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Following the differential geometric way of expressing the requirement of non-maximum suppression proposed by Lindeberg,<ref name=lin98/><ref name=lin93>[http://kth.diva-portal.org/smash/record.jsf?pid=diva2%3A473368&dswid=5061 T. Lindeberg (1993) "Discrete derivative approximations with scale-space properties: A basis for low-level feature extraction", J. of Mathematical Imaging and Vision, 3(4), pages 349–376.]</ref> let us introduce at every image point a local coordinate system <math>(u, v)</math>, with the <math>v</math>-direction parallel to the gradient direction. Assuming that the image has been pre-smoothed by Gaussian smoothing and a [[scale space representation]] <math>L(x, y; t)</math> at scale <math>t</math> has been computed, we can require that the gradient magnitude of the [[scale space representation]], which is equal to the first-order directional derivative in the <math>v</math>-direction <math>L_v</math>, should have its first order directional derivative in the <math>v</math>-direction equal to zero
:<math>\partial_v(L_v) = 0</math>
while the second-order directional derivative in the <math>v</math>-direction of <math>L_v</math> should be negative,
:<math>\partial_{vv}(L_v) \leq 0.</math>
Written out as an explicit expression in terms of local partial derivatives <math>L_x, L_y, \ldots , L_{yyy}</math>, this edge definition can be expressed as the zero-crossing curves of the differential invariant
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