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Adding a reference with relevant information about measurements that can be computed in order to infer the shape of the tensors. Those techniques are commonly used in medical imaging to analyze DTI MRI's. |
→Continuous version: Expressing the same with the tensor product operator for completeness. |
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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 <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===
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