Results 1  10
of
12
Exact Combinatorial BranchandBound for Graph Bisection
"... We present a novel exact algorithm for the minimum graph bisection problem, whose goal is to partition a graph into two equallysized cells while minimizing the number of edges between them. Our algorithm is based on the branchandbound framework and, unlike most previous approaches, it is fully co ..."
Abstract

Cited by 7 (3 self)
 Add to MetaCart
(Show Context)
We present a novel exact algorithm for the minimum graph bisection problem, whose goal is to partition a graph into two equallysized cells while minimizing the number of edges between them. Our algorithm is based on the branchandbound framework and, unlike most previous approaches, it is fully combinatorial. We present stronger lower bounds, improved branching rules, and a new decomposition technique that contracts entire regions of the graph without losing optimality guarantees. In practice, our algorithm works particularly well on instances with relatively small minimum bisections, solving large realworld graphs (with tens of thousands to millions of vertices) to optimality.
Structured learning of sumofsubmodular higher order energy functions
, 1309
"... Submodular functions can be exactly minimized in polynomial time, and the special case that graph cuts solve with max flow [18] has had significant impact in computer vision [5, 20, 27]. In this paper we address the important class of sumofsubmodular (SoS) functions [2, 17], which can be efficient ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
(Show Context)
Submodular functions can be exactly minimized in polynomial time, and the special case that graph cuts solve with max flow [18] has had significant impact in computer vision [5, 20, 27]. In this paper we address the important class of sumofsubmodular (SoS) functions [2, 17], which can be efficiently minimized via a variant of max flow called submodular flow [6]. SoS functions can naturally express higher order priors involving, e.g., local image patches; however, it is difficult to fully exploit their expressive power because they have so many parameters. Rather than trying to formulate existing higher order priors as an SoS function, we take a discriminative learning approach, effectively searching the space of SoS functions for a higher order prior that performs well on our training set. We adopt a structural SVM approach [14, 33] and formulate the training problem in terms of quadratic programming; as a result we can efficiently search the space of SoS priors via an extended cuttingplane algorithm. We also show how the stateoftheart max flow method for vision problems [10] can be modified to efficiently solve the submodular flow problem. Experimental comparisons are made against the OpenCV implementation of the GrabCut interactive segmentation technique [27], which uses handtuned parameters instead of machine learning. On a standard dataset [11] our method learns higher order priors with hundreds of parameter values, and produces significantly better segmentations. While our focus is on binary labeling problems, we show that our techniques can be naturally generalized to handle more than two labels. 1.
Smart scribbles for sketch segmentation
 Computer Graphics Forum
, 2012
"... We present Smart Scribbles—a new scribblebased interface for userguided segmentation of digital sketchy drawings. In contrast to previous approaches based on simple selection strategies, Smart Scribbles exploits richer geometric and temporal information, resulting in a more intuitive segmentatio ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
We present Smart Scribbles—a new scribblebased interface for userguided segmentation of digital sketchy drawings. In contrast to previous approaches based on simple selection strategies, Smart Scribbles exploits richer geometric and temporal information, resulting in a more intuitive segmentation interface. We introduce a novel energy minimization formulation in which both geometric and temporal information from digital input devices is used to define stroketostroke and scribbletostroke relationships. Although the minimization of this energy is, in general, a NPhard problem, we use a simple heuristic that leads to a good approximation and permits an interactive system able to produce accurate labelings even for cluttered sketchy drawings. We demonstrate the power of our technique in several practical scenarios such as sketch editing, asrigidaspossible deformation and registration, and onthefly labeling based on preclassified guidelines.
