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This paper is a study on texture analysis of Computer Tomography (CT) liver images using orthogonal moment features. Orthogonal moments are used as image feature representation in many applications like invariant pattern recognition of images. Orthogonal moments are proposed here for the diagnosis of any abnormalities on the CT images. The objective of the proposed work is to carry out the comparative study of the performance of orthogonal moments like Zernike, Racah and Legendre moments for the detection of abnormal tissue on CT liver images. The Region of Interest (ROI) based segmentation and watershed segmentation are applied to the input image and the features are extracted with the orthogonal moments and analyses are made with the combination of orthogonal moment with segmentation that provides better accuracy while detecting the tumor. This computational model is tested with many inputs and the performance of the orthogonal moments with segmentation for the texture analysis of CT scan images is computed and compared.

A tumor is the solid lesion which is produced by an abnormal cells growth which seems to be like swelling. The body is composed of many cells and each has a special functions. The extra cells form a mass of tissue called a tumor. In order to detect tumor, some computerized techniques are essential at the moment for easy diagnose. The advancement in the medical imaging technologies like Computer Tomography (CT), Magnetic Resonance Imaging (MRI) and ultrasonography has significantly raised the accuracy in diagnosing any abnormality in human organs [

The sample of discrete orthogonal moments like Zernike moment and Racah moment is taken for computation. The sample of continuous orthogonal moment like Legendre moment is considered for computation. It is a novel approach of stating the performance of orthogonal moments in terms of computing the accuracy for diagnosing the diseases in medical images. The particular combination of segmentation with orthogonal moments provides very good accuracy while detecting the tumor is studied and compared. The following section covers the implementation of orthogonal moments.

Regular moments have been extensively used as shape features in a variety of applications in image analysis. The regular moment suffer from the case that the basis function is not orthogonal, and certain degree of information redundancy is also possible. Moments with orthogonal basis functions solve this problem. A brief review of the three orthogonal moments implementation considered in this paper is illustrated as follows.

Legendre moments are a class of continuous orthogonal moments. Teague [

where the functions P_{p}(x_{i}) denote the Legendre polynomials of order “p”. The x_{i} and y_{j} are the normalized pixel coordinates in the range of [−1, 1]. The Legendre polynomial P_{p}(x_{i}) of order “p” is defined as,

with |x_{i}| ≤ 1 and (p - k) is even.

Zernike [^{2} + y^{2} = 1. These polynomials are defined as,

where p is positive integer or zero and q is positive and negative integers subject to constraints p - |q| even and |q| ≤ p R_{pq}(x, y): radial polynomial defined as,

Teague [

the center of the image is taken as origin for computing the Zernike moment and pixel coordinates are mapped in such a way that (x^{2} + y^{2}) ≤ 1. Those pixels falling outside the unit circle are not used in the computation.

The (n + m) order Racah moment of an image f(s, t) with size N × N

the set of weighted Racah polynomials being defined as

The generalized hyper geometric function

and the parameters a, b, α and β are restricted to

The weighted set of Racah polynomial values can be obtained by implementing Equation (7).

Classification of CT scan images using hepatic lesions were proposed by Glestos et al. [

mentation and Watershed segmentation is applied to the pre-processed image. The two segmented images are applied to the orthogonal moment computation for extracting the features. The discrete and continuous orthogonal moments such as Zernike, Racah and Legendre moments are computed from the ROI and watershed segmented image thereby six different features can be obtained. The mathematical functions like Energy, Contrast, Auto correlation, Homogeneity and variance are computed to extract intensity features of input image. From the six different methods of features, the optimized value is calculated. Based on the optimized values, the threshold is set and using this value the tumor present in the input image is identified. The two segmentation methods output, features are extracted using the Legendre, Zernike and Racah moment so that six different methods can be obtained, applying the following mathematical functions for computing the intensity features.

Energy

Contrast

Auto correlation

Homogeneity

Variance

After computing the above Equations (12)-(16) on the computed orthogonal moments, Energy, autocorrelation, contrast, homogeneity and variance value are obtained for all the input images as in

The Results of the inputs both normal and abnormal CT scan images which are given as sample inputs and the intermediate outputs are received as presented in the following section.

