12,079 research outputs found
Shape Interaction Matrix Revisited and Robustified: Efficient Subspace Clustering with Corrupted and Incomplete Data
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.Comment: This is an extended version of our iccv15 pape
A Multi-cut Formulation for Joint Segmentation and Tracking of Multiple Objects
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
Nearness to Local Subspace Algorithm for Subspace and Motion Segmentation
There is a growing interest in computer science, engineering, and mathematics
for modeling signals in terms of union of subspaces and manifolds. Subspace
segmentation and clustering of high dimensional data drawn from a union of
subspaces are especially important with many practical applications in computer
vision, image and signal processing, communications, and information theory.
This paper presents a clustering algorithm for high dimensional data that comes
from a union of lower dimensional subspaces of equal and known dimensions. Such
cases occur in many data clustering problems, such as motion segmentation and
face recognition. The algorithm is reliable in the presence of noise, and
applied to the Hopkins 155 Dataset, it generates the best results to date for
motion segmentation. The two motion, three motion, and overall segmentation
rates for the video sequences are 99.43%, 98.69%, and 99.24%, respectively
Multi-Cue Structure Preserving MRF for Unconstrained Video Segmentation
Video segmentation is a stepping stone to understanding video context. Video
segmentation enables one to represent a video by decomposing it into coherent
regions which comprise whole or parts of objects. However, the challenge
originates from the fact that most of the video segmentation algorithms are
based on unsupervised learning due to expensive cost of pixelwise video
annotation and intra-class variability within similar unconstrained video
classes. We propose a Markov Random Field model for unconstrained video
segmentation that relies on tight integration of multiple cues: vertices are
defined from contour based superpixels, unary potentials from temporal smooth
label likelihood and pairwise potentials from global structure of a video.
Multi-cue structure is a breakthrough to extracting coherent object regions for
unconstrained videos in absence of supervision. Our experiments on VSB100
dataset show that the proposed model significantly outperforms competing
state-of-the-art algorithms. Qualitative analysis illustrates that video
segmentation result of the proposed model is consistent with human perception
of objects
Multi-body Non-rigid Structure-from-Motion
Conventional structure-from-motion (SFM) research is primarily concerned with
the 3D reconstruction of a single, rigidly moving object seen by a static
camera, or a static and rigid scene observed by a moving camera --in both cases
there are only one relative rigid motion involved. Recent progress have
extended SFM to the areas of {multi-body SFM} (where there are {multiple rigid}
relative motions in the scene), as well as {non-rigid SFM} (where there is a
single non-rigid, deformable object or scene). Along this line of thinking,
there is apparently a missing gap of "multi-body non-rigid SFM", in which the
task would be to jointly reconstruct and segment multiple 3D structures of the
multiple, non-rigid objects or deformable scenes from images. Such a multi-body
non-rigid scenario is common in reality (e.g. two persons shaking hands,
multi-person social event), and how to solve it represents a natural
{next-step} in SFM research. By leveraging recent results of subspace
clustering, this paper proposes, for the first time, an effective framework for
multi-body NRSFM, which simultaneously reconstructs and segments each 3D
trajectory into their respective low-dimensional subspace. Under our
formulation, 3D trajectories for each non-rigid structure can be well
approximated with a sparse affine combination of other 3D trajectories from the
same structure (self-expressiveness). We solve the resultant optimization with
the alternating direction method of multipliers (ADMM). We demonstrate the
efficacy of the proposed framework through extensive experiments on both
synthetic and real data sequences. Our method clearly outperforms other
alternative methods, such as first clustering the 2D feature tracks to groups
and then doing non-rigid reconstruction in each group or first conducting 3D
reconstruction by using single subspace assumption and then clustering the 3D
trajectories into groups.Comment: 21 pages, 16 figure
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