5. Comparison o f a broad set o f Texture Analysis A lgorithm s
5.3.1 Correlations and Reproducibility
Peak correlation coefficients between features and BM D are shown in Table 5-2 through Table
5-4. The spatial size(s) o f the features are also quoted (where appropriate). The correlations
between textural data and image greyscale statistics are shown in Table 5-6 through Table 5-8.
The reproducibility test results and partial correlations between TA data and BM D correcting
for greyscale m ean and SD are also included in Table 5-6 through Table 5-8. Tables are split by
textural paradigm (e.g. topological, N*-order, or matched-filter/spectral).
5.3.1.1 1** Order Statistics
The mean greylevel correlated significantly with BMD (r=0.4,/?<0.01). Other 1®‘ order image
characteristics did not correlate with BMD. None o f the 1®* order statistics were found to be
reproducible. Pre-processing the images with a high-pass filter and histogram-equalisation
resulted in images which had 1®‘ order characteristics that did not correlate with BMD.
5.3.1.2 Amplitude Varying Rate Matrix (AVRM)
Amplitude Vary Rate M atrix features “e”, “//” and “wwm” correlated with BM D (r=0.28, r=-
0.46 and r=-0.55, respectively). A non-linear correlation was found between “A” and BMD
(rs=-0.26,p<0.05). The “e”, “//” and “«wm” feature data were found to be reproducible. High-
pass filtering and histogram equalisation did not alter the correlation coefficients significantly.
Pre-processing the images with a low-pass median filter resulted in no correlations being found
between BM D and any features.
The “//” and “«wm” features were found to have a moderate correlation with both mean
and SD o f image greyscale. Correcting for the greylevel m ean and SD had the effect o f reducing
5.3.1.3 Auto correlation
A correlation was found for the Auto-correlation (AC) and Auto-correlation o f Sobel Edge
transform ed images (ACSE) across the femoral neck, but not along it. The details o f these
correlations for the ACSE are given in Chapter 4,
AC feature correlation drops slowly from r=0.3 at d=\ to r=0.26 at J=18 for Pearson’s
correlations but was only significant for d=\ in rank-order correlations. The correlation between
ACSE and BM D increased with displacement, levelling o ff after 30 pixels, but with two peaks
at 7 and 11 pixels (r=0.51 and r=0.60). High-pass filtering and histogram equalisation did not
increase the correlation with BMD (correlation coefficients were reduced). Pre-processing the
images with a low-pass median filter resulted in no correlations being found between BMD and
ACSE at 7 and 11 pixels across the femoral neck. The data for both the AC and two ACSE
peaks (7 and 11 pixels) were reproducible.
The AC correlated weakly with greylevel mean and strongly with greylevel SD.
However, correcting for the greylevel mean/SD did not reduce the correlation between AC and
BMD. Both ACSE peaks had a moderate correlation with both mean and SD o f image
greyscale. Correcting for the greylevel mean and SD had the effect o f reducing the correlation
coefficients but did not remove the relationships completely.
5.3.1.4 Coarseness
A correlation between the density o f maxima/minima across the femoral neck and BMD was
observed (r=0.26) and the data was reproducible. The correlation was poor and was not found in
any other direction or rank-ordered correlations. High-pass filtering and histogram equalisation
did not have a significant effect. Low-pass, median filtered images did not show any correlation
between extrema density and BMD. The maxima density o f the image corresponded to a
greyscale peak every 5.81mm, or 0.172 peaks per mm (Table 5-5).
The extrema density across the femoral neck correlated weakly with greyscale mean
and moderately with SD. Correcting for greylevel mean and SD reduced the correlation
coefficient below the significance threshold.
5.3.1.5 Co-occurrence Matrix
The results o f the Co-occurrence M atrix IDM feature correlated with BMD (r=-0.69) as
described in Chapter 4. Other features (Energy, Entropy, Correlation and Contrast) also
correlated with BMD but to a lesser extent and peak correlations were not found across the
femoral neck but along it or at 45/135 degrees. The IDM feature was reproducible but did
correlate weakly or moderately with both greyscale mean and SD. Correcting for greylevel
m ean and SD had the effect o f reducing the correlation coefficients between the features and
BM D but the coefficients were still statistically significant.