The sample of input images are used for the experimental study is shown in

Algorithm | Energy | Contrast | Auto Correlation | Homogeneity | Variance | |
---|---|---|---|---|---|---|

Input Image 2 | Legendre ROI | 4.655e−005 | 21,472.2289 | 61,518.8844 | 0.020666 | 85,160.0753 |

Legendre Watershed | 4.4531e−006 | 43,129.4174 | 63,026.9963 | 0.021474 | 84,408.8421 | |

Zernike ROI | 6.5791e−005 | 22,140.55 | 62,511.7316 | 0.0099835 | 72,536.5954 | |

Zernike Watershed | −2.8791e−005 | 20,722.8896 | 49,470.7831 | −0.00083027 | 30,991.6697 | |

Racah ROI | 4.753e−005 | 16,584.0676 | 54,874.0723 | 0.018438 | 70,935.5669 | |

Racah Watershed | 2.0716e−005 | 20,019.3059 | 64,739.852 | 0.02322 | 84,574.3151 |

Image | Algorithm | Optimized Value |
---|---|---|

Input Image 2 | Legendre ROI | 0.13452 |

Legendre Watershed | 0.15245 | |

Zernike ROI | 0.12575 | |

Zernike Watershed | 0.080948 | |

Racah ROI | 0.11391 | |

Racah Watershed | 0.13547 |

Then the three orthogonal moments viz Legendre, Zernike and Racah moments are computed on the two segmented outputs. The intensity features are extracted from the obtained computed moments is presented in

The various intensity features are extracted from the CT scan input images using Energy, Contrast, Auto correlation etc as shown in

As with many inputs are given and tested, the threshold values have been set as 0.110 by absorbing the Legendre ROI optimized value. Similarly it is possible to set the threshold values for all the six methods. The graph show the analysis of intensity features extracted using the mathematical function like Energy, Contrast, Auto correlation, Homogeneity and variance when compared with six different methods for the sample input images are shown in

The accuracy are calculated based on the parameter of true positive, true negative, false positive, false negative, sensitivity, specificity and positive prediction value and negative prediction value are shown in

Image Name | Legendre ROI | Legendre Watershed | Zernike ROI | Zernike Watershed | Racah ROI | Racah Watershed | Liver Tumor |
---|---|---|---|---|---|---|---|

Input Image 1 | 0.11975 | 0.1491 | 0.11223 | 0.069421 | 0.13413 | 0.13274 | Found |

Input Image 2 | 0.13452 | 0.15245 | 0.12575 | 0.080948 | 0.11391 | 0.13547 | Found |

Input Image 3 | 0.13182 | 0.1499 | 0.12182 | 0.080992 | 0.13737 | 0.13817 | Found |

Input Image 4 | 0.12448 | 0.14935 | 0.11045 | 0.075662 | 0.13713 | 0.1355 | Found |

Input Image 5 | 0.14015 | 0.15099 | 0.12063 | 0.080489 | 0.13581 | 0.14079 | Found |

Input Image 6 | 0.13708 | 0.15085 | 0.1224 | 0.07299 | 0.13771 | 0.14317 | Found |

Input Image 7 | 0.16802 | 0.15498 | 0.13078 | 0.089357 | 0.11243 | 0.13927 | Found |

Input Image 8 | 0.1254 | 0.14961 | 0.11156 | 0.1073 | 0.15042 | 0.14001 | Found |

Input Image 9 | 0.1433 | 0.1521 | 0.13266 | 0.079602 | 0.12572 | 0.14137 | Found |

Input Image 10 | 0.13327 | 0.14945 | 0.084317 | 0.080179 | 0.15242 | 0.14702 | Found |

Input Image 11 | 0.13268 | 0.15062 | 0.17135 | 0.077297 | 0.13399 | 0.13255 | Not Found |

Input Image 12 | 0.10327 | 0.15523 | 0.064337 | 0.1193 | 0.11847 | 0.11513 | Not Found |

Input Image 13 | 0.084486 | 0.15024 | 0.046296 | 0.15804 | 0.089116 | 0.11707 | Not Found |

Input Image 14 | 0.099032 | 0.15136 | 0.046378 | 0.1005 | 0.10478 | 0.10881 | Not Found |

Input Image 15 | 0.093409 | 0.15032 | 0.070749 | −0.25465 | 0.11739 | 0.13646 | Not Found |

