Automatic classification for pathological prostate images based on fractal analysis
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Automatic Classification for Pathological Prostate Images Based on Fractal Analysis. Introduction. Accurate grading for prostatic cancer in pathological images is important to prognosis and treatment planning. The problems of human grading: Time-consuming Very subjective

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Automatic Classification for Pathological Prostate Images Based on Fractal Analysis

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Automatic classification for pathological prostate images based on fractal analysis

Automatic Classification forPathological Prostate Images Based on Fractal Analysis


Introduction

Introduction

  • Accurate grading for prostatic cancer in pathological images is important to prognosis and treatment planning.

  • The problems of human grading:

    • Time-consuming

    • Very subjective

  • This paper presents an automated system to classify pathological images to appropriate cancer grade according to Gleason grading system.

    • The Gleason grading system is the most widespread method for histological grading of prostate.


Introduction1

Introduction

  • According to related work, the use of texture analysis for prostatic lesions is very essential to the identification of tissue composition in prostatic neoplasia.

Gleason grade 2

Gleason grade 3

The Gleason grading diagram

Gleason grade 5

Gleason grade 4


Introduction2

Introduction

  • Since the texture of prostate tissue plays an important role for prostate cancer, two texture analysis methods based on fractal dimension are proposed:

    • Method-1: Differential Box-Counting (DBC) method

      • Analysis of the intensity variance of local regions

    • Method-2: Entropy-Based Fractal Dimension Estimation (EBFDE) method.

      • Analysis of the texture complexity of local regions


Feature extraction fractal dimension

Feature Extraction – Fractal Dimension

  • Based on Mandelbrot’s concept, many natural objects exhibit the fractal property of self-similarity.

    • Given a bounded set S in Euclidean n-space, S is self-similar if it is the union of Nr distinct (non-overlapping) copies of itself scaled down by a ratio r.

      The fractal dimension D of S can be derived from the following basic equation:


Extracting feature by dbc

s

s

5 20 1 7

k

3 12 5 2

s

2 70 3 2

15 8 1 6

s

s’

l

Nr is counted for different values of r, i.e. different values of s, s = 2, 4, 8, 16…)

s

s

(s’ = s× G / M)

Extracting Feature by DBC

s

s

M

M

(r = s/M)

(choose a box of sizes×s, where 1 < s < M/2 )

M

M


Extracting feature by dbc1

Extracting Feature by DBC

log (Nr)

log (Nr)

log( 1 / r )

log( 1 / r )


Extracting feature by ebfde

s

s

5 20 1 7

3 12 5 2

s

2 70 3 2

15 8 1 6

s

Extracting Feature by EBFDE

s

s

M

(r = s/M)

(choose a box of sizes×s, where 1 < s < M/2 )

M

The entropy value of each grid:

Taking entropy values form all grids:


Extracting feature by ebfde1

Extracting Feature by EBFDE

(a)

(b)

(c)

log (Nr)

log (Nr)

log( 1 / r )

log( 1 / r )


Combination of two fractal dimension texture features

Combination of Two Fractal Dimension Texture Features

  • Representation of FD-based Features

    • ( fD1 , fD2 , fD3 , fD4 , fE1 , fE2 , fE3 , fE4 )

      • fD1is the fractal dimension calculated from the grids with size s (s = 2, 4, 8) using DBC method.

      • fD2is the fractal dimension calculated from the grids with size s (s = 8, 16, 32) using DBC method.

      • fD3is the fractal dimension calculated from the grids with size s (s = 32, 64, 128) using DBC method.

      • fD4is the fractal dimension calculated from the grids with size s (s = 2, 4, 8, 16, 32, 64, 128) using DBC method.


Automatic classification for pathological prostate images based on fractal analysis

  • Representation of FD-based Features

    • ( fD1 , fD2 , fD3 , fD4 , fE1 , fE2 , fE3 , fE4)

      • fE1is the fractal dimension calculated from the grids with size s (s = 2, 4, 8) using EBFDE method.

      • fE2is the fractal dimension calculated from the grids with size s (s = 8, 16, 32) using EBFDE method.

      • fE3is the fractal dimension calculated from the grids with size s (s =32, 64, 128) using EBFDE method.

      • fE4is the fractal dimension calculated from the grids with size s (s = 2, 4, 8, 16, 32, 64, 128) using EBFDE method.


Classification

Classification

  • Three different classifiers are used to evaluate the effectiveness of our FD-based feature set, respectively.

    • Three classifiers: Bayesian, k-nearest neighbor (k-NN), and Support Vector Machine (SVM) classifiers.

  • The leave-One-Out (LOO) and k-fold cross-validation procedures was adopted to estimate the correct classification rate (CCR).


Experimental results

Experimental results

  • There were 205 pathological images with resolution 512×384 pixels captured.

    • These images were analyzed by experienced pathologists in Taichung Veterans General Hospital of Taiwan and classified into four classes in advance as “gold standard”.

  • Since Grade-1 patterns are very rare, Grade-1 and Grade-2 patterns are regarded as the same class.

    • As a result, our image set was divided into four classes:

      • Class-1: 50 images

      • Class-2: 72 images

      • Class-3: 31 images

      • Class-4: 52 images


Experimental results1

Experimental results

  • Feature Sets Used for Comparison

    • We use the feature sets derived from multiwavelets, Gabor filters, and GLCM methods to compare with our FD-based feature set and demonstrate the superiority of our approach over other methods.


