# Human Motion Segmentation Based On Structure Constraint Matrix Factorization

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### ARTICULATED AND EFORMABLE MOTION ANALYSIS FROM OTION CAPTURE DATA

KEY WORDS: Gait analysis, Human body models, Factorization, Non-linear modelling, Biomechanics. ABSTRACT: Human 3D models and motion analysis are nowadays used in a wide range of applications, spanning from medicine to security and surveillance. In this work, we will focus on the creation of biomechanical models for clinical and sports analysis.

### Euclidean Reconstruction of Deformable Structure Using a

in all image frames is known as the measurement matrix W. For rigid objects when the measurement matrix is rescaled with the correct projective depths its rank is constrained to be at most 4. This rank constraint can then be exploited to factorize W into its motion and shape components. When the object is deforming the non-rigid 3D shape

### Unifying Nuclear Norm and Bilinear Factorization Approaches

Low-rank matrix factorization is a long standing prob-lem in computer vision. The seminal factorization method for Structure from Motion of Tomasi and Kanade [35] has been extended to encompass non-rigid and articulated cases, as well as photometric stereo [5] and multiple bod-ies [12]. Unfortunately, in the presence of missing data or

### Workshop New Challenges in Neural Computation 2011

This is very useful for motion trajectories, since one basis primitive is allowed to share a common part of its trajectory with other primitives and to specialize later. 2 Non-negative Matrix Factorization Like other approaches, e. g. PCA and ICA, non-negative matrix factorization (NMF) [3] is meant to solve the source separation problem.

### Joint Segmentation and Pose Tracking of Human in Natural Videos

Foreground/background segmentation problem in mov-ing camera environment has been studied actively these days. Sheikh et al.[21] proposes an algorithm to construct foreground and background appearance models for pixel-wise labeling based on a sparse set of motion trajectories. Similarly, a matrix factorization is employed in [6]tode-

### Articulated Structure From Motion by Factorization

dent motion (e.g. subspace-based motion segmentation [4]). If we are to recover accurate structure and motion that satis-ﬁes articulation constraints , this dependency should be in-corporated from the beginning (i.e. during factorization). Speciﬁcally, in this work we show how to detect articu-

### Automated Articulated Structure and 3D Shape Recovery from

Motion Segmentation. Motion segmentation is a partic-ularly challenging problem in the case of articulated motion due to the dependencies between the linked parts. The orig-inal solution to the multi-body segmentation problem [5], based on rigid factorization [20], was inﬂuential but unable to solve problems containing dependent motions. This was

### Introduction: what is motion segmentation?

Some EM-based approach to motion segmentation: Sugaya, Y., & Kanatani, K. (2004). Geometric structure of degeneracy for multi-body motion segmentation. In Workshop on statis tical methods in video processing. Gruber, A., & Weiss, Y. (2004). Multibody factor ization with uncertainty and missing data using the EM algorithm. In CVPR (Vol.

### Inter/intra-frame constrained vascular segmentation in X-ray

based enhancement easily introduces the non-vascular noise and motion artefacts when dealing with X-ray angiogram im-ages. While subtraction-based enhancement utilizes the an-giograms with and without vessels. It can effectively remove the motion artefacts in the final enhanced vascular angio-grams and improve the subsequent segmentation accuracy.

### Real-Time Sequential Model-Based Non-Rigid SFM

al. [12], the authors develop a method for model-based segmentation and tracking based on the assumption that, given an accurate 3D model of an object, its segmentation from any given image is fully dened by its pose. Non-rigid factorization was introduced by the seminar work by Bregler et al [13], modelling deformations as a

### DUST: Dual Union of Spatio-Temporal Subspaces for Monocular

model, factorization-based approaches have been typically used [4, 10, 19, 31, 37]. Alternatively, other approaches impose the low-rank constraint by means of robust PCA-like formulations in which the rank of a matrix repre-senting the shape is minimized. These type of methods either assume the data lies on a single low dimensional

### Human Action Recognition Using SURF and HOG Features from

by applying non-negative matrix factorization on the entire video sequence. This detector is based on the extraction of dynamic textures, which are used to synthesize motion and identify important regions in motion. The detector extracts structural information, the location of moving parts in a video, and searches

