Extraction of a bias field invariant biomarker from an image

Abstract

The present invention provides a method of computer analysis of a data set representing an image to extract a texture based measure therefrom, said image including a multiplicative bias in intensity within the image of unknown magnitude, the method comprising applying to said data set a bank of texture extracting filters, such that said filters are chosen from filters that are invariant to the presence of a multiplicative bias field. By providing such a method, rather than attempting to correct the bias field before extraction of a texture based-biomarker, a texture-based biomarker that is bias field invariant is extracted. This makes correction of the bias field unnecessary.

Claims

1. A method of analysis of a data set representing an image, said image has a multiplicative bias field in intensity, the method comprising: using a processor, extracting a texture based measure from the image by applying to said data set a texture extracting filter that is invariant to the presence of a multiplicative bias field; wherein the image is a medical image and said texture based measure is a biomarker.

2. The method as claimed in claim 1, wherein the texture extracting filter is one of three eigenvalues of a Hessian matrix defined by:
λ.sub.i(x;σ), i=1,2,3, |λ.sub.1|≥|λ.sub.2|≥|λ.sub.3| where x=[x, y, z].sup.T is a voxel and the Hessian matrix is defined as $H\left(x;\sigma \right)=\left[\begin{array}{ccc}{I}_{\mathrm{xx},\sigma }& I_{\mathrm{xy},\sigma }& I_{\mathrm{xz},\sigma }\\ I_{\mathrm{xy},\sigma }& I_{\mathrm{yy},\sigma }& I_{\mathrm{yz},\sigma }\\ I_{\mathrm{xz},\sigma }& I_{\mathrm{yz},\sigma }& I_{\mathrm{zz},\sigma }\end{array}\right].$

3. The method as claimed in claim 2, wherein extracting the texture based measure is by further applying the other two eigenvalues of the Hessian matrix as texture extracting filters.

4. The method as claimed in claim 1, wherein the texture extracting filter is a gradient magnitude defined by: ${.Math.\nabla G\left(x;\sigma \right).Math.}_2=\sqrt{I_{x,\sigma }^2+I_{y,\sigma }^2+I_{z,\sigma }^2}.$

5. The method as claimed in claim 1, wherein the texture extracting filter is a Laplacian of a Gaussian defined by:
∇.sup.2G(x;σ)=λ.sub.1(x;σ)+λ.sub.2(x;σ)+λ.sub.3(x;σ).

6. The method as claimed in claim 1, wherein the texture extracting filter is a Gaussian curvature defined by:
K(x;σ)=λ.sub.1(x;σ)λ.sub.2(x;σ)λ.sub.3(x;σ).

7. The method as claimed in claim 1, wherein the texture extracting filter is a Frobenius norm of a Hessian matrix defined by:
∥H(x;σ)∥.sub.F=√{square root over (λ.sub.1(x;σ).sup.2+λ.sub.2(x;σ).sup.2+λ.sub.3(x;σ).sup.2)}.

8. The method as claimed in claim 1, wherein the texture extracting filter is applied at multiple scales a.

9. The method as claimed in claim 8, wherein said scales a lie in a range from 0.3 to 25 mm.

10. The method as claimed in claim 8, wherein said scales a lie in a range from 0.3 to 2.5 mm.

11. The method as claimed in claim 8, wherein said scales a lie in a range from 0.3 to 25 μm.

12. The method as claimed in claim 1, wherein extracting the texture based measure is by applying multiple texture extracting filters at N scales, where N is computed using: $N=\frac{1}{p}{\log }_2\left(\frac{{\sigma }_{\mathrm{high}}}{{\sigma }_{\mathrm{low}}}\right)+1.$

13. The method as claimed in claim 1, wherein extracting the texture based measure is by applying from 3 to 8 texture extracting filters at 1 to 25 scales.

14. The method as claimed in claim 1, wherein extracting the texture based measure is by applying multiple texture extracting filters and concatenating histograms of filter responses of the multiple texture extracting filters.

15. The method as claimed in claim 14, wherein the histograms of filter responses are estimated using fixed binning, adaptive binning, or soft assignments as in locally orderless images.

16. The method as claimed in claim 1, further comprising labeling said image as being included in a class of images by applying a statistical classifier to said texture based measure.

17. The method of claimed in claim 1, wherein the image is an MRI image.

18. The method as claimed in claim 17, wherein the MRI image is of a brain or part thereof.

19. The method as claimed in claim 18, wherein the image derives from a person with mild cognitive impairment (MCI).

20. The method as claimed in claim 19, further comprising labeling said image according to a likelihood of the person progressing from MCI to increased severity of dementia, by applying a statistical classifier to said biomarker.

21. The method as claimed in claim 20, wherein said increased severity of dementia is Alzheimer's disease.

22. A computer program product comprising a non-transitory computer readable medium having instructions recorded thereon, the instructions when executed by a computer system implementing the method of claim 1.

23. The method as claimed in claim 1, wherein the biomarker comprises a multi-dimensional representation that characterizes texture of the image.

Description

(1) The invention will be further described and illustrated by the following example making reference to the appended drawing in which:—

(2) FIG. 1 shows scatter plots of test set texture scores in original MRIs versus bias corrected MRIs. Panel (A) Texture scores obtained using GFBZERO. Panel (B) Texture scores obtained using GFB. The full line is the identity line.

