Structure tensor: Difference between revisions

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Complex version: re-worded "Parseval relationship" to Parseval's identity
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If the [[gradient]] <math>\nabla I = (I_x,I_y)^\text{T}</math> of <math>I</math> is viewed as a 2×1 (single-column) matrix, where <math>(.)^\text{T}</math> denotes [[transpose]] operation, turning a row vector to a column vector, the matrix <math>S_0</math> can be written as the [[matrix product]] <math>(\nabla I)(\nabla I)^\text{T}</math> or [[tensor product|tensor or outer product]] <math>\nabla I \otimes \nabla I</math>, also known as an outer product, or tensor product. Note however that the structure tensor <math>S_w(p)</math> cannot be factored in this way in general except if <math>w</math> is a [[Dirac delta function]].
 
===Discrete version===