We propose an effective subspace selection scheme as a post-processing step to improve results obtained by sparse subspace clustering (SSC). Our method starts by the computation of stable subspaces using a novel random sampling scheme. Thus constructed preliminary subspaces are used to identify the initially incorrectly clustered data points and then to reassign them to more suitable clusters based on their goodness-of-fit to the preliminary model. To improve the robustness of the algorithm, we use a dominant nearest subspace classification scheme that controls the level of sensitivity against reassignment. We demonstrate that our algorithm is convergent and superior to the direct application of a generic alternative such as principal component analysis. On several popular datasets for motion segmentation and face clustering pervasively used in the sparse subspace clustering literature the proposed method is shown to reduce greatly the incidence of clustering errors while introducing negligible disturbance to the data points already correctly clustered.
Recently, Minimum Cost Multicut Formulations have been proposed and proven to be successful in both motion trajectory segmentation and multi-target tracking scenarios. Both tasks benefit from decomposing a graphical model into an optimal number of connected components based on attractive and repulsive pairwise terms. The two tasks are formulated on different levels of granularity and, accordingly, leverage mostly local information for motion segmentation and mostly high-level information for multi-target tracking. In this paper we argue that point trajectories and their local relationships can contribute to the high-level task of multi-target tracking and also argue that high-level cues from object detection and tracking are helpful to solve motion segmentation. We propose a joint graphical model for point trajectories and object detections whose Multicuts are solutions to motion segmentation {\it and} multi-target tracking problems at once. Results on the FBMS59 motion segmentation benchmark as well as on pedestrian tracking sequences from the 2D MOT 2015 benchmark demonstrate the promise of this joint approach.
Real time outdoor navigation in highly dynamic environments is an crucial problem. The recent literature on real time static SLAM don't scale up to dynamic outdoor environments. Most of these methods assume moving objects as outliers or discard the information provided by them. We propose an algorithm to jointly infer the camera trajectory and the moving object trajectory simultaneously. In this paper, we perform a sparse scene flow based motion segmentation using a stereo camera. The segmented objects motion models are used for accurate localization of the camera trajectory as well as the moving objects. We exploit the relationship between moving objects for improving the accuracy of the poses. We formulate the poses as a factor graph incorporating all the constraints. We achieve exact incremental solution by solving a full nonlinear optimization problem in real time. The evaluation is performed on the challenging KITTI dataset with multiple moving cars.Our method outperforms the previous baselines in outdoor navigation.
We present an approach for object segmentation in videos that combines frame-level object detection with concepts from object tracking and motion segmentation. The approach extracts temporally consistent object tubes based on an off-the-shelf detector. Besides the class label for each tube, this provides a location prior that is independent of motion. For the final video segmentation, we combine this information with motion cues. The method overcomes the typical problems of weakly supervised/unsupervised video segmentation, such as scenes with no motion, dominant camera motion, and objects that move as a unit. In contrast to most tracking methods, it provides an accurate, temporally consistent segmentation of each object. We report results on four video segmentation datasets: YouTube Objects, SegTrackv2, egoMotion, and FBMS.
We present a method for temporally consistent motion segmentation from RGB-D videos assuming a piecewise rigid motion model. We formulate global energies over entire RGB-D sequences in terms of the segmentation of each frame into a number of objects, and the rigid motion of each object through the sequence. We develop a novel initialization procedure that clusters feature tracks obtained from the RGB data by leveraging the depth information. We minimize the energy using a coordinate descent approach that includes novel techniques to assemble object motion hypotheses. A main benefit of our approach is that it enables us to fuse consistently labeled object segments from all RGB-D frames of an input sequence into individual 3D object reconstructions.
Although commercial and open-source software exist to reconstruct a static object from a sequence recorded with an RGB-D sensor, there is a lack of tools that build rigged models of articulated objects that deform realistically and can be used for tracking or animation. In this work, we fill this gap and propose a method that creates a fully rigged model of an articulated object from depth data of a single sensor. To this end, we combine deformable mesh tracking, motion segmentation based on spectral clustering and skeletonization based on mean curvature flow. The fully rigged model then consists of a watertight mesh, embedded skeleton, and skinning weights.
