What is an image manifold?

Abstract. 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, geometrical properties of image manifolds can be studied either theoretically or experimentally.

Is the Earth a 2d manifold?

Locally, the surface of the Earth looks like a 2-dimensional plane, so it is a 2-manifold.

What exactly is a manifold?

The more typical definition is that a manifold is a space that is locally like Rn. To formalize it, you can say that a manifold is a space in which any sufficiently small neighborhood is homeomorphic to an open set in Rn. Homeomorphic means that you can find a homeomorphism between them.

Why is a circle a manifold?

Circles and Spheres as Manifolds. A manifold is a topological space that “locally” resembles Euclidean space. Each arc of the circle locally looks closer to a line segment, and if you take an infinitesimal arc, it will “locally” resemble a one dimensional line segment.

What is a manifold in construction?

A manifold is a wide and/or bigger pipe, or channel, into which smaller pipes or channels lead. A pipe fitting or similar device that connects multiple inputs or outputs.

What is a manifold in equipment?

A manifold is a fluid or gas distribution system or device that serves to bring many junctions into one place or a single channel into an area where many points meet. Complex pneumatic and hydraulic circuits can utilize manifolds and manifold systems with interfaces to sophisticated electronic networks.

Is a cylinder a manifold?

A cylinder manifold is a group of large gas cylinders, commonly used to supply gases via a pipeline to a building such as a hospital. Gas manifolds should be stored in an area separate from the main building.