The set of Gaussian derivative operators up to a certain order is often referred to as the " N-jet " and constitutes a basic type of feature within the scale-space framework.
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Because of this property, the Laplace variable is also known as " operator variable " in the domain : either " derivative operator " or ( for " integration operator ".
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When Gaussian derivative operators and differential invariants are used in this way as basic feature detectors at multiple scales, the uncommitted first stages of visual processing are often referred to as a " visual front-end ".
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Interestingly, the uniqueness of the Gaussian derivative operators as local operations derived from a scale-space representation can be obtained by similar axiomatic derivations as are used for deriving the uniqueness of the Gaussian kernel for scale-space smoothing.
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Where " V " is the function space and \ langle-,-\ rangle the L 2 ( as would, for example, be the case for the second derivative operator on a compact interval ? ).
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If you assume he's dropping constants ( as theorists often do ) then it looks like a derivative operator in x acting on an energy times some interaction function B . What B is, I haven't a clue.
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A major branch of numerical analysis is devoted to the development of efficient algorithms for matrix computations, a subject that is centuries old and is today an expanding area of research . derivative operator, which acts on the Taylor series of a function.
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Where } } is the material derivative operator, also denoted by in capital notation as } }, is the flow velocity, is the local fluid density, is the local pressure, is the viscous stress tensor and represents the sum of the external body forces.
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When computing several derivatives in the N-jet simultaneously, discrete scale-space smoothing with the discrete analogue of the Gaussian kernel, or with a recursive filter approximation, followed by small support difference operators, may be both faster and more accurate than computing recursive approximations of each derivative operator.
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The computation of the second moment matrix ( sometimes also referred to as the structure tensor ) A in the Harris operator, requires the computation of image derivatives, and ( ii ) an " integration scale " for accumulating the non-linear operations on derivative operators into an integrated image descriptor.
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