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These three results coincide with gamma correction of the bottom layer with γ=2 (for top black), unchanged bottom layer (or, what is the same, γ=1; for top neutral gray), and γ=0.5 (for top white). The formula used by Photoshop as of 2012 has a discontinuity of local contrast, and other formulas correct it. Photoshop's formula is: [6]
Computing the convex hull means that a non-ambiguous and efficient representation of the required convex shape is constructed. The complexity of the corresponding algorithms is usually estimated in terms of n , the number of input points, and sometimes also in terms of h , the number of points on the convex hull.
In geometry, the convex hull, convex envelope or convex closure [1] of a shape is the smallest convex set that contains it. The convex hull may be defined either as the intersection of all convex sets containing a given subset of a Euclidean space , or equivalently as the set of all convex combinations of points in the subset.
Convex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets (or, equivalently, maximizing concave functions over convex sets). Many classes of convex optimization problems admit polynomial-time algorithms, [1] whereas mathematical optimization is in general NP-hard. [2 ...
An example of a convex polygon: a regular pentagon. In geometry, a convex polygon is a polygon that is the boundary of a convex set. This means that the line segment between two points of the polygon is contained in the union of the interior and the boundary of the polygon. In particular, it is a simple polygon (not self-intersecting). [1]
Conic optimization is a subfield of convex optimization that studies problems consisting of minimizing a convex function over the intersection of an affine subspace and a convex cone. The class of conic optimization problems includes some of the most well known classes of convex optimization problems, namely linear and semidefinite programming.
A convex polytope is a special case of a polytope, having the additional property that it is also a convex set contained in the -dimensional Euclidean space . Most texts [ 1 ] [ 2 ] use the term "polytope" for a bounded convex polytope, and the word "polyhedron" for the more general, possibly unbounded object.
The intersection of two convex cones in the same vector space is again a convex cone, but their union may fail to be one. The class of convex cones is also closed under arbitrary linear maps . In particular, if C {\displaystyle C} is a convex cone, so is its opposite − C {\displaystyle -C} , and C ∩ − C {\displaystyle C\cap -C} is the ...