### Allan Z. Ding - GitHub Pages

Transferable Subspace for Human Motion Segmentation, 32nd AAAI Conference on Artiﬁcial Intelligence (AAAI), 2018 [C-11] Zhengming Ding, Ming Shao and Yun Fu. Low-Rank Embedded Ensemble Semantic Dictionary for Zero-Shot Learning. IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017. [C-12] Shuhui Jiang, Zhengming Ding and

### Automated Articulated Structure and 3D Shape Recovery from

Motion Segmentation. Motion segmentation is a partic-ularly challenging problem in the case of articulated motion due to the dependencies between the linked parts. The orig-inal solution to the multi-body segmentation problem [3], based on rigid factorization [20], was inﬂuential but un-able to solve problems containing dependent motions. This

### Non-rigid face modelling using shape priors

Clearly, the rank of the measurement matrix is constrained to be at most 3K, where K is the number of deformations. This rank constraint can be exploited to factorize the measurement matrix into a motion matrix ^Mand a shape matrix ^Sby truncating the SVD of Wto rank 3K. However, this factorization is not unique since any invertible 3K 3K

### INVOLUNTARY CREATION OF SOCIAL OCCURRENCE STORYBOARD FROM

Illustration of approximate non-negative matrix factorization the matrix V is represented by the two smaller matrices W and H. When multiplied approximately reconstruct V. There is no significant difference between queries from two adjacent days. To achieve this constraint, an approach known as SNMF is introduced.

### C280, Computer Vision - People

Possible solution: decompose matrix into dense sub-blocks, factorize each sub-block, and fuse the results Finding dense maximal sub-blocks of the matrix is NP-complete (equivalent to finding maximal cliques in a graph) Incremental bilinear refinement (1) Perform factorization on a dense sub-block (2) Solve for a new 3D point visible by

### Pattern recognition : 35th German conference, GCPR 2013

Structure from Motion Using Rigidly Coupled Discriminative Joint Non-negative Matrix Factorization for Human Level Set Based Cerebral Vessel Segmentation andBone

### Subspace Clustering via New Low-Rank Model with Discrete

We propose a novel low-rank segmentation model to solve the above assumption based subspace clustering problem. In-stead of learning the afﬁnity matrix done by previous sub-space clustering methods including SSC [Elhamifar and Vi-dal, 2013 ]and LRR [Liu et al., 2013 , we propose to learn the group indicator directly such that the low-rank

### Shifted Subspaces Tracking on Sparse Outlier for Motion

solving a matrix factorization model. This framework in-vokes a sequence of matrix decompositions as subroutines, which can be summarized in two steps, i.e., background modeling and ﬂow tracking. For the ﬁrst step, we proposes semi-soft GoDec which replaces the cardinality constraint in GoDec with an 1 penalty. This small change

### Human Pose Extraction from Monocular Videos using Constrained

2 Non Rigid Factorization Apart from structure from motion, factorization techniques can be applied to a wide range of application like data segmentation, data de-noising and data imputation. Data de-noising and im-putation are of signiﬁcant interest to us since the feature tracks from the off-the shelf trackers are

### IEEE TRANS ON MEDICAL IMAGING, 2018 1 A Sparse Non-negative

parts-based and interpretable representation. Speciﬁcally, NMF with a sparsity constraint operates on input matrices whose entries are non-negative, thus allowing us to model a data matrix as sparse linear combinations of a set of basis vectors (or building blocks). NMF with a sparsity constraint only allows non-negative combinations of

### ARTICULATED MOTION ANALYSIS FROM MOTION CAPTURE DATA

matrices respectively. This forces a rank constraint on the measurements W (i.e. rank(W) ≤ 3). Given this rank constraint, we can compute an initial factorization of W by performing a SVD giving: T r r r T i i r i i T i i P i i W SVD → ∑u v =∑u v =U ΣV = = σ σ 1 1 where Urr a r×r diagonal matrix and Vr a P×r orthogonal matrix.

