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Edge detection of intestinal parasites in stool microscopic images using multi-scale wavelet transform

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Abstract

Biomedical image processing is experiencing a significant progress with many applications. However, automatic recognition of microscopic pathogens from their images remains a challenge that will allow clinical laboratories to increase both the speed of tests and the reliability of diagnoses. We present an algorithm for edge detection of parasites in microscopic images of stools, using the multi-scale wavelet transform. This method is an evolution of the Canny–Mallat detector which gives the possibility to vary the frequency of the analysis in order to find the outlines of the most significant edges. The various contours obtained are chained across the scales from the coarsest to the finest. Using this algorithm, we were able to correctly represent the contours of the features of parasites found in microscopic images. The results obtained were compared with those produced by classical edge detectors on the same images. It comes out from both subjective and objective quantitative performances evaluation that our detector, better than all others, can clearly mark the outlines of the structures of the pathogen on an image of stools.

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Abbreviations

\(\psi (x)\) :

The wavelet function

\(a, b\) :

The scale factor or expansion factor and the shifting factor

\(\psi _{a,b} (x)\) :

The family of wavelets associated with the mother wavelet \(\psi \)

\(W_a f(b)\) :

The wavelet transform of the function \(f(x)\)

\(L^{2}(\mathbb {R}^{2})\) :

The set of square integrable function defined on \(\mathbb {R}^{2}\)

\((x, y)\) :

The pixel image coordinates

\(f(x,y)\) :

The input image function

\(I\times J\) :

The dimension of the input image function \(f\)

\(D^{1}f(2^{j},b_x,b_y)\), \(D^{2}f(2^{j},b_x,b_y)\) :

The discrete wavelet transform components

\(M_{2^{j}} f(x,y)\) :

The module of the wavelet transform

\(A_{2^{j}} f(x,y)\) :

The angle between the wavelet transform vector and the horizontal axis of the image plane \((x, y)\)

\(G(x,y)\) :

The Gaussian function

\(\beta ^{n}(x)\) :

The B-spline function of degree \(n\)

\(\theta \) :

The low-pass filter representing a smoothing matrix

\(D_x, D_y \) :

The high-pass discrete filters for the derivation

ROC:

The receiver operating characteristic

AUC:

The area under the ROC curve

TP, TN :

The numbers of true positive and true negative

FP, FN:

The numbers of false positive and false negative

TPR :

The true positive rate

FPR:

The false positive rate

\(F\) :

The \(F\)-measure or harmonic mean of precision and recall

TL, TH:

The low and high thresholds

\(\varepsilon \) :

The oscillations threshold

EGT:

The estimated ground truth

PS:

The best parameter set for an estimated ground truth

PSROC:

The parameter set ROC curve

\({N}_{\text {th}}\) :

The number of detection threshold

\(N_{\text {sc}}\) :

The number of analyzing scale

CT:

The correspondence threshold

PGTi :

The potential ground truth for the i correspondence threshold

CTROC :

The correspondence threshold ROC

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Acknowledgments

The authors greatly thank the anonymous reviewers for their very constructive remarks.

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Authors and Affiliations

  1. P.O. Box 134, Bandjoun, Cameroon

    Daniel Tchiotsop, Beaudelaire Saha Tchinda, René Tchinda & Godpromesse Kenné

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  1. Daniel Tchiotsop
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Correspondence to Daniel Tchiotsop.

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Tchiotsop, D., Saha Tchinda, B., Tchinda, R. et al. Edge detection of intestinal parasites in stool microscopic images using multi-scale wavelet transform. SIViP 9 (Suppl 1), 121–134 (2015). https://doi.org/10.1007/s11760-014-0716-6

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