Geometric Properties of Image Manifolds
نویسندگان
چکیده
Recently, the notion of data as manifolds has come into being. The subject of image manifolds has been explored but not extensively and not from the point of view of di erential geometry. It is a well known fact that image manifolds are curved. Using some basic techniques of di erential geometry this paper explores image manifold curvature and attempts get a feel for the magnitude of this curvature, leading to some geometric insights of image manifolds.
منابع مشابه
Image Manifolds
A collection of related N by M images, such as a set of faces, may be modeled by a manifold embedded in an NM -dimensional Euclidean space called an image manifold. With the modeling of image spaces as manifolds, geometric properties of image manifolds can be studied either theoretically or experimentally. A practical result of the investigation of image manifolds provides an insight into image...
متن کاملImage alignment via kernelized feature learning
Machine learning is an application of artificial intelligence that is able to automatically learn and improve from experience without being explicitly programmed. The primary assumption for most of the machine learning algorithms is that the training set (source domain) and the test set (target domain) follow from the same probability distribution. However, in most of the real-world application...
متن کاملWarped product and quasi-Einstein metrics
Warped products provide a rich class of physically significant geometric objects. Warped product construction is an important method to produce a new metric with a base manifold and a fibre. We construct compact base manifolds with a positive scalar curvature which do not admit any non-trivial quasi-Einstein warped product, and non compact complete base manifolds which do not admit any non-triv...
متن کاملGeometric Sampling of Manifolds for Image Representation and Processing
It is often advantageous in image processing and computer vision to consider images as surfaces imbedded in higher dimensional manifolds. It is therefore important to consider the theoretical and applied aspects of proper sampling of manifolds. We present a new sampling theorem for surfaces and higher dimensional manifolds. The core of the proof resides in triangulation results for manifolds wi...
متن کاملThe Bochner identities for the Kählerian gradients
We discuss algebraic properties for the symbols of geometric first order differential operators on almost Hermitian manifolds and Kähler manifolds. Through study on the universal enveloping algebra and higher Casimir elements, we know algebraic relations for the symbols like the Clifford algebra. From the relations, we have all the Bochner identities for the operators. As applications, we have ...
متن کامل