Osteoarthritis severity of the hip by computer-aided grading of radiographic images

Abstract

A computer-aided classification system was developed for the assessment of the severity of hip osteoarthritis (OA) . Sixty-four radiographic images of normal and osteoarthritic hips were digitized and enhanced. Employing the Kellgren and Lawrence scale, the hips were grouped by three experienced orthopaedists into three OA-severity categories: Normal, Mild/Moderate and Severe. Utilizing custom-developed software, 64 ROIs corresponding to the radiographic Hip Joint Spaces were manually segmented and novel textural features were generated. These features were used in the design of a two-level classification scheme for characterizing hips as normal or osteoarthritic (1st level) and as of Mild/Moderate or Severe OA (2nd level). At each classification level, an ensemble of three classifiers was implemented. The proposed classification scheme discriminated correctly all normal hips from osteoarthritic hips (100% accuracy), while the discrimination accuracy between Mild/Moderate and Severe osteoarthritic hips was 95.7%. The proposed system could be used as a diagnosis decision-supporting tool.

Appendix

1.1 Generation of Gabor textural features

A two-dimensional (2-D) Gabor filter G(x,y) can be considered as a sinusoidal plane wave of certain spatial frequency and orientation, modulated by a 2-D Gaussian envelope [12].

For the needs of this study, four (4) filter orientations were used: θ° = 0°, 45°, 90°, and 135°. For each orientation θ, a pair of filters with an anti-symmetric phase relationship was used [16]: G _f,θ,0°(x,y) and G _f,θ,−90°(x,y).

Each HJS image, corresponding to the determined Region Of Interest (ROI), was convolved with the, G _f,θ,0°(x,y) as well as with the G _f,θ,−90°(x,y) filter, according to Eqs. 6 and 7, respectively:

$$ {\text{GFIM}}_{{{\text{f}},\theta ,0^{ \circ } }} (i,j) = {\sum\limits_{x = - m}^{ + m} {{\sum\limits_{y = - m}^{ + m} {G_{{{\text{f}},\theta ,0^{ \circ } }} (x,y)I(i + x,j + y)} }} },\,m = \frac{{z - 1}} {2},z = 5. $$

(6)

$$ {\text{GFIM}}_{{{\text{f}},\theta , - 90^{ \circ } }} (i,j) = {\sum\limits_{x = - m}^{ + m} {{\sum\limits_{y = - m}^{ + m} {G_{{{\text{f}},\theta , - 90^{ \circ } }} (x,y)I(i + x,j + y)} }} },m = \frac{{z - 1}} {2},z = 5, $$

(7)

where I(i,j) is the input HJS-ROI image, G _f,θ,0°(x,y) and G _f,θ,−90°(x,y) are the z × z Gabor filters, while GFIM_f,θ,0°(i,j) and GFIM_{f, θ, −90°}(i,j) represent the filtered images corresponding to the G _f,θ,0°(x,y) and G_f,θ,−90°(x,y) filters, respectively.

Based on the filtered images GFIM_f,θ,0°(i,j) and GFIM_f,θ,−90°(i,j), an image labelled as Gabor Energy Image (GEN_Image) was produced, according to Eq. 8:

$$ {\text{GEN}}\_\text{Im} {\text{age}}(i,j) = {\sqrt {{\left( {{\text{GFIM}}_{{{\text{f}},\theta ,0^{ \circ } }} (i,j)} \right)}^{2} + {\left( {{\text{GFIM}}_{{{\text{f}},\theta , - 90^{ \circ } }} (i,j)} \right)}^{2} } }. $$

(8)

Each point of the GEN_Image represents a measurement that is characterized as Gabor Energy [16].

Four (4) GEN_Images, corresponding to the filter orientations of θ = 0°, 45°, 90°, and 135°, were produced. From each GEN_Image, the following statistics were calculated as textural features and were used by the classification algorithms: mean value, variance, skewness, kurtosis, range and standard deviation.

Following multiple trials regarding the filter specifications, the best classification scores were achieved for textural features that were extracted from images that had been convolved with z × z Gabor filters, z = 5.

1.2 Generation of Gabor energy measure run length textural features

In the present study, new features are proposed based on the combination of GLRLM features and Gabor textural features.

These new features, labelled as Gabor Energy Measure Run Length (GEMRL) features, were extracted from each one of four Gabor Energy Images according to the following approach.

The Gabor Energy values of a Gabor Energy Image were transformed into the region 0–15 by means of a linear transformation providing a grey-level image of 16 discrete grey tones. Denoting this image as GEN_Image_θ_16 (where θ: 0, 45, 90 and 135° represents the orientation of the Gabor filter applied on the image), the new features were generated employing the Eqs. 9–13:

$$ {\text{GEMRL}}1 = \frac{1} {P}{\sum\limits_{j = 1}^R {\frac{{r_{d} (j)}} {{j^{2} }}} }. $$

(9)

$$ {\text{GEMRL}}2 = \frac{1} {P}{\sum\limits_{j = 1}^R {r_{d} (j)j^{2} } }. $$

(10)

$$ {\text{GEMRL}}3 = \frac{1} {P}{\sum\limits_{i = 0}^{G - 1} {[g_{d} (i)]^{2} } }. $$

(11)

$$ {\text{GEMRL}}4 = \frac{1} {P}{\sum\limits_{j = 1}^R {[r_{d} (j)]^{2} } }. $$

(12)

$$ \text{GEMRL} 5 = \frac{1} {{PN}}{\sum\limits_{j = 1}^R {r_{d} (j)} }, $$

(13)

where, j represents the length of the run for the grey tone i, G and R are the numbers of grey tones and run-lengths in the GEN_Image_θ_16, respectively, PN is the number of pixels in the GEN_Image_θ_16, while the r _d , g _d , P are defined in the Eqs. 14–16:

$$ r_{d} (j) = {\sum\limits_{i = 0}^{G - 1} {q_{d} (i,j)} }. $$

(14)

$$ g_{d} (i) = {\sum\limits_{j = 1}^R {q_{d} (i,j)} }. $$

(15)

$$ P = {\sum\limits_{i = 0}^{G - 1} {{\sum\limits_{j = 1}^R {q_{d} (i,j} }} }) = {\sum\limits_{i = 0}^{G - 1} {g_{d} } }(i) = {\sum\limits_{j = 1}^R {r_{d} } }(j), $$

(16)

where, q _d (i,j) represents each element of the GLRLM computed along the angular direction d (d: 0, 45, 90 and 135°).

From each GEN_Image_θ_16, four GLRLM were calculated for the angular directions d of 0, 45, 90 and 135°. For each one of the GEMRL features, described by Eqs. 9–13, four values were extracted (one value from each GLRLM), as proposed by Galloway [14]. The mean of these four values was used as the final feature value [14].