Pre-processing the images with a low-pass median filter resulted in no correlations
being found between BMD and any CM feature across the femoral neck.
5.3.1.6 Edge Co-occurrences
Significant correlations between the Edge Co-occurrence and BM D were found across the
femoral neck with a peak correlation coefficient at 7 pixels (r=-0.36). The data for the peak
correlation coefficient at 7 pixels was reproducible. A correlation was also found along the
femoral neck for 1 pixel but was not reproducible. High-pass filtering and histogram
equalisation reduced the correlation coefficients while m edian filtering resulted in no significant
correlations being found.
The Edge Co-occurrence at 7 pixels had a strong negative correlation with greyscale SD
(r=-0.71). Correcting for this relationship reduced the correlation with BM D but the correlation
was still statistically significant. The entropy o f the Edge Co-occurrence function did not
correlate with BMD.
5.3.1.7 Fractal Signature
The results o f the analysis o f correlations can be found in Chapter 4 (r=0.35). Directional fractal
signatures were not found to show significant correlations with BMD for either the horizontal or
vertical axis.
The data was found to be reproducible. The fractal signature correlated moderately with
but the correlation was still statistically significant. The application o f low-pass median filters
and histogram equalisation did not affect the fractal dimension.
5.3.1.8 Fourier Spectral Statistics
A correlation between the second Principal Component Analysis factor o f the 2-dimensional
FFT spectrum and BM D was found (r=0,39). No other features o f the 1- or 2-dimensional
spectra were found to correlate with BMD.
Reproducibility analysis was not undertaken because the correlation was not sufficiently
strong but the second PCA factor did correlate moderately with mean greyscale. The mean
spectral power o f the ID function and the first PCA factor o f the 2D spectrum correlated weakly
with greylevel SD, while the second PCA factor correlated moderately with greylevel mean.
Correcting for these factors reduced the correlations with BM D below the significance
threshold.
The application o f high-pass filters, low-pass median filters and histogram equalisation
resulted in no significant correlations being found.
5.3.1.9 Geraets et al Features
Significant correlations were found between BMD and the Area (r=-0.36), Circ (r=-0.36). M esh
(r=-0.39). Nodes (r=-0.25) and Ends (r=0.34) features. A filter o f size 8 square was found to
produce the highest correlations between BMD and topological features.
Area, Circ and M esh features were reproducible but m oderate-strongly correlated with
both greyscale mean and SD. After correcting for mean and SD the correlation between the
features and BMD were reduced but remained significant.
Pre-processing the images with a low-pass median filter resulted in no correlations
being found between BMD and any o f Geraets features.
5.3.1.10 Laws Energy Masks
Thirteen 2-dimensional matched-filters were found to correlate with BM D (Table 5-4) with
widths o f 3 to 7 pixels. High-pass filtering and histogram equalising images prior to the
application o f the convolution masks did not show any significant correlations between Laws
texture energy and BMD. Similarly, pre-processing the images with a low-pass median filter
resulted in no correlations being found between BM D and any o f the texture masks.
Reproducibility analysis was not undertaken because the correlations were not
sufficiently strong (|r|<0.5). All filters correlated moderately or m oderately-strongly with
greyscale mean. Ten filters also correlated with greyscale SD. Correcting for these factors
marginally reduced the correlation between the matched-filter energy and BM D for some filters
but m arginally increased the correlation for others. Only one filter’s correlation was reduced
below the significance level (L7S7).
5.3.1.11 Neighbourhood Grey-Tone Difference Matrix (NGTDM)
The NGTDM algorithm using a filter with fc = 2 m m and a neighbourhood o f 3 pixels (7
pixels/0.94mm wide) was found to be optimal. The feature fcon^ had the highest correlation with
BMD (r=0.51), while fstr had a low non-linear correlation with BM D (r^=-0.28).
