Gabor filters and phase portraits for the detection of architectural distortion in mammograms

1 Erratum to: Med Biol Eng Comput DOI 10.1007/s11517-006-0088-3

Due to a processing error the presentation of the sixth sequence of Sect. 2.1 and Eqs. 8 and 10 was incorrect. The correct versions are given below.

Let θ(x,y) be the texture orientation at (x,y), and g _k (x,y), k = 0, 1,..., 179, be the Gabor filter oriented at α _k  = –π/2 + πk/180. Let I _HPF(x,y) be the high-pass-filtered version of the mammogram being processed, and I _k (x,y) = (I _HPF * g _k )(x,y) represent the Gabor-filtered images, where the asterisk denotes linear convolution. Then, the orientation field angle of I(x,y) is given by

$$ \theta {\left( {x,y} \right)} = \alpha _{{k_{{\max }} }} \quad {\text{where}}\;k_{{\max }} = \arg {\left\{ {{\mathop {\max }\limits_k }{\left[ {{\left| {I_{k} {\left( {x,y} \right)}} \right|}} \right]}} \right\}}. $$

(2)

$$ \theta _{{\text{f}}} {\left( {x,y} \right)} = \frac{1} {2}\arctan {\left( {\frac{{{\left( {h*s} \right)}{\left( {x,y} \right)}}} {{{\left( {h*c} \right)}{\left( {x,y} \right)}}}} \right)}, $$

(8)

$$ M_{{\text{f}}} {\left( {x,y} \right)} = {\left( {h*M_{{{\text{CLS}}}} } \right)}{\left( {x,y} \right)}, $$

(10)