Discrete Optimization of Ray Potentials for Semantic 3D Reconstruction
"... Dense semantic 3D reconstruction is typically formulated as a discrete or continuous problem over label assignments in a voxel grid, combining semantic and depth likelihoods in a Markov Random Field framework. The depth and semantic information is incorporated as a unary potential, smoothed by a ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
Dense semantic 3D reconstruction is typically formulated as a discrete or continuous problem over label assignments in a voxel grid, combining semantic and depth likelihoods in a Markov Random Field framework. The depth and semantic information is incorporated as a unary potential, smoothed by a pairwise regularizer. However, modelling likelihoods as a unary potential does not model the problem correctly leading to various undesirable visibility artifacts. We propose to formulate an optimization problem that directly optimizes the reprojection error of the 3D model with respect to the image estimates, which corresponds to the optimization over rays, where the cost function depends on the semantic class and depth of the first occupied voxel along the ray. The 2label formulation is made feasible by transforming it into a graphrepresentable form under QPBO relaxation, solvable using graph cut. The multilabel problem is solved by applying αexpansion using the same relaxation in each expansion move. Our method was indeed shown to be feasible in practice, running comparably fast to the competing methods, while not suffering from ray potential approximation artifacts. 1.
Faster and More Dynamic Maximum Flow by Incremental BreadthFirst Search
"... Abstract. We introduce the Excesses Incremental BreadthFirst Search (Excesses IBFS) algorithm for maximum flow problems. We show that Excesses IBFS has the best overall practical performance on realworld instances, while maintaining the same polynomial running time guarantee of O(mn2) as IBFS, wh ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. We introduce the Excesses Incremental BreadthFirst Search (Excesses IBFS) algorithm for maximum flow problems. We show that Excesses IBFS has the best overall practical performance on realworld instances, while maintaining the same polynomial running time guarantee of O(mn2) as IBFS, which it generalizes. Some applications, such as video object segmentation, require solving a series of maximum flow problems, each only slightly different than the previous. Excesses IBFS naturally extends to this dynamic setting and is competitive in practice with other dynamic methods. 1
Math. Program., Ser. A manuscript No. (will be inserted by the editor) An Exact Combinatorial Algorithm for Minimum Graph Bisection
"... Abstract We present a novel exact algorithm for the minimum graph bisection problem, whose goal is to partition a graph into two equallysized cells while minimizing the number of edges between them. Our algorithm is based on the branchandbound framework and, unlike most previous approaches, it is ..."
Abstract
 Add to MetaCart
Abstract We present a novel exact algorithm for the minimum graph bisection problem, whose goal is to partition a graph into two equallysized cells while minimizing the number of edges between them. Our algorithm is based on the branchandbound framework and, unlike most previous approaches, it is fully combinatorial. We introduce novel lower bounds based on packing trees, as well as a new decomposition technique that contracts entire regions of the graph while preserving optimality guarantees. Our algorithm works particularly well on graphs with relatively small minimum bisections, solving to optimality several large realworld instances (with up to millions of vertices) for the first time.
Parsimonious Labeling
"... We propose a new family of discrete energy minimization problems, which we call parsimonious labeling. Our energy function consists of unary potentials and highorder clique potentials. While the unary potentials are arbitrary, the clique potentials are proportional to the diversity of the set of u ..."
Abstract
 Add to MetaCart
(Show Context)
We propose a new family of discrete energy minimization problems, which we call parsimonious labeling. Our energy function consists of unary potentials and highorder clique potentials. While the unary potentials are arbitrary, the clique potentials are proportional to the diversity of the set of unique labels assigned to the clique. Intuitively, our energy function encourages the labeling to be parsimonious, that is, use as few labels as possible. This in turn allows us to capture useful cues for important computer vision applications such as stereo correspondence and image denoising. Furthermore, we propose an efficient graphcuts based algorithm for the parsimonious labeling problem that provides strong theoretical guarantees on the quality of the solution. Our algorithm consists of three steps. First, we approximate a given diversity using a mixture of a novel hierarchical Pn Potts model. Second, we use a divideandconquer approach for each mixture component, where each subproblem is solved using an efficient αexpansion algorithm. This provides us with a small number of putative labelings, one for each mixture component. Third, we choose the best putative labeling in terms of the energy value. Using both synthetic and standard real datasets, we show that our algorithm significantly outperforms other graphcuts based approaches. 1.