The Shape Interaction Matrix (SIM) is one of the earliest approaches to performing subspace clustering (i.e., separating points drawn from a union of subspaces). In this paper, we revisit the SIM and reveal its connections to several recent subspace clustering methods. Our analysis lets us derive a simple, yet effective algorithm to robustify the SIM and make it applicable to realistic scenarios where the data is corrupted by noise. We justify our method by intuitive examples and the matrix perturbation theory. We then show how this approach can be extended to handle missing data, thus yielding an efficient and general subspace clustering algorithm. We demonstrate the benefits of our approach over state-of-the-art subspace clustering methods on several challenging motion segmentation and face clustering problems, where the data includes corrupted and missing measurements.
Motion segmentation is currently an active area of research in computer Vision. The task of comparing different methods of motion segmentation is complicated by the fact that researchers may use subtly different definitions of the problem. Questions such as "Which objects are moving?", "What is background?", and "How can we use motion of the camera to segment objects, whether they are static or moving?" are clearly related to each other, but lead to different algorithms, and imply different versions of the ground truth. This report has two goals. The first is to offer a precise definition of motion segmentation so that the intent of an algorithm is as well-defined as possible. The second is to report on new versions of three previously existing data sets that are compatible with this definition. We hope that this more detailed definition, and the three data sets that go with it, will allow more meaningful comparisons of certain motion segmentation methods.
In this paper, we describe work in progress towards a real-time vision-based traffic flow prediction (TFP) system. The proposed method consists of three elemental operators, that are dynamic texture model based motion segmentation, feature extraction and Gaussian process (GP) regression. The objective of motion segmentation is to recognize the target regions covering the moving vehicles in the sequence of visual processes. The feature extraction operator aims to extract useful features from the target regions. The extracted features are then mapped to the number of vehicles through the operator of GP regression. A training stage using historical visual data is required for determining the parameter values of the GP. Using a low-resolution visual data set, we performed preliminary evaluations on the performance of the proposed method. The results show that our method beats a benchmark solution based on Gaussian mixture model, and has the potential to be developed into qualified and practical solutions to real-time TFP.
In this paper, we propose a new framework for segmenting feature-based moving objects under affine subspace model. Since the feature trajectories in practice are high-dimensional and contain a lot of noise, we firstly apply the sparse PCA to represent the original trajectories with a low-dimensional global subspace, which consists of the orthogonal sparse principal vectors. Subsequently, the local subspace separation will be achieved via automatically searching the sparse representation of the nearest neighbors for each projected data. In order to refine the local subspace estimation result and deal with the missing data problem, we propose an error estimation to encourage the projected data that span a same local subspace to be clustered together. In the end, the segmentation of different motions is achieved through the spectral clustering on an affinity matrix, which is constructed with both the error estimation and sparse neighbors optimization. We test our method extensively and compare it with state-of-the-art methods on the Hopkins 155 dataset and Freiburg-Berkeley Motion Segmentation dataset. The results show that our method is comparable with the other motion segmentation methods, and in many cases exceed them in terms of precision and computation time.
Subspace clustering refers to the problem of segmenting data drawn from a union of subspaces. State-of-the-art approaches for solving this problem follow a two-stage approach. In the first step, an affinity matrix is learned from the data using sparse or low-rank minimization techniques. In the second step, the segmentation is found by applying spectral clustering to this affinity. While this approach has led to state-of-the-art results in many applications, it is sub-optimal because it does not exploit the fact that the affinity and the segmentation depend on each other. In this paper, we propose a joint optimization framework --- Structured Sparse Subspace Clustering (S$^3$C) --- for learning both the affinity and the segmentation. The proposed S$^3$C framework is based on expressing each data point as a structured sparse linear combination of all other data points, where the structure is induced by a norm that depends on the unknown segmentation. Moreover, we extend the proposed S$^3$C framework into Constrained Structured Sparse Subspace Clustering (CS$^3$C) in which available partial side-information is incorporated into the stage of learning the affinity. We show that both the structured sparse representation and the segmentation can be found via a combination of an alternating direction method of multipliers with spectral clustering. Experiments on a synthetic data set, the Extended Yale B data set, the Hopkins 155 motion segmentation database, and three cancer data sets demonstrate the effectiveness of our approach.