EXAMPLE 1

(3) In this example, a proposed descriptor of the invention is compared to an alternative bias field variant version where the Gaussian function is kept in the descriptor and MRI images are not log transformed.

(4) We used the baseline T1-weighted “complete annual year 2 visits” 1.5-T MRI dataset 2.5 from the collection of standardized datasets released by the Alzheimer's Disease Neuroimaging Initiative (ADNI) [11]. The dataset definition was downloaded from the ADNI website (http://adni.loni.usc.edu/methods/mri-analysis/adni-standardized-data/) on Sep. 28, 2012. The dataset comprises 504 persons, 169 normal controls (NC), 234 subjects with MCI, and 101 AD patients.

(5) Two datasets were defined, a training set comprising all NCs and ADs, and a test set comprising all MCIs. The MCIs in the test set were labeled according their two year follow-up diagnosis; stable (had a NC or MCI diagnosis at follow-up) or converter (had an AD diagnosis at follow-up). The training set was used for method training, and the test set was used to evaluate the consistency of the methods.

(6) We consider the hippocampus as ROI in the following experiments because it is affected early in the AD disease process and because it is generally severely affected [12, 13]. The left and right hippocampus were segmented using cross-sectional FreeSurfer [14], and the hippocampi were jointly used as ROI. Prior to computing the texture descriptor, the segmentation was post-processed using morphological erosion with a spherical structuring element of radius 1 mm in order to remove noise from the segmentation boundary and ensure that texture was computed in the interior of the hippocampus.

(7) The number of histogram bins was determined as

(8) $N_b=.Math.\sqrt[3]{731}.Math.=9$
in the experiments. The smallest morphologically cleaned bilateral hippocampal segmentation in the training set, which contained 731 voxels, determined this number in order to ensure an adequate number of voxels for histogram estimation.

(9) We compare two methods that are both based on an SVM for classification. The second method is in accordance with the invention. In each case, the SVM is trained using the training set as described above. The two methods deviate in how the image data is represented and are as follows: Gaussian derivative-based Filter Bank with Zero-order information (GFBZERO): Image data represented using the hippocampal texture descriptor described above augmented with the Gaussian function by convolving the image with the Gaussian at the same four scales as considered earlier and appending the corresponding filter response histograms to the existing representation;

(10) $\left[h_{{\lambda }_1\left(x;0.6\right)},\mathrm{.Math.},h_{{.Math.H\left(x;0.6\right).Math.}_F},\mathrm{.Math.},h_{{.Math.H\left(x;1.7\right).Math.}_F}\right].Math..Math.\left[h_{G\left(x;0.6\right)},\mathrm{.Math.},h_{G\left(x;1.7\right)}\right].$ The Gaussian function is also one of the filters used in References 3 and 4.

(11) Prior to SVM training, the MRI images in the training set are bias field corrected using the nonparametric non-uniform intensity normalization (N3) method [2]. Gaussian derivative-based Filter Bank (GFB): log transformed image data represented using the descriptor of described in the section above. The image data is log transformed to achieve multiplicative bias field invariance as described in the section above. Note that the training data is N3 corrected and log transformed, by using log(1+I), prior to entering the SVM training. One is added to the image to avoid taking the logarithm of zero.

(12) The two methods are applied to score two versions of the test set, the original MRIs and the N3 bias field corrected MRIs. In GFB, log(1+I) is further applied.

(13) The consistency between texture-scores obtained on original- and N3 corrected MRIs, respectively was visually inspected by scatter plotting (see FIG. 1 panels A and B). The associated Pearson correlation coefficients were as follows (original MRIs vs. N3 corrected MRIs): Panel A (comparative) GFBZERO 0.86 and Panel B GFB 0.97. Both correlations were significant.

(14) The prognostic stability as a function of using either original MRIs or N3 corrected MRIs of the two methods was further evaluated using ROC-analysis (see Table 1).

(15) TABLE-US-00001 TABLE 1 Diagnostic AUCs. Original MRIs Bias corrected MRIs GFBZERO 0.667 0.693 GBF 0.719 0.726

(16) It can be seen that a superior result is obtained according to the invention (GBF) both on original MRIs and on Bias corrected MRIs and the result achieved according to the invention is better without bias correction than is achieved according to the comparator with bias correction. Thus it is shown that using a bank of texture extracting filters, such that said filters are invariant to the presence of a multiplicative bias field gives a better result than correcting for the bias and using a set of filters that are not bias field invariant.

(17) Another beneficial effect demonstrated by this evaluation is the “stability of prognostic performance”. That is, the difference between AUCs when a method is applied to original MRIs and Bias corrected MRIs, respectively.

(18) For GFB, the gap in AUC is small, i.e. it does not matter whether we bias correct or not. For the GFBZERO, the difference in AUC is substantially greater according to whether bias correction is applied or not. Thus, the method of the invention will be more robust against uncertainties as to whether a bias correction has been effectively applied.

(19) In this specification, unless expressly otherwise indicated, the word ‘or’ is used in the sense of an operator that returns a true value when either or both of the stated conditions is met, as opposed to the operator ‘exclusive or’ which requires that only one of the conditions is met. The word ‘comprising’ is used in the sense of ‘including’ rather than in to mean ‘consisting of’. All prior teachings acknowledged above are hereby incorporated by reference. No acknowledgement of any prior published document herein should be taken to be an admission or representation that the teaching thereof was common general knowledge in Australia or elsewhere at the date hereof.

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