Principal Component Analysis with Missing Data and Its Application to Polyhedral Object Modeling

Shum, Harry; Ikeuchi, Katsushi; Reddy, Raj

doi:10.1007/978-1-4615-0797-0_1

Cited by 70 publications

(96 citation statements)

References 11 publications

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“…In the application of PCA, several methods that extract principal components without any preprocessing of data have been proposed. Ruhe [5], Wiberg [6], and Shibayama [7] proposed PCA-like methods for capturing the structure of incomplete multivariate data without any imputations and statistical assumptions, and Shum et al [8] applied such techniques to object modeling. The methods are based on the lower rank approximation of the data matrix, which accomplishes the minimization of the least square criterion, and they extract principal components of the covariance matrix of the sample data set.…”

Section: Introductionmentioning

confidence: 99%

Linear Fuzzy Clustering Techniques With Missing Values and Their Application to Local Principal Component Analysis

Honda

Ichihashi

2004

IEEE Trans. Fuzzy Syst.

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Section: Introductionmentioning

confidence: 99%

Linear Fuzzy Clustering Techniques With Missing Values and Their Application to Local Principal Component Analysis

Honda

Ichihashi

2004

IEEE Trans. Fuzzy Syst.

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“…Wiberg [23] has proposed a method based on the weighted least squares technique, which was later extended by Shum et al [20]. Gabriel and Zamir [7] proposed a method for subspace learning with any choice of weights, where each data point can have a different weight determined on the basis of reliability.…”

Section: Related Workmentioning

confidence: 99%

“…The method for performing PCA in the presence of missing pixels, which is presented in this paper, is related to these methods [23,20]. However, we have paid a special attention to the high-dimensional nature of image data and adapted the algorithms to avoid an ill-posedness of the problem.…”

Section: Related Workmentioning

confidence: 99%

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A Robust PCA Algorithm for Building Representations from Panoramic Images

Skočaj

Bischof

Leonardis

2002

Computer Vision — ECCV 2002

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Abstract. Appearance-based modeling of objects and scenes using PCA has been successfully applied in many recognition tasks. Robust methods which have made the recognition stage less susceptible to outliers, occlusions, and varying illumination have further enlarged the domain of applicability. However, much less research has been done in achieving robustness in the learning stage. In this paper, we propose a novel robust PCA method for obtaining a consistent subspace representation in the presence of outlying pixels in the training images. The method is based on the EM algorithm for estimation of principal subspaces in the presence of missing data. By treating the outlying points as missing pixels, we arrive at a robust PCA representation. We demonstrate experimentally that the proposed method is efficient. In addition, we apply the method to a set of panoramic images to build a representation that enables surveillance and view-based mobile robot localization.

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“…Let us consider a simple case where our interesting object is polyhedral. Then, reconstructing the whole 3D shape using several 3D point clouds taken from different viewpoints requires extracting at least three common planar patches from every 3D point cloud [2] . This extraction is known as surface segmentation.…”

Section: Introductionmentioning

confidence: 99%

Discrete plane segmentation and estimation from a point cloud using local geometric patterns

Kenmochi

Buzer

Sugimoto

et al. 2008

Int. J. Autom. Comput.

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This paper presents a method for segmenting a 3D point cloud into planar surfaces using recently obtained discretegeometry results. In discrete geometry, a discrete plane is defined as a set of grid points lying between two parallel planes with a small distance, called thickness. Contrarily to the continuous case, there exist a finite number of local geometric patterns (LGPs) appearing on discrete planes. Moreover, such a LGP does not possess the unique normal vector but a set of normal vectors. By using those LGP properties, we first reject non-linear points from a point cloud, and then classify non-rejected points whose LGPs can have common normal vectors into a planar-surface-point set. From each segmented point set, we also estimate parameters of a discrete plane by minimizing its thickness.

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Principal Component Analysis with Missing Data and Its Application to Polyhedral Object Modeling

Cited by 70 publications

References 11 publications

Linear Fuzzy Clustering Techniques With Missing Values and Their Application to Local Principal Component Analysis

Linear Fuzzy Clustering Techniques With Missing Values and Their Application to Local Principal Component Analysis

A Robust PCA Algorithm for Building Representations from Panoramic Images

Discrete plane segmentation and estimation from a point cloud using local geometric patterns

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