The classification of brain tumors is a difficult task in the field of medical image analysis. Improving algorithms and machine learning technology helps radiologists to easily diagnose the tumor without surgical intervention. In recent years, deep learning techniques have made excellent progress in the field of medical image processing and analysis. However, there are many difficulties in classifying brain tumors using magnetic resonance imaging; first, the difficulty of brain structure and the intertwining of tissues in it; and secondly, the difficulty of classifying brain tumors due to the high density nature of the brain. We propose a differential deep convolutional neural network model (differential deep-CNN) to classify different types of brain tumor, including abnormal and normal magnetic resonance (MR) images. Using differential operators in the differential deep-CNN architecture, we derived the additional differential feature maps in the original CNN feature maps. The derivation process led to an improvement in the performance of the proposed approach in accordance with the results of the evaluation parameters used. The advantage of the differential deep-CNN model is an analysis of a pixel directional pattern of images using contrast calculations and its high ability to classify a large database of images with high accuracy and without technical problems. Therefore, the proposed approach gives an excellent overall performance. To test and train the performance of this model, we used a dataset consisting of 25,000 brain magnetic resonance imaging (MRI) images, which includes abnormal and normal images. The experimental results showed that the proposed model achieved an accuracy of 99.25%. This study demonstrates that the proposed differential deep-CNN model can be used to facilitate the automatic classification of brain tumors.

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The process of diagnosing brain tumors is very complicated for many reasons, including the brain’s synaptic structure, size, and shape. Machine learning techniques are employed to help doctors to detect brain tumor and support their decisions. In recent years, deep learning techniques have made a great achievement in medical image analysis. This paper proposed a deep wavelet autoencoder model named “DWAE model”, employed to divide input data slice as a tumor (abnormal) or no tumor (normal). This article used a high pass filter to show the heterogeneity of the MRI images and their integration with the input images. A high median filter was utilized to merge slices. We improved the output slices’ quality through highlight edges and smoothened input MR brain images. Then, we applied the seed growing method based on 4-connected since the thresholding cluster equal pixels with input MR data. The segmented MR image slices provide two two-layer using the proposed deep wavelet auto-encoder model. We then used 200 hidden units in the first layer and 400 hidden units in the second layer. The softmax layer testing and training are performed for the identification of the MR image normal and abnormal. The contribution of the deep wavelet auto-encoder model is in the analysis of pixel pattern of MR brain image and the ability to detect and classify the tumor with high accuracy, short time, and low loss validation. To train and test the overall performance of the proposed model, we utilized 2500 MR brain images from BRATS2012, BRATS2013, BRATS2014, BRATS2015, 2015 challenge, and ISLES, which consists of normal and abnormal images. The experiments results show that the proposed model achieved an accuracy of 99.3%, loss validation of 0.1, low FPR and FNR values. This result demonstrates that the proposed DWAE model can facilitate the automatic detection of brain tumors.

In this paper, we consider three similar optimization problems: the fault-tolerant metric dimension problem, the local metric dimension problem and the strong metric dimension problem. These problems have applications in many diverse areas, including network discovery and verification, robot navigation and chemistry, etc. We give integer linear programming formulations of the faulttolerant metric dimension problem and the local metric dimension problem. Also, we study local metric dimension and strong metric dimension of two convex polytopes S n and U n .

Let G 1 and G 2 be disjoint copies of a graph G and g :In this paper, we extend the study of distinguishing numbers of a graph to its functigraph. We discuss the behavior of distinguishing number in passing from G to F G and find its sharp lower and upper bounds. We also discuss the distinguishing number of functigraphs of complete graphs and join graphs.