Current algorithmic approaches for piecewise affine motion estimation are based on alternating motion segmentation and estimation. We propose a new method to estimate piecewise affine motion fields directly without intermediate segmentation. To this end, we reformulate the problem by imposing piecewise constancy of the parameter field, and derive a specific proximal splitting optimization scheme. A key component of our framework is an efficient 1D piecewise-affine estimator for vector-valued signals. The first advantage of our approach over segmentation-based methods is its absence of initialization. The second advantage is its lower computational cost, which is independent of the complexity of the motion field. In addition to these features, we demonstrate competitive accuracy with other piecewise-parametric methods on standard evaluation benchmarks. Our new regularization scheme also outperforms the more standard use of total variation and total generalized variation.
Most of the computational effort is spent on the image-partitioning problem. The earliest works retain at most five regions to make the problem tractable . More recently, the layered approach handles a larger number of regions but requires several hours of computation, and the primal dual approach can take up to one hour despite a GPU implementation. The method proposed in @cite_36 achieves around fifteen minutes for @math image, with a graph cut minimization approach.
@cite_36
1915301860
Balanced graph partitioning in the streaming setting is a key problem to enable scalable and efficient computations on massive graph data such as web graphs, knowledge graphs, and graphs arising in the context of online social networks. Two families of heuristics for graph partitioning in the streaming setting are in wide use: place the newly arrived vertex in the cluster with the largest number of neighbors or in the cluster with the least number of non-neighbors. In this work, we introduce a framework which unifies the two seemingly orthogonal heuristics and allows us to quantify the interpolation between them. More generally, the framework enables a well principled design of scalable, streaming graph partitioning algorithms that are amenable to distributed implementations. We derive a novel one-pass, streaming graph partitioning algorithm and show that it yields significant performance improvements over previous approaches using an extensive set of real-world and synthetic graphs. Surprisingly, despite the fact that our algorithm is a one-pass streaming algorithm, we found its performance to be in many cases comparable to the de-facto standard offline software METIS and in some cases even superiror. For instance, for the Twitter graph with more than 1.4 billion of edges, our method partitions the graph in about 40 minutes achieving a balanced partition that cuts as few as 6.8 of edges, whereas it took more than 81 2 hours by METIS to produce a balanced partition that cuts 11.98 of edges. We also demonstrate the performance gains by using our graph partitioner while solving standard PageRank computation in a graph processing platform with respect to the communication cost and runtime. As a preprocessing step, image segmentation, which can do partition of an image into different regions, plays an important role in computer vision, objects recognition, tracking and image analysis. Till today, there are a large number of methods present that can extract the required foreground from the background. However, most of these methods are solely based on boundary or regional information which has limited the segmentation result to a large extent. Since the graph cut based segmentation method was proposed, it has obtained a lot of attention because this method utilizes both boundary and regional information. Furthermore, graph cut based method is efficient and accepted world-wide since it can achieve globally optimal result for the energy function. It is not only promising to specific image with known information but also effective to the natural image without any pre-known information. For the segmentation of N-dimensional image, graph cut based methods are also applicable. Due to the advantages of graph cut, various methods have been proposed. In this paper, the main aim is to help researcher to easily understand the graph cut based segmentation approach. We also classify this method into three categories. They are speed up-based graph cut, interactive-based graph cut and shape prior-based graph cut. This paper will be helpful to those who want to apply graph cut method into their research. Similarity search finds application in specialized database systems handling complex data such as images or videos, which are typically represented by high-dimensional features and require specific indexing structures. This paper tackles the problem of better utilizing GPUs for this task. While GPUs excel at data-parallel tasks, prior approaches are bottlenecked by algorithms that expose less parallelism, such as k-min selection, or make poor use of the memory hierarchy. We propose a design for k-selection that operates at up to 55 of theoretical peak performance, enabling a nearest neighbor implementation that is 8.5x faster than prior GPU state of the art. We apply it in different similarity search scenarios, by proposing optimized design for brute-force, approximate and compressed-domain search based on product quantization. In all these setups, we outperform the state of the art by large margins. Our implementation enables the construction of a high accuracy k-NN graph on 95 million images from the Yfcc100M dataset in 35 minutes, and of a graph connecting 1 billion vectors in less than 12 hours on 4 Maxwell Titan X GPUs. We have open-sourced our approach for the sake of comparison and reproducibility. A novel graph theoretic approach for data clustering is presented and its application to the image segmentation problem is demonstrated. The data to be clustered are represented by an