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Shape descriptors can be classified by their invariance with respect to the transformations allowed in the associated shape definition. Many descriptors are invariant with respect to congruency, meaning that congruent shapes (shapes that could be translated, rotated and mirrored) will have the same descriptor (for example moment or spherical harmonic based descriptors or Procrustes analysis ...
The structure of a crystal is often represented by the pole figure of its crystallographic planes. A plane is chosen as the equator, usually the (001) or (011) plane; its pole is the center of the figure. Then, the poles of the other planes are placed on the figure, with the Miller indices for each pole. The poles that belong to a zone are ...
The pruning algorithm is a technique used in digital image processing based on mathematical morphology. [1] It is used as a complement to the skeleton and thinning algorithms to remove unwanted parasitic components (spurs).
In geometric algebra, however, the blades of different grades can exhibit a complex structure. Since both vectors and pseudovectors can act as eigenblades, they may each have a set of eigenvalues matching the degrees of freedom of the complex eigenvalues that would be found in ordinary linear algebra.
Mathematical Morphology was developed in 1964 by the collaborative work of Georges Matheron and Jean Serra, at the École des Mines de Paris, France.Matheron supervised the PhD thesis of Serra, devoted to the quantification of mineral characteristics from thin cross sections, and this work resulted in a novel practical approach, as well as theoretical advancements in integral geometry and ...
A three-dimensional model of a figure-eight knot.The figure-eight knot is a prime knot and has an Alexander–Briggs notation of 4 1.. Topology (from the Greek words τόπος, 'place, location', and λόγος, 'study') is the branch of mathematics concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling ...
A drawing of a butterfly with bilateral symmetry, with left and right sides as mirror images of each other.. In geometry, an object has symmetry if there is an operation or transformation (such as translation, scaling, rotation or reflection) that maps the figure/object onto itself (i.e., the object has an invariance under the transform). [1]
Geometric relevance: The torsion τ(s) measures the turnaround of the binormal vector. The larger the torsion is, the faster the binormal vector rotates around the axis given by the tangent vector (see graphical illustrations). In the animated figure the rotation of the binormal vector is clearly visible at the peaks of the torsion function.