### Allan Z. Ding - GitHub Pages

Transferable Subspace for Human Motion Segmentation, 32nd AAAI Conference on Artiﬁcial Intelligence (AAAI), 2018 [C-12] Zhengming Ding, Ming Shao and Yun Fu. Low-Rank Embedded Ensemble Semantic Dictionary for Zero-Shot Learning. IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017. [C-13] Shuhui Jiang, Zhengming Ding and

### A Factorization-Based Approach for Articulated Non-rigid

term of motion subspaces. B. Motion Segmentation Early motion segmentation techniques based on the factorization method are proposed in [2], [10], which iteratively generate hypotheses of segmentation and verify them. Costeira&Kanade[8] proposes an inﬂuential technique using the shape interaction matrix to directly segment motions.

### BIRS Workshop on Mathematical Methods in Computer Vision

The motion of points on the observed surface is modeled using a set of intersecting subspaces. By adopting an aﬃne projection model for the camera, the observed motion can be analyzed and recovered using subspace methods. Overall, the approach allows motion segmentation to be performed to recover the underlying kinematic chains and object shape.

### Clustering in pursuit of temporal correlation for human

matrix factorization under manifold regularization to explore the neighborhood relationship among the image regions [27]. Aiming at the human motion problem, we try to exploit the temporal neighborhood inherent in frames to address the motion segmentation problem under the graph-based framework. 3 Proposed method

### Motion Segmentation using the Hadamard Product and Spectral

method for the estimation of 3D structure and motion. The classic approach in factorization is to exploit the rank constraint to factorize the measurement matrix into a motion matrix M and a shape matrix S by truncating the SVD of W to the rank r speciﬁc to the problem as W = MS = UD12 D 1 2 V, where M = UD 1 2 is the motion ma-

### For Peer Review

document clustering. The matrix factorization was used to compute a low-rank approximation of a sparse matrix along with preservation of natural data property. Wang et al. [31] applied the NMF framework to gene-expression data to iden-tify different cancer classes. Anderson et al. [32] presented an NMF-based clustering method to differential

### IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE

A Factorization-Based Approach for Articulated Nonrigid Shape, Motion, and Kinematic Chain Recovery from Video Jingyu Yan and Marc Pollefeys,Senior Member, IEEE Abstract Recovering articulated shape and motion, especially human body motion, from video is a challenging problem with a wide

### Recovering Articulated Non-rigid Shapes, Motions and

human body motion with non-rigid facial motion, is completely ignored. We propose a factorization-based approach to recover the shape, motion and kinematic chain of an articulated object with non-rigid parts altogether directly from video sequences under a uniﬂed framework. The proposed approach is based on our modeling of the articu-

### Learning the Combinatorial Structure of Demonstrated

inverse optimal control approach, coupled with a sparsity constraint on the task representation can be used to discover relevant features in the task space. Finally Brillinger [18] has developed an algorithm based on least square re-gression to learn potential functions modeling the motion of wild animals in natural parks.

### Using In-frame Shear Constraints for Monocular Motion

Motion Segmentation is a well-studied problem with algorithms inspired from various sources like, matrix factorization [4, 23, 40], tensor decomposition [3, 26, 43], statistical model estimation [7, 35, 39] and per-ception [29, 34, 38]. The problem has been analyzed

### Article DM-SLAM: Monocular SLAM in Dynamic Environments

Jan 12, 2020 motion model and the number of features points which motion model includes. The closer features are more likely to belong to the same motion model. Models between different moving objects shares a few inliers. Based on above observations, our algorithm aims to obtain motion model which is solved by set

### Robust Nonnegative Matrix Factorization with Ordered

and recognition. Nonnegative matrix factorization (NMF) [3] as a fundamental approach for such data representation has attracted great attentions. NMF based approaches have been widely used in the ﬁelds of machine learning and computer vision such as motion segmentation [4], [5], human activity recognition [6] and face recognition [7].

### DUST: Dual Union of Spatio-Temporal Subspaces for Monocular

and camera motion G from 2D point tracks P. Early solutions based on the factorization method [10], constrained the matrix X^ to be low-rank. For a given rank Kit was shown that rank(X^) was 3K. Shape could then be estimated applying a rank 3Kfactorization over P fol-lowed by constraints ensuring rotation orthonormality [5].