Dimensionality Reduction for Vision Applications: A Manifold-Learning Approach
Date Issued
2006
Date
2006
Author(s)
Chen, Hwann-Tzong
DOI
en-US
Abstract
The thesis concerns a manifold-learning view on performing dimensionality reduction for applications in computer vision. We examine the recent progress in this field, and set out on better advancing the existing techniques and broadening the related vision applications, including face and texture recognition, tracking, and content-based image retrieval.
Previous studies on reducing the dimensionality of image data often emphasize maintaining the principal image characteristics or capturing the discriminant image structure if the class labels of data are given. The popular subspace approaches are good examples to typify efforts along this line. However, such methods do not take account of how image data are scattered in a high-dimensional space, a useful property for solving many vision problems. Alternatively, manifold learning can be used to uncover the data's underlying manifold structure, while reducing the dimensionality. Our approach achieves this effect by re-embedding the manifold structure of data into a low-dimensional space. Depending on the formulation of a vision problem, a task-related neighborhood for every data point in the embedding space is preserved such that the nearest neighbor criterion in the low-dimensional embedding space becomes more reliable. In this work, we describe three manifold-learning frameworks, each of which is formulated for specific vision applications, and makes use of available information, such as class labels, pairwise similarity relations, or relevance feedback, in deriving the low-dimensional embeddings. The efficiency of our algorithms on learning the manifolds stems from solving generalized eigenvalue problems, whose solutions can be readily computed by existing numerical methods. Among other important issues, we also propose useful insights and new techniques on how to appropriately represent an image as a point in the high-dimensional space, and how to measure the distance between two points in accordance with the similarity relation entailed by their corresponding images. All these efforts further boost the performance of our manifold-learning methods, where we shall illustrate their advantages with extensive experimental results.
Subjects
降維方法
電腦視覺
Dimensionality Reduction
Computer Vision
Manifold Learning
Type
thesis
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