undirected adjacency graph G with arc capacities assigned to reflect the similarity between the linked vertices. Clustering is achieved by removing arcs of G to form mutually exclusive subgraphs such that the largest inter-subgraph maximum flow is minimized. For graphs of moderate size ( approximately 2000 vertices), the optimal solution is obtained through partitioning a flow and cut equivalent tree of G, which can be efficiently constructed using the Gomory-Hu algorithm (1961). However for larger graphs this approach is impractical. New theorems for subgraph condensation are derived and are then used to develop a fast algorithm which hierarchically constructs and partitions a partially equivalent tree of much reduced size. This algorithm results in an optimal solution equivalent to that obtained by partitioning the complete equivalent tree and is able to handle very large graphs with several hundred thousand vertices. The new clustering algorithm is applied to the image segmentation problem. The segmentation is achieved by effectively searching for closed contours of edge elements (equivalent to minimum cuts in G), which consist mostly of strong edges, while rejecting contours containing isolated strong edges. This method is able to accurately locate region boundaries and at the same time guarantees the formation of closed edge contours. > Randomized coordinate descent (RCD) methods are state-of-the-art algorithms for training linear predictors via minimizing regularized empirical risk. When the number of examples ( @math ) is much larger than the number of features ( @math ), a common strategy is to apply RCD to the dual problem. On the other hand, when the number of features is much larger than the number of examples, it makes sense to apply RCD directly to the primal problem. In this paper we provide the first joint study of these two approaches when applied to L2-regularized ERM. First, we show through a rigorous analysis that for dense data, the above intuition is precisely correct. However, we find that for sparse and structured data, primal RCD can significantly outperform dual RCD even if @math , and vice versa, dual RCD can be much faster than primal RCD even if @math . Moreover, we show that, surprisingly, a single sampling strategy minimizes both the (bound on the) number of iterations and the overall expected complexity of RCD. Note that the latter complexity measure also takes into account the average cost of the iterations, which depends on the structure and sparsity of the data, and on the sampling strategy employed. We confirm our theoretical predictions using extensive experiments with both synthetic and real data sets. In this paper, we address the problem of person re-identification, which refers to associating the persons captured from different cameras. We propose a simple yet effective human part-aligned representation for handling the body part misalignment problem. Our approach decomposes the human body into regions (parts) which are discriminative for person matching, accordingly computes the representations over the regions, and aggregates the similarities computed between the corresponding regions of a pair of probe and gallery images as the overall matching score. Our formulation, inspired by attention models, is a deep neural network modeling the three steps together, which is learnt through minimizing the triplet loss function without requiring body part labeling information. Unlike most existing deep learning algorithms that learn a global or spatial partition-based local representation, our approach performs human body partition, and thus is more robust to pose changes and various human spatial distributions in the person bounding box. Our approach shows state-of-the-art results over standard datasets, Market- @math , CUHK @math , CUHK @math and VIPeR. This paper presents a volumetric formulation for the multiview stereo problem which is amenable to a computationally tractable global optimization using Graph-cuts. Our approach is to seek the optimal partitioning of 3D space into two regions labeled as "object" and "empty" under a cost functional consisting of the following two terms: 1) A term that forces the boundary between the two regions to pass through photo-consistent locations; and 2) a ballooning term that inflates the "object" region. To take account of the effect of occlusion on the first term, we use an occlusion robust photo-consistency metric based on normalized cross correlation, which does not assume any geometric knowledge about the reconstructed object. The globally optimal 3D partitioning can be obtained as the minimum cut solution of a weighted graph. We present primal-dual decomposition algorithms for convex optimization problems with cost functions @math , where @math and @math have inexpensive proximal operators and @math can be decomposed as a sum of two structured matrices. The methods are based on the Douglas--Rachford splitting algorithm applied to various splittings of the primal-dual optimality conditions. We discuss applications to image deblurring problems with nonquadratic data fidelity terms, different types of convex regularization, and simple convex constraints. In these applications, the primal-dual splitting approach allows us to handle general boundary conditions for the blurring operator. Numerical results indicate that the primal-dual splitting methods compare favorably with the alternating direction method of multipliers, the Douglas--Rachford algorithm applied to a reformulated primal problem, and the Chambolle--Pock primal-dual algorithm. Graph partitioning is one of the most studied NP-complete problems. Given a graph G=(V, E) , the task is to partition the vertex set V into k disjoint subsets of about the same size, such that the number of edges with endpoints in different subsets is minimized. In this paper, we present a highly effective multilevel memetic algorithm, which integrates a new multiparent crossover operator and a powerful