The problem of determining whether an object is in motion, irrespective of camera motion, is far from being solved. We address this challenging task by learning motion patterns in videos. The core of our approach is a fully convolutional network, which is learned entirely from synthetic video sequences, and their ground-truth optical flow and motion segmentation. This encoder-decoder style architecture first learns a coarse representation of the optical flow field features, and then refines it iteratively to produce motion labels at the original high-resolution. We further improve this labeling with an objectness map and a conditional random field, to account for errors in optical flow, and also to focus on moving "things" rather than "stuff". The output label of each pixel denotes whether it has undergone independent motion, i.e., irrespective of camera motion. We demonstrate the benefits of this learning framework on the moving object segmentation task, where the goal is to segment all objects in motion. Our approach outperforms the top method on the recently released DAVIS benchmark dataset, comprising real-world sequences, by 5.6%. We also evaluate on the Berkeley motion segmentation database, achieving state-of-the-art results.
Dynamic scene understanding is a challenging problem and motion segmentation plays a crucial role in solving it. Incorporating semantics and motion enhances the overall perception of the dynamic scene. For applications of outdoor robotic navigation, joint learning methods have not been extensively used for extracting spatio-temporal features or adding different priors into the formulation. The task becomes even more challenging without stereo information being incorporated. This paper proposes an approach to fuse semantic features and motion clues using CNNs, to address the problem of monocular semantic motion segmentation. We deduce semantic and motion labels by integrating optical flow as a constraint with semantic features into dilated convolution network. The pipeline consists of three main stages i.e Feature extraction, Feature amplification and Multi Scale Context Aggregation to fuse the semantics and flow features. Our joint formulation shows significant improvements in monocular motion segmentation over the state of the art methods on challenging KITTI tracking dataset.
We propose a new multi-frame method for efficiently computing scene flow (dense depth and optical flow) and camera ego-motion for a dynamic scene observed from a moving stereo camera rig. Our technique also segments out moving objects from the rigid scene. In our method, we first estimate the disparity map and the 6-DOF camera motion using stereo matching and visual odometry. We then identify regions inconsistent with the estimated camera motion and compute per-pixel optical flow only at these regions. This flow proposal is fused with the camera motion-based flow proposal using fusion moves to obtain the final optical flow and motion segmentation. This unified framework benefits all four tasks - stereo, optical flow, visual odometry and motion segmentation leading to overall higher accuracy and efficiency. Our method is currently ranked third on the KITTI 2015 scene flow benchmark. Furthermore, our CPU implementation runs in 2-3 seconds per frame which is 1-3 orders of magnitude faster than the top six methods. We also report a thorough evaluation on challenging Sintel sequences with fast camera and object motion, where our method consistently outperforms OSF [Menze and Geiger, 2015], which is currently ranked second on the KITTI benchmark.
This paper addresses the task of segmenting moving objects in unconstrained videos. We introduce a novel two-stream neural network with an explicit memory module to achieve this. The two streams of the network encode spatial and temporal features in a video sequence respectively, while the memory module captures the evolution of objects over time. The module to build a "visual memory" in video, i.e., a joint representation of all the video frames, is realized with a convolutional recurrent unit learned from a small number of training video sequences. Given a video frame as input, our approach assigns each pixel an object or background label based on the learned spatio-temporal features as well as the "visual memory" specific to the video, acquired automatically without any manually-annotated frames. The visual memory is implemented with convolutional gated recurrent units, which allows to propagate spatial information over time. We evaluate our method extensively on two benchmarks, DAVIS and Freiburg-Berkeley motion segmentation datasets, and show state-of-the-art results. For example, our approach outperforms the top method on the DAVIS dataset by nearly 6%. We also provide an extensive ablative analysis to investigate the influence of each component in the proposed framework.
