Issue34

Z. Jijun et alii, Frattura ed Integrità Strutturale, 34 (2015) 590-598; DOI: 10.3221/IGF-ESIS.34.65 592 ' ( , ) { ( , )} ln ( , ) z x y LPF z x y i x y   Thus, we can use the original image to subtract the image after lowpass filtering to get the image with increasing high- frequency part (reflected light): ' ( , ) ( , ) ( , ) ln ( , ) s x y z x y z x y r x y    Finally, we should conduct antilog operation to ( , ) s x y to achieve correct results: ' ( , ) exp[ ( , )] ( , ) s x y s x y r x y   However, it’s clear that if we just use the original image to subtract the image after lowpass filtering, it’s similar to conducting common lowpass filtering to the image, and we can get what we want. As a result, we consider conducting weighted approach on the lowpass filtering to get the expected effect of increasing high-frequency part and suppressing low-frequency part: ' ( , ) ( , ) ( , ) ln ( , ) (1 )ln ( , ) s x y z x y tz x y r x y t i x y      Assume 1 u t   , and the formula above will be: ( , ) ln ( , ) ln ( , ) s x y r x y u i x y   u is the weighting variable, and 0 1 u   , of which the meaning is the reserved weigh of low-frequency information in the image. Next, to study the influence of value of u on the image, we will take 0.2 as step size, and conduct spatial homomorphic filtering to the original image. The results are as shown in Fig. 2. (a) (b) (c) (d) (e) (f) Figure 2: Figs. a-f show the effects of homomorphic filtering under 0, 0.2, 0.4, 0.6, 0.8 and 1, respectively. From the analysis about a-f, we can infer that higher value of u indicates closer distance between the image and high-pass filtering, stressing the reflection of details, and resulting in loss of some necessary high-frequency information. Lower