Advances in matrix manifolds for computer vision
نویسنده
چکیده
This paper presents an overview of various matrix manifolds that are commonly used in computer vision applications. It covers the following manifoldsLie groups, Stiefel manifolds, Grassmann manifolds and Riemannian manifolds. A manifold of dimension n is a topological space that near each point resembles n-dimensional Euclidean space. More precisely, each point of an n-dimensional manifold has a neighbourhood that is homeomorphic to the Euclidean space of dimension n. Eg:Lines and circles are onedimensional manifolds, but not figure eights.
منابع مشابه
A Geometry Preserving Kernel over Riemannian Manifolds
Abstract- Kernel trick and projection to tangent spaces are two choices for linearizing the data points lying on Riemannian manifolds. These approaches are used to provide the prerequisites for applying standard machine learning methods on Riemannian manifolds. Classical kernels implicitly project data to high dimensional feature space without considering the intrinsic geometry of data points. ...
متن کاملHuman Computer Interaction Using Vision-Based Hand Gesture Recognition
With the rapid emergence of 3D applications and virtual environments in computer systems; the need for a new type of interaction device arises. This is because the traditional devices such as mouse, keyboard, and joystick become inefficient and cumbersome within these virtual environments. In other words, evolution of user interfaces shapes the change in the Human-Computer Interaction (HCI). In...
متن کاملHuman Computer Interaction Using Vision-Based Hand Gesture Recognition
With the rapid emergence of 3D applications and virtual environments in computer systems; the need for a new type of interaction device arises. This is because the traditional devices such as mouse, keyboard, and joystick become inefficient and cumbersome within these virtual environments. In other words, evolution of user interfaces shapes the change in the Human-Computer Interaction (HCI). In...
متن کاملOptimized Kernel-based Projection Space of Riemannian Manifolds
Recent advances in computer vision suggest that encoding images through Symmetric Positive Definite (SPD) matrices can lead to increased classification performance. Taking into account manifold geometry is typically done via embedding the manifolds in tangent spaces, or Reproducing Kernel Hilbert Spaces (RKHS). Recently it was shown that projecting such manifolds into a kernel-based random proj...
متن کاملA Novel Noise Reduction Method Based on Subspace Division
This article presents a new subspace-based technique for reducing the noise of signals in time-series. In the proposed approach, the signal is initially represented as a data matrix. Then using Singular Value Decomposition (SVD), noisy data matrix is divided into signal subspace and noise subspace. In this subspace division, each derivative of the singular values with respect to rank order is u...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Image Vision Comput.
دوره 30 شماره
صفحات -
تاریخ انتشار 2012