Most state-of-the-art motion segmentation algorithms draw their potential from modeling motion differences of local entities such as point trajectories in terms of pairwise potentials in graphical models. Inference in instances of minimum cost multicut problems defined on such graphs al- lows to optimize the number of the resulting segments along with the segment assignment. However, pairwise potentials limit the discriminative power of the employed motion models to translational differences. More complex models such as Euclidean or affine transformations call for higher-order potentials and a tractable inference in the resulting higher-order graphical models. In this paper, we (1) introduce a generalization of the minimum cost lifted multicut problem to hypergraphs, and (2) propose a simple primal feasible heuristic that allows for a reasonably efficient inference in instances of higher-order lifted multicut problem instances defined on point trajectory hypergraphs for motion segmentation. The resulting motion segmentations improve over the state-of-the-art on the FBMS-59 dataset.
Community recovery is a central problem that arises in a wide variety of applications such as network clustering, motion segmentation, face clustering and protein complex detection. The objective of the problem is to cluster data points into distinct communities based on a set of measurements, each of which is associated with the values of a certain number of data points. While most of the prior works focus on a setting in which the number of data points involved in a measurement is two, this work explores a generalized setting in which the number can be more than two. Motivated by applications particularly in machine learning and channel coding, we consider two types of measurements: (1) homogeneity measurement which indicates whether or not the associated data points belong to the same community; (2) parity measurement which denotes the modulo-2 sum of the values of the data points. Such measurements are possibly corrupted by Bernoulli noise. We characterize the fundamental limits on the number of measurements required to reconstruct the communities for the considered models.
In this paper, we present a kernel subspace clustering method that can handle non-linear models. In contrast to recent kernel subspace clustering methods which use predefined kernels, we propose to learn a low-rank kernel matrix, with which mapped data in feature space are not only low-rank but also self-expressive. In this manner, the low-dimensional subspace structures of the (implicitly) mapped data are retained and manifested in the high-dimensional feature space. We evaluate the proposed method extensively on both motion segmentation and image clustering benchmarks, and obtain superior results, outperforming the kernel subspace clustering method that uses standard kernels[Patel 2014] and other state-of-the-art linear subspace clustering methods.
Beam search is a desirable choice of test-time decoding algorithm for neural sequence models because it potentially avoids search errors made by simpler greedy methods. However, typical cross entropy training procedures for these models do not directly consider the behaviour of the final decoding method. As a result, for cross-entropy trained models, beam decoding can sometimes yield reduced test performance when compared with greedy decoding. In order to train models that can more effectively make use of beam search, we propose a new training procedure that focuses on the final loss metric (e.g. Hamming loss) evaluated on the output of beam search. While well-defined, this "direct loss" objective is itself discontinuous and thus difficult to optimize. Hence, in our approach, we form a sub-differentiable surrogate objective by introducing a novel continuous approximation of the beam search decoding procedure. In experiments, we show that optimizing this new training objective yields substantially better results on two sequence tasks (Named Entity Recognition and CCG Supertagging) when compared with both cross entropy trained greedy decoding and cross entropy trained beam decoding baselines.
A general framework for solving the subspace clustering problem using the CUR decomposition is presented. The CUR decomposition provides a natural way to construct similarity matrices for data that come from a union of unknown subspaces $\mathscr{U}=\underset{i=1}{\overset{M}\bigcup}S_i$. The similarity matrices thus constructed give the exact clustering in the noise-free case. Additionally, this decomposition gives rise to many distinct similarity matrices from a given set of data, which allow enough flexibility to perform accurate clustering of noisy data. We also show that two known methods for subspace clustering can be derived from the CUR decomposition. An algorithm based on the theoretical construction of similarity matrices is presented, and experiments on synthetic and real data are presented to test the method. Additionally, an adaptation of our CUR based similarity matrices is utilized to provide a heuristic algorithm for subspace clustering; this algorithm yields the best overall performance to date for clustering the Hopkins155 motion segmentation dataset.