Input Image 16 | 0.082372 | 0.14984 | 0.21157 | 0.04008 | 0.16208 | 0.14963 | Not Found |

Input Image 17 | 0.091154 | 0.15001 | 0.091762 | −0.095406 | 0.10255 | 0.11613 | Not Found |

Input Image 18 | 0.085922 | 0.15027 | −0.4817 | 0.29364 | 0.10172 | 0.10492 | Not Found |

Input Image 19 | 0.099113 | 0.14974 | 0.18833 | 0.12873 | 0.13063 | 0.13001 | Not Found |

ALGORITHM | TP | TN | FP | FN | Accuracy | Sensitivity | Specificity | PPV | NPV | |
---|---|---|---|---|---|---|---|---|---|---|

Input Image 1 | Legendre ROI | 46.933 | 49.217 | 3.066 | 0.782 | 96.151 | 0.9836 | 0.94135 | 0.93867 | 0.98435 |

Zernike ROI | 43.988 | 48.466 | 6.011 | 1.533 | 92.454 | 0.96631 | 0.88965 | 0.87977 | 0.96932 | |

Racah ROI | 47.430 | 49.344 | 2.569 | 0.655 | 96.775 | 0.98637 | 0.95051 | 0.94861 | 0.98689 | |

Legendre WS | 44.357 | 48.103 | 5.643 | 1.896 | 92.460 | 0.95899 | 0.89501 | 0.88714 | 0.96206 | |

Zernike WS | 20.652 | 40.134 | 29.347 | 9.865 | 60.787 | 0.67674 | 0.57762 | 0.41304 | 0.8027 | |

Racah WS | 39.489 | 46.467 | 10.510 | 3.533 | 85.956 | 0.91788 | 0.81553 | 0.78979 | 0.92934 | |

Input Image 2 | Legendre ROI | 45.844 | 48.967 | 4.156 | 1.032 | 94.811 | 0.97798 | 0.92177 | 0.91688 | 0.97935 |

Zernike ROI | 49.374 | 49.844 | 0.6254 | 0.155 | 99.219 | 0.99686 | 0.98761 | 0.98749 | 0.99689 | |

Racah ROI | 45.860 | 48.971 | 4.139 | 1.028 | 94.832 | 0.97807 | 0.92206 | 0.91721 | 0.97943 | |

Legendre WS | 46.428 | 48.827 | 3.571 | 1.172 | 95.255 | 0.97536 | 0.93184 | 0.92857 | 0.97654 | |

Zernike WS | 24.652 | 41.676 | 25.347 | 8.323 | 66.329 | 0.74759 | .062181 | 0.49305 | 0.83354 | |

Racah Watershed | 41.255 | 47.128 | 8.744 | 2.871 | 88.384 | 0.93493 | 0.84349 | 0.82511 | 0.94257 |

Based on the results, it is observed that the Racah polynomial feature extraction for ROI based segmentation provides better accuracy in many input images for 1, 3, 4, 5, 6, 8, 10, 11, 12, 13, 14, 15, 16, 17 and 18. Second to the contribution is Legendre feature extraction for ROI based segmentation and watershed segmentation are placed in terms of accuracy in most of the images. This analysis aids the medical industry to accurately detect tumour and to follow the best orthogonal moment features and segmentation methods.

Based on the results, it is observed that the orthogonal moments both discrete and continuous are showing a better feature extraction even in medical images too. The Racah orthogonal moment with ROI based segmentation is showing a very good result in terms of accuracy when compared with other orthogonal moments for the medical images. Followed to this is Legendre moment with ROI based segmentation that shows the better results in accuracy for many images. In order to detect the abnormality present in any CT scan images, the orthogonal moments show very good features representation particularly when combined with ROI based segmentation when compared with other segmentation. Finally, the Racah moment and Legendre moment provide a good contribution when working with Medical images and hence aid the medical field to diagnose the diseases easily. In order to improve the accuracy for diagnosing the diseases in medical images, the proposed work reveals the solution and in future other moments with segmentation can be taken for the study.

Nallasivan Gomathinayagam,Janakiraman Subbiah, (2016) A Simple Computational Approach for the Texture Analysis of CT Scan Images Using Orthogonal Moments. Circuits and Systems,07,1884-1892. doi: 10.4236/cs.2016.78163