All o f the features were found to be reproducible. The fcon feature correlated strongly
with mean greylevel (r=0.84) but not SD. The fcos, fcom and fstr features correlated weakly and/or
moderately with greylevel mean and SD. Correcting for mean and SD greylevel, reduced the
correlation between fon and BMD, but the correlation rem ained significant.
Applying histogram equalisation did not significantly affect the correlation coefficients
between BMD and the NGTDM features (i.e. did not affect correlations more than the
significant figure). Pre-processing the images with a low-pass m edian filter resulted in no
correlations being found between BM D and NGTDM features.
5.3.1.12 Texture Spectrum.
Black-W hite Symmetry (BWS) and Degree o f Direction (DD) features o f the Texture Spectrum
were found to correlate with BMD (r=-0.33 & r=0.52). High-pass filtering and histogram
equalisation did not affect the correlation coefficients. BWS and DD features o f median-filtered
B W S and D D features w ere reproducible. B W S co rrelated w eak ly w ith m ean greylevel. C o rrectin g for the greylevel m ean and SD red u ced the co rrelatio n co efficien ts b u t the
relatio n sh ip rem ain ed significant.
Correlation analysis with femoral neck BMD
Texture Analysis Feature Maximum Correlation Spatial Size in pixels Method Pearson’s (Spearman’s) (mm) D* Order moment (Mean) 0.40" (0.30') -
Greyscale 2"‘* moment (SD) N S (7V5;) -
Moments 3^'^ moment (Skew) N S -
4* moment (Kurtosis) (7V6;) - Amplitude e 0.28' - Varying 11 -0 .4 6 "' (-0.41 ) - Rate Matrix Is N S (-0.26') - num -0 .5 5 '" (-0 .5 0 '") - crl N S - cr2 N S -
Auto-correlation f ' Peak across NOF 0 .5 1 '" (0 .5 6 '" ) 7 (0.94mm) o f Sobel Edges 2""^ Peak across NOF 0 .6 0 '" (0 .6 5 '") 11 (1.47mm)
Along NOF N S -
Auto-correlation Highest r across NOF 0.31* (0.27') 1 (0.13mm) Co-occurrence Contrast along NOF -0.29' (-0.34") 2 (0.25mm) Matrix Correlation along NOF 0.31" (0.36") 2 (0.25mm) Energy 45° to NOF -0 .5 0 '" (-0 .6 0 '") 10 (1.85mm) Entropy 45° to NOF -0 .5 3 '" (-0 .6 5 '") 10 (1.85mm) IDM across NOF -0 .6 9 '" (-.6 9 '" ) 7 (0.94mm Edge Densities Peak along NOF -0.28' (-0.26') 1 (0.13mm)
Peak across NOF -0.36" (-0.32") 7 (0.13mm) Neighbourhood fcos N S - Grey-Tone fcon 0 .5 1 '" (0 .6 6 '" ) 7 (0.91mm) Difference fbus N S - Matrix fcom N S - fs.r (-0.28') 7 (0.91mm) Texture BWS -0 .4 4 '" (-0.40") 3 (0.39mm) Spectrum GS N S (W5:) 3 (0.39mm) DD 0 .5 2 '" (0 .5 5 '" ) 3 (0.39mm)
T able 5-2: C orrelations between BMD and 2"*^- and H ig h er-O rd er tex tu re analysis algorithm s on 62 radiographs of the fem oral neck selectively sam pled from low and high fra c tu re risk groups. *p<0.05, **p<0.0\, ***/?<0.001, N S = Non-Significant. NO F = Neck of
Fem ur.