Experimental results2

Experimental results

  • Performance of FD-based Feature Set

    • Table I and Table II show the performance of feature setsfD, fE, and (fD+fE) using Bayesian, k-NN, and SVM classifiers evaluated by leave-one-out and 5-fold cross-validation methods, respectively.

    • fD={ fD1, fD2, fD3, fD4}

    • fE={ fE1, fE2, fE3, fE4}

    • fD + fE={ fD1, fD2, fD3, fD4 ,fE1, fE2, fE3, fE4}


Experimental results3

Experimental results

TABLE I

COMPARISONS OF CCR FOR THE FEATURE SETS PROPOSED IN THIS PAPER USING

BAYESIAN, k-NN, AND SVM CLASSIFIERS EVALUATED

BY LEAVE-ONE-OUT METHOD


Experimental results4

Experimental results

TABLE II

COMPARISONS OF CCR FOR THE FEATURE SETS PROPOSED IN THIS PAPER USING

BAYESIAN, k-NN, AND SVM CLASSIFIERS EVALUATED

BY 5-FOLD CROSS-VALIDATION METHOD


Experimental results5

Experimental results

  • Comparison of CCR Using Classifiers without Feature Selection

    • In following Table III, IV, and V, we want to evaluate the performance of other feature sets (multiwavelets, Gabor filters, and GLCM) and compare with the performance of our feature set fD+fE.


Experimental results6

Experimental results

TABLE III

COMPARISONS OF CCR FOR VARIOUS FEATURE SETS USING BAYESIAN CLASSIFIER EVALUATED BY LEAVE-ONE-OUT AND 5-FOLD CROSS-VALIDATION PROCEDURES


Automatic classification for pathological prostate images based on fractal analysis

TABLE IV

COMPARISONS OF CCR FOR VARIOUS FEATURE SETS USING k-NN CLASSIFIER EVALUATED BY LEAVE-ONE-OUT AND 5-FOLD CROSS-VALIDATION PROCEDURES


Experimental results7

Experimental results

TABLE V

COMPARISONS OF CCR FOR VARIOUS FEATURE SETS USING SVM CLASSIFIER EVALUATED BY LEAVE-ONE-OUT AND 5-FOLD CROSS-VALIDATION PROCEDURES


Experimental results8

Experimental results

  • Comparison of CCR Using Classifiers with Feature Selection

    • Tables VI, VII, and VIII show the classification performance of various feature sets after feature selection using Bayesian, k-NN, and SVM classifiers, respectively.

    • Two important aspects based on the results shown in these three tables:

      • a trend that feature set fD+ fE has the highest CCR was observed

      • the feature set fD+ fE has the smallest dimension


Experimental results9

Experimental results

TABLE VI

COMPARISONS OF CCR FOR VARIOUS FEATURE SETS WITH SFFS FEATURE SELECTION USING BAYESIAN CLASSIFIER EVALUATED BY LEAVE-ONE-OUT AND 5-FOLD CROSS-VALIDATION PROCEDURES


Experimental results10

Experimental results

TABLE VII

COMPARISONS OF CCR FOR VARIOUS FEATURE SETS WITH SFFS FEATURE SELECTION USING k-NN CLASSIFIER EVALUATED BY LEAVE-ONE-OUT AND 5-FOLD CROSS-VALIDATION PROCEDURES


Experimental results11

Experimental results

TABLE VIII

COMPARISONS OF CCR FOR VARIOUS FEATURE SETS WITH SFFS FEATURE SELECTION USING SVM CLASSIFIER EVALUATED BY LEAVE-ONE-OUT AND 5-FOLD CROSS-VALIDATION PROCEDURES


Discussion and conclusions

Discussion and conclusions

  • Experimental results demonstrated that the FD-based feature set proposed in this paper can provide very useful information for classifying pathological prostate images into four cancer classes.

  • As compared to other feature sets derived from multiwavelets, Gabor filters, and GLCM methods, our feature set has the highest correct classification rate and smallest dimensionality.

    • With feature selection, our proposed feature set achieved a CCR of 93.7% using Bayesian classifier, a CCR of 94.2% using k-NN classifier, and a CCR of 94.6% using SVM classifier if leave-one-out was used as the evaluation procedure.

    • When 5-fold cross-validation was used as the evaluation procedure, a CCR of 94.6%, 94.2%, and 94.1% was achieved by Bayesian, k-NN, and SVM classifiers, respectively.


Discussion and conclusions1

Discussion and conclusions

  • The main contributions of this paper:

    • We successfully propose a fractal dimension feature set of very small size to grade prostate images effectively.

    • We successfully provide an elaborative design for defining the sub-ranges of scales so that feasible FD texture features can be extracted from prostate images.

    • This paper propose a EBFDE method to calculate Nr based on entropy.

    • If we want to select a single category of features for grading prostate images, we demonstrate by extensive experiments that FD category has either better or at least the same performance statistically as compared to multi-wavelet, Gabor, and GLCM categories. However, the feature set in FD category proposed in this paper has the smallest size.


Automatic classification for pathological prostate images based on fractal analysis

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