Digital StepEdgesfromZeroCrossing ofSecondDirectional Derivatives
Robertm . Haralick · 1984
We usethefacet modeltoaccomplish stepedgedetection. Theessence ofthefacet modelisthatanyanalysis madeonthebasis of thepixel values insomeneighborhood hasitsfinal authoritative inter- pretation relative totheunderlying graytoneintensity surface ofwhich theneighborhood pixel values areobserved noisy samples. Withregard toedgedetection, wedefine anedgetooccurinapixel ifandonlyif there issomepoint inthepixel's areahaving anegatively sloped zero crossing ofthesecond directional derivative takeninthedirection ofa nonzero gradient atthepixel's center. Thus, todetermine whether or notapixel should bemarkedasastepedgepixel, itsunderlying gray toneintensity surface mustbeestimated onthebasis ofthepixels inits neighborhood. Forthis, weuseafunctional formconsisting ofalinear combination ofthetensor products ofdiscrete orthogonal polynomials ofuptodegree three. Theappropriate directional derivatives areeasily computed fromthis kindofafunction. Uponcomparing theperformance ofthis zerocrossing ofsecond di- rectional derivative operator withthePrewitt gradient operator andthe Marr-Hildreth zerocrossing oftheLaplacian operator, wefindthatitis thebestperformer; nextisthePrewitt gradient operator. TheMarr- Hildreth zerocrossing oftheLaplacian operator performs theworst. IndexTerms-Edge operator, facet model, imageprocessing, image segmentation, zerocrossings ofsecond directional derivative.