Intelligent Restoration of Historical Parametric Geometric Patterns by Zernike Moments and Neural Networks

Historical Islamic ornaments include a fantastic treasury of geometric and mathematical algorithms. Inevitably, restoration of these ornaments in periodic patterns consisting of repeated elements has been faced following and substituting the other available similar ingredients instead of vanished parts. Still, the prediction of parametric, quasi, or non-periodic patterns, where components are not identical, needs to be carried out in a more challenging process than the periodic ones due to shape, scale, or angle of rotation alteration. Intelligent restoration could facilitate the forecasting of damaged parts in such geometric patterns that an algorithm has changed their geometric characteristics. In some architectural heritage, geometric patterns include a parametric algorithm like parametric patterns in the ceiling of Sheikh Lotfollahmosque in Isfahan, Iran, and the dominant structure of Persian domes Karbandi. In this article, the aim is to propose a new method for the smart restoration of the parametric geometric patterns in which, by having access to the image of the existing patterns, the vanished parts could be reconstructed spontaneously. Our approach is based on image processing by detecting boundaries of deterioration, finding every individual element, and extracting features of detected individual patterns via Zernike moments. The order of individual patterns starts from the farthest pattern to detected deterioration. Then by creating a time series, the Back-propagation neural network would be trained by extracted features, and the vanished patterns’ features could be predicted and reconstructed. Eventually, the reconstructed and real patterns are compared to determine differences between them by mean-squared error and to evaluate the performance of our method. To validate the process, a parametric geometric pattern is designed by the assumption that some parts are disappeared. The proposed method’s results, in this case, hold an efficient performance with the accuracy of 92.99%. Furthermore, Sheikh Lotfollah’s patterns and Naseredin Mirza mansion’s patterns as two real cases are tested by the proposed method, representing reliable and suitable performance results.

Optimized lung tumor diagnosis system using enhanced version of crow search algorithm, Zernike moments, and support vector machine

Early detection of lung tumors is so important to heal this disease in the initial steps. Automatic computer-aided detection of this disease is a good method for reducing human mistakes and improving detection precision. The major concept here is to propose the best CAD system for lung tumor detection. In the presented technique, after pre-processing and segmentation of the lung area, its features including different orders of Zernike moments have been extracted. After features extraction, they have been injected into an optimized version of Support Vector Machine (SVM) for final diagnosis. The optimization of the SVM is based on an enhanced design of the Crow Search Algorithm (ECSA). For validating the proposed method, it was applied to three datasets including Lung CT-Diagnosis, TCIA, and RIDER Lung CT collection, and the results are validated by comparing with three state-of-the-art methods including Walwalker method, Mon method, and Naik method to indicate the system superiority toward the compared methods. The system is also analyzed based on different orders of Zernike moment to select the best order. The final results indicate that the suggested method has a suitable accuracy for diagnosing lung cancer.

Efficient and Stable Voxel-Based Algorithm for Computing 3D Zernike Moments and Shape Reconstruction

3D Zernike moments based on 3D Zernike polynomials have been successfully applied to the field of voxelized 3D shape retrieval and have attracted more attention in biomedical image processing. As the order of 3D Zernike moments increases, both computational efficiency and numerical accuracy decrease. Due to this phenomenon, a more efficient and stable method for computing high-order 3D Zernike moments was proposed in this study. The proposed recursive formula for computing 3D Zernike radial polynomials combines the recursive calculation of spherical harmonics to develop a voxel-based algorithm for the calculation of 3D Zernike moments. The algorithm was applied to the 3D shape Michelangelo's David with a size of 150×150×150 voxels. As compared to the method without additional acceleration, the proposed method uses a group action of order sixteen orthogonal group and saving unnecessary iterations, the factor of speed-up is 56.783±3.999 when the order of Zernike moments is between 10 and 450. The proposed method also obtained an accurate reconstructed shape with the error rate (normalized mean square error) of 0.00 (4.17×10^-3) when the reconstruction was computed for all moments up to order 450.

On the classification of simple and complex biological images using Krawtchouk moments and Generalized pseudo-Zernike moments: a case study with fly wing images and breast cancer mammograms

In image analysis, orthogonal moments are useful mathematical transformations for creating new features from digital images. Moreover, orthogonal moment invariants produce image features that are resistant to translation, rotation, and scaling operations. Here, we show the result of a case study in biological image analysis to help researchers judge the potential efficacy of image features derived from orthogonal moments in a machine learning context. In taxonomic classification of forensically important flies from the Sarcophagidae and the Calliphoridae family (n = 74), we found the GUIDE random forests model was able to completely classify samples from 15 different species correctly based on Krawtchouk moment invariant features generated from fly wing images, with zero out-of-bag error probability. For the more challenging problem of classifying breast masses based solely on digital mammograms from the CBIS-DDSM database (n = 1,151), we found that image features generated from the Generalized pseudo-Zernike moments and the Krawtchouk moments only enabled the GUIDE kernel model to achieve modest classification performance. However, using the predicted probability of malignancy from GUIDE as a feature together with five expert features resulted in a reasonably good model that has mean sensitivity of 85%, mean specificity of 61%, and mean accuracy of 70%. We conclude that orthogonal moments have high potential as informative image features in taxonomic classification problems where the patterns of biological variations are not overly complex. For more complicated and heterogeneous patterns of biological variations such as those present in medical images, relying on orthogonal moments alone to reach strong classification performance is unrealistic, but integrating prediction result using them with carefully selected expert features may still produce reasonably good prediction models.

Combination of Texture and Shape Features Using Machine and Deep Learning Algorithms for Breast Cancer Diagnosis

Worldwide, breast cancer is a commonly occurring disease in women. Automatic diagnosis of the lesions based on mammographic images is playing an essential role to assist experts. A novel Computer-Aided Diagnosis (CADx) scheme of breast lesion classification is proposed in this paper based on an optimized combination of texture and shape features using machine and deep learning algorithms for mass classification as benign-malignant namely C(M-ZMs)*. The main advantage of using Zernike moments for shape feature extraction is their scale, translation, and rotation invariance property, this allows omitting some of the preprocessing stages in our case. We implemented for texture feature extraction the Monogenic-Local Binary Pattern taking the advantage of lower time and space complexity because monogenic signal analysis needs fewer convolutions and generates more compact feature vectors. Therefore, we used Zernike moments for shape feature extraction due to their scale, translation, and rotation invariance property, this allows omitting some of the preprocessing stages in our proposed system. The proposed system proves its performance on some challenging breast cancer cases where the lesions exist in dense breast tissues. Validation has been undertaken on 520 mammograms from the Digital Database for Screening Mammography Database (DDSM), yielding an accuracy rate of 99.5\%.