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In image analysis, the generalized structure tensor (GST) is an extension of the Cartesian structure tensor to curvilinear coordinates. [1] It is mainly used to detect and to represent the "direction" parameters of curves, just as the Cartesian structure tensor detects and represents the direction in Cartesian coordinates.
Vector and tensor calculus in general curvilinear coordinates is used in tensor analysis on four-dimensional curvilinear manifolds in general relativity, [8] in the mechanics of curved shells, [6] in examining the invariance properties of Maxwell's equations which has been of interest in metamaterials [9] [10] and in many other fields.
In computer vision, the Lucas–Kanade method is a widely used differential method for optical flow estimation developed by Bruce D. Lucas and Takeo Kanade.It assumes that the flow is essentially constant in a local neighbourhood of the pixel under consideration, and solves the basic optical flow equations for all the pixels in that neighbourhood, by the least squares criterion.
The complex representation of the structure tensor is frequently used in fingerprint analysis to obtain direction maps containing certainties which in turn are used to enhance them, to find the locations of the global (cores and deltas) and local (minutia) singularities, as well as automatically evaluate the quality of the fingerprints.
They are useful for forming direction cosine matrices that express one set of orthonormal basis vectors in terms of another set, or for expressing a known vector in a different basis. Simply put, direction cosines provide an easy method of representing the direction of a vector in a Cartesian coordinate system.
Powell's method, strictly Powell's conjugate direction method, is an algorithm proposed by Michael J. D. Powell for finding a local minimum of a function. The function need not be differentiable, and no derivatives are taken. The function must be a real-valued function of a fixed number of real-valued inputs.
[a] [1] [2] [3] It is also the modern name for what used to be called the absolute differential calculus (the foundation of tensor calculus), tensor calculus or tensor analysis developed by Gregorio Ricci-Curbastro in 1887–1896, and subsequently popularized in a paper written with his pupil Tullio Levi-Civita in 1900. [4]
The TRIAD method is the earliest published algorithm for determining spacecraft attitude, which was first introduced by Harold Black in 1964. [ 1 ] [ 2 ] [ 3 ] Given the knowledge of two vectors in the reference and body coordinates of a satellite, the TRIAD algorithm obtains the direction cosine matrix relating to both frames.