Texture Analysis Method
Correlation analysis with femoral neck BMD
Feature Maximum Correlation Pearson’s (Spearman’s)
Spatial Size in pixels (mm) Coarseness - Extrema Density (Maxima « Minima)_______ Overall Across NOF Along NOF
Filtered (All directions)
0.26' NS Geraets et al Features Area Circ Mesh Nets Axis Nodes Ends -0.36 -0.36* -0.39* NS NS -0.25* 0.34** (-0.32 ) (-0.30*) (-0.33 (-0.36* (-0.36* (-0.44**
T able 5-3: C orrelations between BMD and Topological texture analysis algorithm s on 62 rad io g rap h s of the fem oral neck selectively sam pled from low and high fra c tu re risk groups. *p<0.05, **/><0.01, ***/;<0.001, N S = Non-Significant. N O F = Neck of Fem ur.
(Spatial size data not applicable to m any topological features).
Texture Analysis Method
Correlation analysis with femoral neck BMD Feature Maximum Correlation
Pearson’s (Spearman’s)
Spatial Size in pixels (mm) Fourier ID mean power NS (A^; -
Spectrum 2D (PCA Factor 1) NS rA5[) -
2D (PCA Factor 2) 0.39*** (0.34**) -
All other 2D features NS rA^) -
Fractal Circular StElt 0.35** (0.34**) 16-18, 19-21 (2.1-2.4, 2.5-2.7mm) Signature Horizontal StElt (A^) -
Vertical StElt A:^ (A5) -
Laws Texture S3S3 -0.31* (-0.29*) 3 (0.39mm) Energy Masks S3E3 -0.28* (-0.26*) 3 (0.39mm) E5L5 0.38** (0.37**) 5 (0.65mm) L5E5 0.34** (0.34**) 5 (0.65mm) R5E5 -0.33** (-0.30*) 5 (0.65mm) R5L5 -0.32* (-0.29*) 5 (0.65mm) S5R5 -0.31* (-0.29*) 5 (0.65mm) R5S5 -0.35** (-0.33**) 5 (0.65mm) R5R5 -0.35** (-0.33**) 5 (0.65mm) E7L7 0.45*** (0.50***) 7 (0.91mm) L7S7 0.39** (0.35**) 7 (0.91mm) R7S7 -0.24* (-0.24*) 7 (0.91mm) R7R7 -0.27* (-0.26*) 7 (0.91mm) All other filters NS -
T able 5-4: C orrelations between BMD and Spectral and M atched-F ilter texture analysis algorithm s on 62 radiographs of the fem oral neck selectively sam pled from low and high fra c tu re risk groups. */?<0.05, **/><0.01, ***/?<0.001, N S = N on-Significant. NOF = Neck of
Fem ur.
Min Max Mean SD M ean Spatial Density per mm (min - max)
Maxima per 200 pixels 15.32 18.08 16.866 0.5682 0.172 (0.160-0.189)
Table 5-5: Statistics of the m axima density across the fem oral neck in a 200 by 200 pixel region.
Results o f Analysis
Texture Analysis Feature Pearson’s Correlation with Mean Pearson’s Correlation with SD of Partial Correlation with Reproducible on repeated Method o f Greyscale (Spearman’s) Greyscale (Spearman’s) BMD corrected for greyscale
mean & SD
analysis o f the same film? T' Order C' moment (Mean) - - N S - A
Greyscale 2"‘‘ moment (SD) N S (A5) - - A
Moments 3'^'* moment (Skew) N S (A5) N S (A^ - A
4'*’ moment (Kurtosis) N S (AS) - A
Amplitude e (A5) -0.29* ____________________ AS A
Varying 11 -0.37** (-0.38 ) .036" (-0.35 ) -0.34** A Rate Matrix Is N S (Aj^ N S (0.29*) AS A
num -0.47*** (-0.46***) 0.39** (0.38**) -0.49*** A crl N S fA57 N S (A5) AS y
cr2 N S (A57 N S AS y ...
