14 research outputs found
Efficient inference for fully-connected CRFs with stationarity
The Conditional Random Field (CRF) is a popular tool for object-based image segmentation. CRFs used in prac-tice typically have edges only between adjacent image pix-els. To represent object relationship statistics beyond adja-cent pixels, prior work either represents only weak spatial information using the segmented regions, or encodes only global object co-occurrences. In this paper, we propose a unified model that augments the pixel-wise CRFs to cap-ture object spatial relationships. To this end, we use a fully connected CRF, which has an edge for each pair of pixels. The edge potentials are defined to capture the spatial in-formation and preserve the object boundaries at the same time. Traditional inference methods, such as belief propa-gation and graph cuts, are impractical in such a case where billions of edges are defined. Under only one assumption that the spatial relationships among different objects only depend on their relative positions (spatially stationary), we develop an efficient inference algorithm that converges in a few seconds on a standard resolution image, where belief propagation takes more than one hour for a single iteration. 1
Efficient SDP Inference for Fully-connected CRFs Based on Low-rank Decomposition
Conditional Random Fields (CRF) have been widely used in a variety of
computer vision tasks. Conventional CRFs typically define edges on neighboring
image pixels, resulting in a sparse graph such that efficient inference can be
performed. However, these CRFs fail to model long-range contextual
relationships. Fully-connected CRFs have thus been proposed. While there are
efficient approximate inference methods for such CRFs, usually they are
sensitive to initialization and make strong assumptions. In this work, we
develop an efficient, yet general algorithm for inference on fully-connected
CRFs. The algorithm is based on a scalable SDP algorithm and the low- rank
approximation of the similarity/kernel matrix. The core of the proposed
algorithm is a tailored quasi-Newton method that takes advantage of the
low-rank matrix approximation when solving the specialized SDP dual problem.
Experiments demonstrate that our method can be applied on fully-connected CRFs
that cannot be solved previously, such as pixel-level image co-segmentation.Comment: 15 pages. A conference version of this work appears in Proc. IEEE
Conference on Computer Vision and Pattern Recognition, 201
Conditional Random Fields as Recurrent Neural Networks
Pixel-level labelling tasks, such as semantic segmentation, play a central
role in image understanding. Recent approaches have attempted to harness the
capabilities of deep learning techniques for image recognition to tackle
pixel-level labelling tasks. One central issue in this methodology is the
limited capacity of deep learning techniques to delineate visual objects. To
solve this problem, we introduce a new form of convolutional neural network
that combines the strengths of Convolutional Neural Networks (CNNs) and
Conditional Random Fields (CRFs)-based probabilistic graphical modelling. To
this end, we formulate mean-field approximate inference for the Conditional
Random Fields with Gaussian pairwise potentials as Recurrent Neural Networks.
This network, called CRF-RNN, is then plugged in as a part of a CNN to obtain a
deep network that has desirable properties of both CNNs and CRFs. Importantly,
our system fully integrates CRF modelling with CNNs, making it possible to
train the whole deep network end-to-end with the usual back-propagation
algorithm, avoiding offline post-processing methods for object delineation. We
apply the proposed method to the problem of semantic image segmentation,
obtaining top results on the challenging Pascal VOC 2012 segmentation
benchmark.Comment: This paper is published in IEEE ICCV 201
Efficient Relaxations for Dense CRFs with Sparse Higher Order Potentials
Dense conditional random fields (CRFs) have become a popular framework for
modelling several problems in computer vision such as stereo correspondence and
multi-class semantic segmentation. By modelling long-range interactions, dense
CRFs provide a labelling that captures finer detail than their sparse
counterparts. Currently, the state-of-the-art algorithm performs mean-field
inference using a filter-based method but fails to provide a strong theoretical
guarantee on the quality of the solution. A question naturally arises as to
whether it is possible to obtain a maximum a posteriori (MAP) estimate of a
dense CRF using a principled method. Within this paper, we show that this is
indeed possible. We will show that, by using a filter-based method, continuous
relaxations of the MAP problem can be optimised efficiently using
state-of-the-art algorithms. Specifically, we will solve a quadratic
programming (QP) relaxation using the Frank-Wolfe algorithm and a linear
programming (LP) relaxation by developing a proximal minimisation framework. By
exploiting labelling consistency in the higher-order potentials and utilising
the filter-based method, we are able to formulate the above algorithms such
that each iteration has a complexity linear in the number of classes and random
variables. The presented algorithms can be applied to any labelling problem
using a dense CRF with sparse higher-order potentials. In this paper, we use
semantic segmentation as an example application as it demonstrates the ability
of the algorithm to scale to dense CRFs with large dimensions. We perform
experiments on the Pascal dataset to indicate that the presented algorithms are
able to attain lower energies than the mean-field inference method