I'm working on semi automatic texture segmentation using level set and gabor feature vector described by Manjunath und Ma [1]. I consider their feature representation is better than others since I can get good result on several images but somehow performs really bad on other images data. So I guess there's something wrong with my understanding.
They describe that the feature vectors consist of $\mu_{mn}$ (mean) and $\sigma_{mn}$ (standard deviation). I use scale $S = 4$ and orientation $K = 6$, thus my feature vector will be 48 dimension (4 * 6 * 2 = 48):
$f = \{ \mu_{00}, \sigma_{00}, \mu_{01}, \sigma_{01}, \mu_{02}...\mu_{35}, \sigma_{35} \} \tag1$
I am confused with their equation:
$W(x, y) = \int I(x_1,y_1)g_{mn} * (x - x_1, y - y_1) dx_1 dy_1 \tag2$
$\mu_{mn} = \int \int |W_{mn}(x,y)|dxdy \tag3$
$\sigma_{mn} = \sqrt{ \int \int (|W_{mn}(x,y) - \mu_{mn}|)^2 dxdy } \tag4$
So my first question is: are $\mu$ and $\sigma$ simply mean and average? So far, I just average every pixel value of the magnitude to obtain $\mu$ and compute the standard deviation to obtain $\sigma$.
After I compute the feature vector, I need to do distance measure between two vectors $f_i$ and $f_j$
$d(i, j) = \sum_{}^{m}\sum_{}^{n} d_{mn}(i, j) \tag5$
$d_{mn}(i, j) = |\frac{\mu_{mn}^i - \mu_{mn}^j}{\alpha(\mu_{mn})}| + |\frac{\sigma_{mn}^i - \sigma_{mn}^j}{\alpha(\sigma_{mn})}| \tag6$
I'm really puzzled with $\alpha(\mu_{mn})$ and $\alpha(\sigma_{mn})$ ? What are they? I have tried to calculate 48 standard deviations from $ (1)$
$\alpha = \{ \alpha(\mu_{00}), \alpha(\sigma_{00}), \alpha(\mu_{01}), \alpha(\sigma_{01}), \alpha(\mu_{02})...\alpha(\mu_{35}), \alpha(\sigma_{35}) )\} \tag7$
and use it to calculate the distance function but I'm not convinced with my calculation since it seems not better than simple euclidean distance.
- Texture Features for Browsing and Retrieval of Image Data by B.S. Manjunath and W.Y. Ma (1996)
