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that satisfy a sign-condition on the following differential invariant
:<math>L_v^3 L_{vvv} = L_x^3 \, L_{xxx} + 3 \, L_x^2 \, L_y \, L_{xxy} + 3 \, L_x \, L_y^2 \, L_{xyy} + L_y^3 \, L_{yyy} \leq 0
where <math>L_x, L_y, \ldots , L_{yyy}</math> denote partial derivatives computed from a [[scale space representation]] <math>L</math> obtained by smoothing the original image with a [[Gaussian kernel]]. In this way, the edges will be automatically obtained as continuous curves with sub-pixel accuracy. Hysteresis thresholding can also be applied to these differential and subpixel edge segments.
In practice, first-order derivative approximations can be computed by central differences as described above, while second-order derivatives can be computed from the [[scale space representation]] <math>L</math> according to:
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