Auto-correlation Highest r across NOF 0.33" (0.26*) -0.75’" (-0.75***) 0.31* y
Auto-correlation D* Peak across NOF 0 .38" (0.39**) -0.35" (-0.35**) 0.44*** y
o f Sobel Edges 2"‘* Peak across NOF 0.46*** (0.44***) -0.35** (-0.35**) 0.55*** y Co-occurrence Contrast along NOF -0.30* (-0.29*) 0.25* (0.26*) -0.28* y Matrix Correlation along NOF 0.32* (0.30**) -0.25* (-0.25*) 0.29* y
Energy 45° to NOF -0.39** (-0.40**) A^ (A^ -0.48*** y Entropy 45° to NOF -0.38** (-0.35**) A^ (A^ -0.54*** y IDM across NOF -0.43*** (-0.40**) 0.39** (0.37**) -0 .5 9 " ' y ... Edge Peak along NOF 0.46*" (0.53***) 0.55*** (0.56***) 0.29* A Co-occurrence Peak across NOF A:^ (A^ -0.71*" (-0.70***) 0.36** y Neighbourhood fcos -0.44*** (-0.38") 0.46*** (0.39**) AS y
Grey-Tone fcon 0.84*** (0.81***) N S (A^ 0.38** y Difference Matrix fbus A^ (A^ N S (A^ AS y
fcom 0.31* (0.45 **) 0.58*** (0 .6 7 ;-) -0.26* y fstr A^ (A^ 0.35** (0.53 ) -0.30* y
Texture BWS -0.34" (-0.36") A^ -0.36" y Spectrum GS 0.29* (A^ -0.30* (-0.27***) AS A DD A.^ (ASl N S (AS) 0.42** y
Table 5-6: C orrelation between greylevel histogram statistics and 2"** and H igher-order algorithm s and reproducibility. N=62. */?<0.05, **/;<0.01, ***p<0.001, N S = Non-Significant. NOF = Neck of Fem ur.
Results o f Analysis
Texture Analysis Feature Pearson’s Correlation with Mean Pearson’s Correlation with SD of Partial Correlation with Reproducible on repeated Method o f Greyscale (Spearman’s) Greyscale (Spearman’s) BMD corrected for greyscale
mean & SD
analysis o f the same film? Extrema Density Across NOF 0 .3 5 " (0.38") 0.52*'* (0 .5 0 '" ) NS
Geraets et al Area -0 .6 9 "' (-0 .7 0 "') -0.67*** (-0 .6 8 '") -0.25* y Features Circ -0.62*" (-0.61***) -0.66*** (-0.69***) -0.26* Mesh -0.67*" (-0.67***) -0.66*** (-0.68*") -0.31* y Axis NS (-0.29*) (-0.56***) -0.25* A Nodes NS (0.34**) (0.49***) 0.31* A Ends A.5 (-0.30*) NS (-0.55***) -0.25* A
Table 5-7: C orrelation between greylevel histogram statistics and topological algorithm s and reproducibility. N=62. */;<0.05, Non-Significant. NOF = Neck of Fem ur.
Results o f Analysis
Texture Analysis Feature Pearson’s Correlation with Mean Pearson’s Correlation with SD of Partial Correlation with Reproducible on repeated Method o f Greyscale (Spearman’s) Greyscale (Spearman’s) BMD corrected for
greyscale mean & SD
analysis o f the same film? Fourier 1D mean power 0.35'* (0.48***) NS -
Spectrum 2D (PCA Factor 1) 2D (PCA Factor 2) NS “5.42*** ( A ^ (0.49***) 0.40*" (0.28**) A ^ ( A 5 ) A ^ A ^ ; All other 2D features - - - A ^ -
fractal signature Circular StElt NS 0 .4 1 " (0.41") -0.33" y Laws Texture S3S3 I -0 .4 6 '" ! (-0.48'") -0.68*" (-0.65***) -0.33" -
Energy Masks S3E3 -0.45*** 1 -0.70*" (-0.67***) i -0.29* 1 E5L5 1 0 .4 2 " ' 1 (0.40' ) A ^ ( A ^ 0.25* L5E5 0.42"* I (0.50') 0.44*** (0.45 * * ) : 0.29* - R5E5 1 -0.54*** 1 (-0.56* *) !1 -0 .6 8 '" (-0.65**') -0.34" - R5L5 -0.55*** i (-0.56***) -0.69*** (-0.68***) -0.31* - S5R5 i -0.42*** (-0.46***) -0.67*** (-0.65***) -0.34" - R5S5 -0.56**' (-0 .5 8 '") -0.66’** (-0.64"*) -0.35" - R5R5
r
-0.56***I
1 (-0.56***) -0.66*** (-0.63***) -0.35** E7L7 0.52**' (0.56') : A ^ I ( A ^ 0.34" L7S7i
0.47*** (0.54") i A ^ ! ( A ^1
A ^ - R7S7 -0.40" (-0 .4 4 '") -0 .7 1 '" (-0 .6 6 "’) ! -0.26* - R7R7 -0.41" 1 (-0.45 ' ) -0.70*** (-0.66***) -0.29* -All other filters -
1
A ^ -Table 5-8: C orrelation between greylevel histogram statistics and Spectral and M atched-Filter algorithm s and reproducibility. R eproducibility analysis not undertaken because correlation w ith BMD insufficient to m eet m inim um level (r>0.5). N=62. */;<0.05, **p<0.01, ***/?<0.001, N S = Non-Significant. NOF =
Neck of Fem ur.
