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Graph-based regularization of inverse problems in imaging

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Ordinal number

In set theory, an ordinal number, or ordinal, is a generalization of ordinal numerals (first, second, nth, etc.) aimed to extend enumeration to infinite sets. A finite set can be enumerated by successively labeling each element with the least natural number that has not been previously used. To extend this process to various infinite sets, ordinal numbers are defined more generally as linearly ordered labels that include the natural numbers and have the property that every set of ordinals has a least element (this is needed for giving a meaning to "the least unused element").

Total order

In mathematics, a total order or linear order is a partial order in which any two elements are comparable. That is, a total order is a binary relation on some set , which satisfies the following for all and in : (reflexive). If and then (transitive). If and then (antisymmetric). or (strongly connected, formerly called total). Reflexivity (1.) already follows from connectedness (4.), but is required explicitly by many authors nevertheless, to indicate the kinship to partial orders.

Depth map

In 3D computer graphics and computer vision, a depth map is an or that contains information relating to the distance of the surfaces of scene objects from a viewpoint. The term is related (and may be analogous) to depth buffer, Z-buffer, Z-buffering, and Z-depth. The "Z" in these latter terms relates to a convention that the central axis of view of a camera is in the direction of the camera's Z axis, and not to the absolute Z axis of a scene. File:Cubic Structure.jpg|Cubic Structure File:Cubic Frame Stucture and Floor Depth Map.

Weak solution

In mathematics, a weak solution (also called a generalized solution) to an ordinary or partial differential equation is a function for which the derivatives may not all exist but which is nonetheless deemed to satisfy the equation in some precisely defined sense. There are many different definitions of weak solution, appropriate for different classes of equations. One of the most important is based on the notion of distributions.

Spherical sector

In geometry, a spherical sector, also known as a spherical cone, is a portion of a sphere or of a ball defined by a conical boundary with apex at the center of the sphere. It can be described as the union of a spherical cap and the cone formed by the center of the sphere and the base of the cap. It is the three-dimensional analogue of the sector of a circle. If the radius of the sphere is denoted by r and the height of the cap by h, the volume of the spherical sector is This may also be written as where φ is half the cone angle, i.

Camera obscura

A camera obscura (; ) is a darkened room with a small hole or lens at one side through which an is projected onto a wall or table opposite the hole. Camera obscura can also refer to analogous constructions such as a box or tent in which an exterior image is projected inside. Camera obscuras with a lens in the opening have been used since the second half of the 16th century and became popular as aids for drawing and painting.

Spherical conic

In mathematics, a spherical conic or sphero-conic is a curve on the sphere, the intersection of the sphere with a concentric elliptic cone. It is the spherical analog of a conic section (ellipse, parabola, or hyperbola) in the plane, and as in the planar case, a spherical conic can be defined as the locus of points the sum or difference of whose great-circle distances to two foci is constant. By taking the antipodal point to one focus, every spherical ellipse is also a spherical hyperbola, and vice versa.

CompactFlash

CompactFlash (CF) is a flash memory mass storage device used mainly in portable electronic devices. The format was specified and the devices were first manufactured by SanDisk in 1994. CompactFlash became one of the most successful of the early memory card formats, surpassing Miniature Card and SmartMedia. Subsequent formats, such as MMC/SD, various Memory Stick formats, and xD-Picture Card offered stiff competition. Most of these cards are smaller than CompactFlash while offering comparable capacity and speed.

Normal space

In topology and related branches of mathematics, a normal space is a topological space X that satisfies Axiom T4: every two disjoint closed sets of X have disjoint open neighborhoods. A normal Hausdorff space is also called a T4 space. These conditions are examples of separation axioms and their further strengthenings define completely normal Hausdorff spaces, or T5 spaces, and perfectly normal Hausdorff spaces, or T6 spaces. A topological space X is a normal space if, given any disjoint closed sets E and F, there are neighbourhoods U of E and V of F that are also disjoint.

Resolution (algebra)

In mathematics, and more specifically in homological algebra, a resolution (or left resolution; dually a coresolution or right resolution) is an exact sequence of modules (or, more generally, of s of an ), which is used to define invariants characterizing the structure of a specific module or object of this category. When, as usually, arrows are oriented to the right, the sequence is supposed to be infinite to the left for (left) resolutions, and to the right for right resolutions.