In computer vision and image processing, Gaussian derivative operators of different orders are frequently used as a basis for expressing various types of visual operations; see scale space and N-jet.
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I'm just not sure why they switch from dY / di to using the partial derivative operator at the end . talk ) 06 : 51, 28 February 2012 ( UTC)
33.
It is indeed quite tempting to formally take a square root of a derivative operator, or square it, but in what sense does applying a differential operator twice lead to energy squared?
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Where the superscript N to the left of the derivative operator indicates the reference frame in which the derivative is taken . cross multiplied with the vector "'a "'itself.
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The respected factor \ zeta _ { i _ k } is anti-commutated to the left until the derivative operator can be directly applied . we may prove the following properties of the derivatives
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Unfortunately the comparable process for the derivative operator " D " is significantly more complex, but it can be shown that " D " is neither commutative nor additive in general.
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The corresponding scale-space framework encompasses a theory for Gaussian derivative operators, which can be used as a basis for expressing a large class of visual operations for computerized systems that process visual information.
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The special case of exponentiating the derivative operator to a non-integer power is called the fractional derivative which, together with the fractional integral, is one of the basic operations of the fractional calculus.
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Due to the commutative property between the derivative operator and the Gaussian smoothing operator, such " scale-space derivatives " can equivalently be computed by convolving the original image with Gaussian derivative operators.
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Due to the commutative property between the derivative operator and the Gaussian smoothing operator, such " scale-space derivatives " can equivalently be computed by convolving the original image with Gaussian derivative operators.