5.4 Discussion
In this chapter, 12 different algorithms were tested as methods o f analysing trabecular patterns
changes caused by osteoporosis. Bone mineral density estimates were used as a surrogate for
osteoporosis since bone mass and cancellous architecture are lost simultaneously in osteoporosis
- which it is hypothesized cause distinct changes in the trabecular pattern. Each o f the
algorithms applied here has, in general, more than one “feature” which may describe texture and
each algorithm has pre-processing and/or analysis parameters to be set. The highest significant
correlation between the TA features and BMD are quoted here. The reproducibility and validity
o f textural features was also considered.
W ith the large search space o f algorithms, features and parameters, it has been
necessary to concentrate on those features that provide the m ost powerful method o f describing
osteoporotic trabecular changes. The first stage o f isolating these features is to select only
algorithms which relate significantly to the disease process as measured (indirectly) by BMD.
Those algorithms for which a peak correlation can be established above an arbitrary correlation
threshold o f (i.e. |r|>0.5) were then submitted to reproducibility tests. The tests used in this
chapter do not determine reproducibility absolutely, but they do established whether or not an
algorithm is reproducible in the sense o f the same radiograph digitized at different times gives
the same results.
From these tests I isolated 8 features which were both reproducible and have a
sufficiently high correlation with femoral neck BMD. Face Validity support for the textural
features was then considered. The ACSE(90:7), ACSE(90.T 1) IDM(90:7), fconO) features were
all found to correlated with BMD at angles and displacements associated with trabecular line
like features, which can be regarded as sufficient face validity support. M oreover, the nature o f
the correlations suggests changes in the trabecular pattern that are consistent with the visual
changes, i.e. an osteoporotic loss o f trabecular textural strength and textural contrast. The local
loss o f trabecular line-like structures results in an image with has less directionality on a local
level.
The fractal signature however, it can be argued, is too large to be a descriptor o f
trabecular texture. The fractal signature size range puts it into the range o f loss trabecular group
areas and a textural descriptor o f trabecular group losses could provide additional textural
information about the osteoporosis progression not seen in the other algorithms.
Some textural features were excluded from subsequent analysis by considering other
factors o f the texture analysis including the image greylevel statistics. It is clear from the data
that there is a statistical link between the image greylevel statistics (mean and standard
deviation) and most textural features. However, accounting for this in a partial correlation
framework does not, in general, “explain” the link between the trabecular texture and BMD.
One can thus conclude that the texture is more than a simple brightness or contrast related
phenomenon, and that the link is likely to be an indirect statistical link (i.e. not causal). It should
be noted that the strong correlations between the NGTDM fcon feature and greylevel mean is
suspicious but does not account for the link between fcon and BMD.
Some textural features were excluded from further analysis on the basis o f Face
V alidity which requires that the textural properties described m ust be physically meaningful.
This is true o f the Co-occurrence M atrix features Contrast, Correlation, Energy and Entropy