perturbation-based tabu search algorithm. The proposed crossover operator tends to preserve the backbone with respect to a certain number of parent individuals, i.e., the grouping of vertices which is common to all parent individuals. Extensive experimental studies on numerous benchmark instances from the graph partitioning archive show that the proposed approach, within a time limit ranging from several minutes to several hours, performs far better than any of the existing graph partitioning algorithms in terms of solution quality. This paper investigates the residential energy consumption scheduling problem, which is formulated as a coupled-constraint game by taking the interaction among users and the temporally-coupled constraint into consideration. The proposed solution consists of two parts. Firstly, dual decomposition is applied to transform the original coupled-constraint game into a decoupled one. Then, Nash equilibrium of the decoupled game is proven to be achievable via best response, which is computed by gradient projection. The proposed solution is also extended to an online version, which is able to alleviate the impact of the price prediction error. Numerical results demonstrate that the proposed approach can effectively shift the peak-hour demand to off-peak hours, enhance the welfare of each user, and minimize the peak-to-average ratio. The scalability of the approach and the impact of the user number are also investigated. We present a method for generating object segmentation proposals from groups of superpixels. The goal is to propose accurate segmentations for all objects of an image. The proposed object hypotheses can be used as input to object detection systems and thereby improve efficiency by replacing exhaustive search. The segmentations are generated in a class-independent manner and therefore the computational cost of the approach is independent of the number of object classes. Our approach combines both global and local search in the space of sets of superpixels. The local search is implemented by greedily merging adjacent pairs of superpixels to build a bottom-up segmentation hierarchy. The regions from such a hierarchy directly provide a part of our region proposals. The global search provides the other part by performing a set of graph cut segmentations on a superpixel graph obtained from an intermediate level of the hierarchy. The parameters of the graph cut problems are learnt in such a manner that they provide complementary sets of regions. Experiments with Pascal VOC images show that we reach state-of-the-art with greatly reduced computational cost. We propose to tackle the optical flow problem by a combination of two recent advances in the computation of dense correspondences, namely the incorporation of image segmentation and robust global optimization via graph-cuts. In the first step, each segment (extracted by colour segmentation) is assigned to an affine motion model from a set of sparse correspondences. Using a layered model, we then identify those motion models that represent the dominant image motion. This layer extraction task is accomplished by optimizing a simple energy function that operates in the domain of segments via graph-cuts. We then estimate the spatial extent that is covered by each layer and identify occlusions. Since treatment of occlusions is hardly possible when using entire segments as matching primitives, we propose to use the pixel level in addition. We therefore define an energy function that measures the quality of an assignment of segments and pixels to layers. This energy function is then extended to work on multiple input frames and minimized via graph-cuts. In the experimental results, we show that our method produces good-quality results, especially in regions of low texture and close to motion boundaries, which are challenging tasks in optical flow computation. One of the most common tasks in image and video editing is the local adjustment of various properties (e.g., saturation or brightness) of regions within an image or video. Edge-aware interpolation of user-drawn scribbles offers a less effort-intensive approach to this problem than traditional region selection and matting. However, the technique suffers a number of limitations, such as reduced performance in the presence of texture contrast, and the inability to handle fragmented appearances. We significantly improve the performance of edge-aware interpolation for this problem by adding a boosting-based classification step that learns to discriminate between the appearance of scribbled pixels. We show that this novel data term in combination with an existing edge-aware optimization technique achieves substantially better results for the local image and video adjustment problem than edge-aware interpolation techniques without classification, or related methods such as matting techniques or graph cut segmentation. We present a novel approach to graph partitioning based on the notion of . Our algorithm, called PUNCH, has two phases. The first phase performs a series of minimum-cut computations to identify and contract dense regions of the graph. This reduces the graph size, but preserves its general structure. The second phase uses a combination of greedy and local search heuristics to assemble the final partition. The algorithm performs especially well on road networks, which have an abundance of natural cuts (such as bridges, mountain passes, and ferries). In a few minutes, it obtains the best known partitions for continental-sized networks, significantly improving on previous results. In this paper, we propose a new decomposition approach named the proximal primal dual algorithm (Prox-PDA) for smooth nonconvex linearly constrained optimization problems. The proposed approach is primal-dual based, where the primal step minimizes certain approximation of the augmented Lagrangian of the problem, and the dual step performs an approximate dual ascent. The approximation used in the primal step is able