Low Dimensional Manifold Model with Semi-local Patches

نویسندگان

  • ZUOQIANG SHI
  • WEI ZHU
چکیده

Abstract. In this paper we integrate semi-local patches and the weighted graph Laplacian [17] into the framework of the low dimensional manifold model [12]. This approach is much faster than the original LDMM algorithm. The number of iterations is typically reduced from 100 to 10 and the equations in each step are much easier to solve. This new approach is tested in image inpainting and denoising and the results are better than the original LDMM and competitive with state-of-the-art methods.

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

nr . IAS - UVA - 02 - 01 Procrustes Analysis to Coordinate Mixtures of Probabilistic Principal Component Analyzers

Mixtures of Probabilistic Principal Component Analyzers can be used to model data that lies on or near a low dimensional manifold in a high dimensional observation space, in effect tiling the manifold with local linear (Gaussian) patches. In order to exploit the low dimensional structure of the data manifold, the patches need to be localized and oriented in a low dimensional space, so that 'loc...

متن کامل

LTPI: A Spectral Clustering Method Based on Local Topology Preserving Indexing and Its Application for Document Clustering

In terms of machine learning theory, the intrinsic geometrical structure of the original data space is usually embedded in the low-dimensional manifold. The extraction of optimized manifold features could improve the performance of clustering. This paper presents a new spectral clustering method called local topology preserving indexing (LTPI). In this algorithm, the data are projected into a l...

متن کامل

3D Point Cloud Denoising using Graph Laplacian Regularization of a Low Dimensional Manifold Model

3D point cloud—a new signal representation of volumetric objects—is a discrete collection of triples marking exterior object surface locations in 3D space. Conventional imperfect acquisition processes of 3D point cloud—e.g., stereo-matching from multiple viewpoint images or depth data acquired directly from active light sensors—imply non-negligible noise in the data. In this paper, we adopt a p...

متن کامل

A Tale of Two Bases: Local-Nonlocal Regularization on Image Patches with Convolution Framelets

We propose an image representation scheme combining the local and nonlocal characterization of patches in an image. Our representation scheme can be shown to be equivalent to a tight frame constructed from convolving local bases (e.g., wavelet frames, discrete cosine transforms, etc.) with nonlocal bases (e.g., spectral basis induced by nonlinear dimension reduction on patches), and we call the...

متن کامل

Charting a Manifold

We construct a nonlinear mapping from a high-dimensional sample space to a low-dimensional vector space, effectively recovering a Cartesian coordinate system for the manifold from which the data is sampled. The mapping preserves local geometric relations in the manifold and is pseudo-invertible. We show how to estimate the intrinsic dimensionality of the manifold from samples, decompose the sam...

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 2016