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Detection of Breast Abnormality from Thermograms Using Curvelet Transform Based Feature Extraction

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Abstract

Breast cancer is one of the leading causes for high mortality rates among young women, in the developing countries. Currently mammography is used as the gold standard for screening breast cancer. Due to its inherent disadvantages, alternative techniques are being considered for this purpose. Breast thermography is one such imaging modality, which represents the temperature variations of breast in the form of intensity variations on an image. In the last decade, several studies have been made to evaluate the potential of breast thermograms in detecting abnormal breast conditions, from an image processing view point. This paper proposes a curvelet transform based feature extraction method for automatic detection of abnormality in breast thermograms. Statistical and texture features are extracted from thermograms in the curvelet domain, to feed a support vector machine for automatic classification. The classifier detects abnormal thermograms with an accuracy of 90.91 %. The results of the study indicate that texture features have better potential to detect abnormality in breast thermograms, when extracted in the multiresolution curvelet domain.

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Declaration of Interest

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Authors and Affiliations

  1. Anna University, Chennai, India

    Sheeja V. Francis, M. Sasikala & S. Saranya

Authors
  1. Sheeja V. Francis
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  2. M. Sasikala
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  3. S. Saranya
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Corresponding author

Correspondence to Sheeja V. Francis.

Appendix I

Appendix I

Haralick’s Texture Features

{p(i, j)} is the Normalized GLCM.

N is the number of gray levels in {p(i, j)}.

$$ \mathrm{Angular}\kern0.5em \mathrm{second}\kern0.5em \mathrm{moment}\kern0.5em \left(\mathrm{Energy}\right):{f}_1={\displaystyle {\sum}_{i=1}^N}{\displaystyle {\sum}_{j=1}^N}{\left\{p\left(i,j\right)\right\}}^2 $$
$$ \mathrm{Contrast}:{f}_2={\displaystyle {\sum}_{i=1}^{N-1}}{n}^2\left\{{\displaystyle {\sum}_{i=1}^N}{\displaystyle {\sum}_{j=1}^N}\left\{p\left(i,j\right)\right\}\right\} $$
$$ \mathrm{Correlation}:{f}_3=\frac{{\displaystyle {\sum}_i}{\displaystyle {\sum}_j}(ij)p\left(i,j\right)-{\mu}_x{\mu}_y}{\sigma_x{\sigma}_y} $$
$$ \mathrm{Sum}\kern0.5em \mathrm{of}\kern0.5em \mathrm{squares}-\mathrm{variance}:{f}_4={\displaystyle \sum_i}{\displaystyle \sum_j}{\left(i-\mu \right)}^2p\left(i,j\right) $$
$$ \mathrm{Inverse}\kern0.5em \mathrm{Difference}\kern0.5em \mathrm{Moment}:{f}_5={\displaystyle \sum_i}{\displaystyle \sum_j}\frac{1}{1+{\left(i-j\right)}^2}p\left(i,j\right) $$
$$ \mathrm{Sum}\kern0.5em \mathrm{Variance}:{f}_7={\displaystyle {\sum}_{i=2}^{2N}}{\left(i-{f}_s\right)}^2{p}_{\left(x+y\right)}(i) $$
$$ \mathrm{Sum}\kern0.5em \mathrm{Entropy}:{f}_8=-{\displaystyle {\sum}_{i=2}^{2N}{p}_{\left(x+y\right)}(i) \log \left\{{p}_{\left(x+y\right)}(i)\right\}} $$
$$ \mathrm{Entropy}:{f}_9=-{\displaystyle {\sum}_i}{\displaystyle {\sum}_j}p\left(i,j\right) \log \left\{p\left(i,j\right)\right\} $$
$$ \mathrm{Difference}\kern0.5em \mathrm{variance}:{f}_{10}= variance\kern0.5em of\kern0.5em {p}_{\left(x-y\right)} $$
$$ \mathrm{Difference}\kern0.5em \mathrm{Entropy}:{f}_{11}=-{\displaystyle \sum_{i=0}^{N-1}{p}_{\left(x-y\right)}(i) \log \left\{{p}_{\left(x-y\right)}(i)\right\}} $$
$$ \mathrm{Information}\kern0.5em \mathrm{measure}\kern0.5em \mathrm{of}\kern0.5em \mathrm{correlation}\kern0.5em 1:{f}_{12}=\frac{ HXY- HXY1}{ \max \left( HX, HY\right)} $$
$$ \mathrm{Information}\kern0.5em \mathrm{measure}\kern0.5em \mathrm{of}\kern0.5em \mathrm{correlation}\kern0.5em 2:{f}_{13}={\left(1- \exp \left[-0.2\left( HXY2- HXY\right)\right]\right)}^{1/2} $$
$$ \mathrm{Where}\kern0.5em \mathrm{HXY}\kern0.5em =-{\displaystyle {\sum}_i}{\displaystyle {\sum}_j}p\left(i,j\right) \log \left\{p\left(i,j\right)\right\} $$

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Francis, S.V., Sasikala, M. & Saranya, S. Detection of Breast Abnormality from Thermograms Using Curvelet Transform Based Feature Extraction. J Med Syst 38, 23 (2014). https://doi.org/10.1007/s10916-014-0023-3

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