ETH
"... Models such as pairwise conditional random fields (CRFs) are extremely popular in computer vision and various other machine learning disciplines. However, they have limited expressive power and often cannot represent the posterior distribution correctly. While learning the parameters of such models ..."
Abstract
 Add to MetaCart
(Show Context)
Models such as pairwise conditional random fields (CRFs) are extremely popular in computer vision and various other machine learning disciplines. However, they have limited expressive power and often cannot represent the posterior distribution correctly. While learning the parameters of such models which have insufficient expressivity, researchers use loss functions to penalize certain misrepresentations of the solution space. Till now, researchers have used only simplistic loss functions such as the Hamming loss, to enable efficient inference. The paper shows how sophisticated and useful higher order loss functions can be incorporated in the learning process. These loss functions ensure that the MAP solution does not deviate much from the ground truth in terms of certain higher order statistics. We propose a learning algorithm which uses the recently proposed lowerenvelop representation of higher order functions to transform them to pairwise functions, which allow efficient inference. We test the efficacy of our method on the problem of foregroundbackground image segmentation. Experimental results show that the incorporation of higher order loss functions in the learning formulation using our method leads to much better results compared to those obtained by using the traditional Hamming loss. 1
Learning Loworder Models for . . .
, 2012
"... Models such as pairwise conditional random fields (CRFs) are extremely popular in computer vision and various other machine learning disciplines. However, they have limited expressive power and often cannot represent the posterior distribution correctly. While learning the parameters of such models ..."
Abstract
 Add to MetaCart
Models such as pairwise conditional random fields (CRFs) are extremely popular in computer vision and various other machine learning disciplines. However, they have limited expressive power and often cannot represent the posterior distribution correctly. While learning the parameters of such models which have insufficient expressivity, researchers use loss functions to penalize certain misrepresentations of the solution space. Till now, researchers have used only simplistic loss functions such as the Hamming loss, to enable efficient inference. The paper shows how sophisticated and useful higher order loss functions can be incorporated in the learning process. These loss functions ensure that the MAP solution does not deviate much from the ground truth in terms of certain higher order statistics. We propose a learning algorithm which uses the recently proposed lowerenvelop representation of higher order functions to transform them to pairwise functions, which allow efficient inference. We test the efficacy of our method on the problem of foregroundbackground image segmentation. Experimental results show that the incorporation of higher order loss functions in the learning formulation using our method leads to much better results compared to those obtained by using the traditional Hamming loss.
Task Matching and Scheduling for Multiple Workers in Spatial Crowdsourcing
"... A new platform, termed spatial crowdsourcing, is emerging which enables a requester to commission workers to physically travel to some specified locations to perform a set of spatial tasks (i.e., tasks related to a geographical location and time). The current approach is to formulate spatial crowdso ..."
Abstract
 Add to MetaCart
(Show Context)
A new platform, termed spatial crowdsourcing, is emerging which enables a requester to commission workers to physically travel to some specified locations to perform a set of spatial tasks (i.e., tasks related to a geographical location and time). The current approach is to formulate spatial crowdsourcing as a matching problem between tasks and workers; hence the primary objective of the existing solutions is to maximize the number of matched tasks. Our goal is to solve the spatial crowdsourcing problem in the presence of multiple workers where we optimize for both travel cost and the number of completed tasks, while taking the tasks ’ expiration times into consideration. The challenge is that the solution should be a mixture of taskmatching and taskscheduling, which are fundamentally different. In this paper, we show that a baseline approach that performs a taskmatching first, and subsequently schedules the tasks assigned per worker in a following phase, does not perform well. Hence, we add a third phase in which we iterate back to the matching phase to improve the assignment per the output of the scheduling phase, and thus further improves the quality of matching and scheduling. Even though this 3phase approach generates high quality results, it is very slow and does not scale. Hence, to scale our algorithm to large number of workers and tasks, we propose a Bisectionbased framework which recursively divides all the workers and tasks into different partitions such that assignment and scheduling can be performed locally in a much smaller and promising space. Our experiments show that this approach is three orders of magnitude faster than the 3phase approach while it only sacrifices 4 % of the results ’ quality.