to decompose the variable blocks, making it possible to obtain simple subproblems by leveraging the problem structures. Theoretically, we show that whenever the penalty parameter in the augmented Lagrangian is larger than a given threshold, the Prox-PDA converges to the set of stationary solutions, globally and in a sublinear manner (i.e., certain measure of stationarity decreases in the rate of @math , where @math is the iteration counter). Interestingly, when applying a variant of the Prox-PDA to the problem of distributed nonconvex optimization (over a connected undirected graph), the resulting algorithm coincides with the popular EXTRA algorithm [ 2014], which is only known to work in convex cases. Our analysis implies that EXTRA and its variants converge globally sublinearly to stationary solutions of certain nonconvex distributed optimization problem. There are many possible extensions of the Prox-PDA, and we present one particular extension to certain nonconvex distributed matrix factorization problem. In this paper, we investigate large scale computers' capability of speeding up deep neural networks (DNN) training. Our approach is to use large batch size, powered by the Layer-wise Adaptive Rate Scaling (LARS) algorithm, for efficient usage of massive computing resources. Our approach is generic, as we empirically evaluate the effectiveness on two neural networks: AlexNet and ResNet-50 trained with the ImageNet-1k dataset while preserving the state-of-the-art test accuracy. Compared to the baseline of a previous study from a group of researchers at Facebook, our approach shows higher test accuracy on batch sizes that are larger than 16K. Using 2,048 Intel Xeon Platinum 8160 processors, we reduce the 100-epoch AlexNet training time from hours to 11 minutes. With 2,048 Intel Xeon Phi 7250 Processors, we reduce the 90-epoch ResNet-50 training time from hours to 20 minutes. Our implementation is open source and has been released in the Intel distribution of Caffe v1.0.7. This paper presents a method for recognizing scene categories based on approximate global geometric correspondence. This technique works by partitioning the image into increasingly fine sub-regions and computing histograms of local features found inside each sub-region. The resulting "spatial pyramid" is a simple and computationally efficient extension of an orderless bag-of-features image representation, and it shows significantly improved performance on challenging scene categorization tasks. Specifically, our proposed method exceeds the state of the art on the Caltech-101 database and achieves high accuracy on a large database of fifteen natural scene categories. The spatial pyramid framework also offers insights into the success of several recently proposed image descriptions, including Torralbas "gist" and Lowes SIFT descriptors. Existing salient object detection models favor over-segmented regions upon which saliency is computed. Such local regions are less effective on representing object holistically and degrade emphasis of entire salient objects. As a result, the existing methods often fail to highlight an entire object in complex background. Toward better grouping of objects and background, in this paper, we consider graph cut, more specifically, the normalized graph cut (Ncut) for saliency detection. Since the Ncut partitions a graph in a normalized energy minimization fashion, resulting eigenvectors of the Ncut contain good cluster information that may group visual contents. Motivated by this, we directly induce saliency maps via eigenvectors of the Ncut, contributing to accurate saliency estimation of visual clusters. We implement the Ncut on a graph derived from a moderate number of superpixels. This graph captures both intrinsic color and edge information of image data. Starting from the superpixels, an adaptive multi-level region merging scheme is employed to seek such cluster information from Ncut eigenvectors. With developed saliency measures for each merged region, encouraging performance is obtained after across-level integration. Experiments by comparing with 13 existing methods on four benchmark datasets, including MSRA-1000, SOD, SED, and CSSD show the proposed method, Ncut saliency, results in uniform object enhancement and achieves comparable better performance to the state-of-the-art methods. In this paper, we propose an object segmentation algorithm driven by minimal user interactions. Compared to previous user-guided systems, our system can cut out the desired object in a given image with only a single finger touch minimizing user effort. The proposed model harnesses both edge and region based local information in an adaptive manner as well as geometric cues implied by the user-input to achieve fast and robust segmentation in a level set framework. We demonstrate the advantages of our method in terms of computational efficiency and accuracy comparing qualitatively and quantitatively with graph cut based techniques. We address the problem of computing the 3-dimensional shape of an arbitrary scene from a set of images taken at known viewpoints. Multi-camera scene reconstruction is a natural generalization of the stereo matching problem. However, it is much more difficult than stereo, primarily due to the difficulty of reasoning about visibility. In this paper, we take an approach that has yielded excellent results for stereo, namely energy minimization via graph cuts. We first give an energy minimization formulation of the multi-camera scene reconstruction problem. The energy that we minimize treats the input images symmetrically, handles visibility properly, and imposes spatial smoothness while preserving discontinuities. As the energy function is NP-hard to minimize exactly, we give a graph cut algorithm that computes a local minimum in a strong sense. We handle all camera configurations where voxel coloring can be used, which is a large and natural class. Experimental data demonstrates the effectiveness of our approach.