of the paper is to consider the use of the two methods for the mapping of domains having sharp corners, where corner singularities occur. We show, by means of numerical examples, that both methods are capable of producing approximations of high accuracy for the mapping of such "difficult" doubly-connected domains. The essential requirement for this is that the basis set {uj} contains singular functions that reflect the asymptotic behaviour of the function H in the neighbourhood of each "singular" corner

Structural Attention Neural Networks for improved sentiment analysis

We introduce a tree-structured attention neural network for sentences and small phrases and apply it to the problem of sentiment classification. Our model expands the current recursive models by incorporating structural information around a node of a syntactic tree using both bottom-up and top-down information propagation. Also, the model utilizes structural attention to identify the most salient representations during the construction of the syntactic tree. To our knowledge, the proposed models achieve state of the art performance on the Stanford Sentiment Treebank dataset.Comment: Submitted to EACL2017 for revie

Fast, Exact and Multi-Scale Inference for Semantic Image Segmentation with Deep Gaussian CRFs

In this work we propose a structured prediction technique that combines the virtues of Gaussian Conditional Random Fields (G-CRF) with Deep Learning: (a) our structured prediction task has a unique global optimum that is obtained exactly from the solution of a linear system (b) the gradients of our model parameters are analytically computed using closed form expressions, in contrast to the memory-demanding contemporary deep structured prediction approaches that rely on back-propagation-through-time, (c) our pairwise terms do not have to be simple hand-crafted expressions, as in the line of works building on the DenseCRF, but can rather be `discovered' from data through deep architectures, and (d) out system can trained in an end-to-end manner. Building on standard tools from numerical analysis we develop very efficient algorithms for inference and learning, as well as a customized technique adapted to the semantic segmentation task. This efficiency allows us to explore more sophisticated architectures for structured prediction in deep learning: we introduce multi-resolution architectures to couple information across scales in a joint optimization framework, yielding systematic improvements. We demonstrate the utility of our approach on the challenging VOC PASCAL 2012 image segmentation benchmark, showing substantial improvements over strong baselines. We make all of our code and experiments available at {https://github.com/siddharthachandra/gcrf}Comment: Our code is available at https://github.com/siddharthachandra/gcr

Numerical conformal mapping of exterior domains

The work of the present paper is closely related to the two numerical procedures described in [11], for determining approximations to the function which maps conformally a bounded simply-connected domain Ω1 , with boundary ∂Ω, onto the unit disc. Here, we consider the use of these procedures for the solution of the corresponding exterior problem, i.e. the problem of determining approximations to the mapping function which maps conformally the exterior domain Ω = compl(ΩI⋃∂Ω) onto the unit disc

Mass Displacement Networks

Despite the large improvements in performance attained by using deep learning in computer vision, one can often further improve results with some additional post-processing that exploits the geometric nature of the underlying task. This commonly involves displacing the posterior distribution of a CNN in a way that makes it more appropriate for the task at hand, e.g. better aligned with local image features, or more compact. In this work we integrate this geometric post-processing within a deep architecture, introducing a differentiable and probabilistically sound counterpart to the common geometric voting technique used for evidence accumulation in vision. We refer to the resulting neural models as Mass Displacement Networks (MDNs), and apply them to human pose estimation in two distinct setups: (a) landmark localization, where we collapse a distribution to a point, allowing for precise localization of body keypoints and (b) communication across body parts, where we transfer evidence from one part to the other, allowing for a globally consistent pose estimate. We evaluate on large-scale pose estimation benchmarks, such as MPII Human Pose and COCO datasets, and report systematic improvements when compared to strong baselines.Comment: 12 pages, 4 figure