Geometrical Consistent Clustering of Linear Subspaces

نویسندگان

  • Nuno Pinho da Silva
  • João P. Costeira
چکیده

The perception of rigid-bodies from affine views of moving 3D point clouds, boils down to clustering the rigid motion subspaces supported by the image trajectories. For a physically meaningful interpretation, clusters must be consistent with the geometry of the underlying subspaces. We find that proper subspace clustering requires invariance both to the orthogonal and the inclusion relationship between subspaces. Most of the existing measures for subspace comparison do not comply with this observation. A practical consequence is that methods based on such (dis)similarities are unstable when the number of rigid bodies increase. This paper introduces the Normalized Subspace Inclusion (NSI) criterion to resolve these issues. Combining it with a robust segmentation method, we propose a robust methodology for rigid motion segmentation, and test it, extensively, on the Hopkins155 database. The geometric consistency of the NSI assures the method’s accuracy when the number of rigid bodies increases, while robustness proves to be suitable for dealing with challenging imaging conditions.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Innovation Pursuit: A New Approach to the Subspace Clustering Problem

This paper presents a new scalable approach, termed Innovation Pursuit (iPursuit), to the problem of subspace clustering. iPursuit rests on a new geometrical idea whereby each subspace is identified based on its novelty with respect to the other subspaces. The subspaces are identified consecutively by solving a series of simple linear optimization problems, each searching for a direction of inn...

متن کامل

Clustering Consistent Sparse Subspace Clustering

Subspace clustering is the problem of clustering data points into a union of lowdimensional linear/affine subspaces. It is the mathematical abstraction of many important problems in computer vision, image processing and machine learning. A line of recent work [4, 19, 24, 20] provided strong theoretical guarantee for sparse subspace clustering [4], the state-of-the-art algorithm for subspace clu...

متن کامل

Graph Connectivity in Noisy Sparse Subspace Clustering

Subspace clustering is the problem of clustering data points into a union of lowdimensional linear/affine subspaces. It is the mathematical abstraction of many important problems in computer vision, image processing and machine learning. A line of recent work [4, 19, 24, 20] provided strong theoretical guarantee for sparse subspace clustering [4], the state-of-the-art algorithm for subspace clu...

متن کامل

Geodesic Distance based Fuzzy Clustering

Clustering is a widely applied tool of data mining to detect the hidden structure of complex multivariate datasets. Hence, clustering solves two kinds of problems simultaneously, it partitions the datasets into cluster of objects that are similar to each other and describes the clusters by cluster prototypes to provide some information about the distribution of the data. In most of the cases th...

متن کامل

High-Rank Matrix Completion and Subspace Clustering with Missing Data

This paper considers the problem of completing a matrix with many missing entries under the assumption that the columns of the matrix belong to a union of multiple low-rank subspaces. This generalizes the standard low-rank matrix completion problem to situations in which the matrix rank can be quite high or even full rank. Since the columns belong to a union of subspaces, this problem may also ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2009