Fuzzy Mathematical Morphology - Medical Image Processing: Advanced Fuzzy Set Theoretic Techniques - page 210

ime=[fe3(i-1,j-1),fe3(i,j-1),fe3(i+1,j-1);fe3(i-1,j),fe3(i,j),...
fe3(i+1,j);fe3(i-1,j+1),fe3(i,j+1),fe3(i+1,j+1)];
te2= (ime+c+(lambda-2)*ime.*c)./(1+(ime.*c)*(lambda-1));
eros= min(min(te2));
td1= (imd.*c)./(lambda+(imd+c-imd.*c*(1-lambda)));
dil= max(max(td1));
morphim_eros(i-1,j-1)=eros;
morphim_dil(i-1,j-1)=dil;
end
end
mxdil=max(max(morphim_dil));
morphim_dil1=255*morphim_dil./mxdil;
mxeros=max(max(morphim_eros));
morphim_eros1=255*morphim_eros./mxeros;
edge= abs(uint8(morphim_dil1)-uint8(morphim_eros1));
figure,imshow(uint8(edge)) % gradient image
% finding binary edge
For i=1:dim1
For j=1:dim2
if edge(i,j)>50
bin_edge (i,j)=1;
else bon_edge(i,j)=0.0;
end
end
end
figure, imshow(bin_edge);
9.7 Summary
This chapter describes morphology in general and fuzzy mathematical mor-
phology in particular. Different fuzzy morphological operators given by
Sinha and Dougherty, De Baets and Bloch are discussed. Also, fuzzy mor-
phology, based on t -norms and t -conorms, and Lukasiewicz operator are dis-
cussed. Dilation and erosion are explained with examples. Application of
fuzzy morphology in medical imaging particularly in edge detection along
with the MATLAB program is also included.
References
1. De Baets, B. and Kerre, E., An introduction to fuzzy mathematical morphol-
ogy, in Proc. of North America Fuzzy Information Processing Society ( NAFIPS'93 ),
Allentown, PA, pp. 129-133, 1993.
2. Bandler, W. and Kohout, I.J., Semantics of implication operator and fuzzy rela-
tional products, International Journal of Man Machine Studies , 12, 89-116, 1980.