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Abol Basher,Samsuddin Ahmed,정호엽 (사)한국스마트미디어학회 2020 스마트미디어저널 Vol.9 No.2
The hippocampal volume atrophy is known to be linked with neuro-degenerative disorders and it is also one of the most important early biomarkers for Alzheimer's disease detection. The measurements of hippocampal pure volumes from Magnetic Resonance Imaging (MRI) is a crucial task and state-of-the-art methods require a large amount of time. In addition, the structural brain development is investigated using MRI data, where brain morphometry (e.g. cortical thickness, volume, surface area etc.) study is one of the significant parts of the analysis. In this study, we have proposed a patch-based ensemble model of 3-D convolutional neural network (CNN) to measure the hippocampal pure volume from MRI data. The 3-D patches were extracted from the volumetric MRI scans to train the proposed 3-D CNN models. The trained models are used to construct the ensemble 3-D CNN model and the aggregated model predicts the pure volume in one-step in the test phase. Our approach takes only 5 seconds to estimate the volumes from an MRI scan. The average errors for the proposed ensemble 3-D CNN model are 11.7±8.8 (error%±STD) and 12.5±12.8 (error%±STD) for the left and right hippocampi of 65 test MRI scans, respectively. The quantitative study on the predicted volumes over the ground truth volumes shows that the proposed approach can be used as a proxy
THE INVARIANT OF IMMERSIONS UNDER ISOTWIST FOLDING
El-Ghoul, Mabrouk Salam,Basher, Mohamed Esmail 충청수학회 2005 충청수학회지 Vol.18 No.1
In this paper we will introduce all types of the isotwist foldings of a manifold M into itself. The limits of the isotwist foldings of a manifold are obtained. Also the relations between conditional retraction and this type of the folding are achieved. Finally the variant and invariant of the immersion under the type of folding are deduced.
The Invariant of Immersions under Isotwist Folding
El-Goul, Mabrouk Salam,Basher, Mohamed Esmail Department of Mathematics 2006 Kyungpook mathematical journal Vol.46 No.1
In this paper, we will introduce the isotwist foldings of a manifold M into itself. The limits of the isotwist foldings of a manifold are obtained. Also the relations be-tween conditional retraction and this type of the foldings are achieved. Finally the variant and invariant of the immersion under this type of foldings are deduced.
El-Kholy, Entesar Mohamed,Basher, Mohamed Esmail Mohamed,El-Deen, Mohamed Ramadaan Zeen 충청수학회 2005 충청수학회지 Vol.18 No.2
In this paper we introduced the concept of perfect folding defined on $E^2$ which equipped by perfect k-coloring of r-monohedral tillings. Then we studied the different cases of perfect foldings of 4-monohedral and 3-monohedral tillings of $E^2$. Also the permutations describe each folding are obtained.
On the Folding of the Rectangular Distribution
El-Shehawy, S.A.,Basher, M. Department of Mathematics 2013 Kyungpook mathematical journal Vol.53 No.1
Based on the concept of the folding, the folding in X-direction and in Y-direction are defined and denoted by the X-Folding and the Y-Folding respectively. We consider a random variable X which follows a rectangular distribution "R(a, b) distribution" with two parameters a, b. This paper aims to apply the folding on the unit area P($a{\leq}X{\leq}b$) and also to study the proposed folding in each direction for R(a, b) distribution and the generated family of the corresponding constructed rectangular probability distributions. Some main properties of this family are reviewed. According to the proposed folding, we derive and discuss some important corresponding functions in closed forms.
The Invariant of Immersions under Isotwist Folding
EL-GOUL, MABROUK SALAM,BASHER, MOHAMED ESMAIL 대한수학회 2006 Kyungpook mathematical journal Vol.46 No.1
In this paper, we will introduce the isotwist foldings of a manifold M into itself. The limits of the isotwist foldings of a manifold are obtained. Also the relations between conditional retraction and this type of the foldings are achieved. Finally the variant and invariant of the immersion under this type of foldings are deduced.
El-Ghoul, Mabrouk Salem,Basher, Mohamed Esmail 충청수학회 2005 충청수학회지 Vol.18 No.2
In this paper, we introduced the tiling, for closed plane curves ${\alpha}(s)$, and we discussed the properties of tiling. Also if ${\alpha}(s)$ was arbitrary plane closed curve equipped by tiling ${\Im}$ then we studied the effect of retraction and tiling retraction on it.
Mabrouk Salem El-Ghoul,Mohamed Esmail Basher 충청수학회 2005 충청수학회지 Vol.18 No.2
In this paper, we introduced the tiling, for closed plane curves α(s), and we discussed the properties of tiling. Also if α(s) was arbitrary plane closed curve equipped by tiling ℑ then we studied the effect of retraction and tiling retraction on it.
Entesar Mohamed El-Kholy,Mohamed Esmail Mohamed Basher,Mohamed Ramadaan Zeen El-Deen 충청수학회 2005 충청수학회지 Vol.18 No.2
In this paper we introduced the concept of perfect folding defined on E 2 which equipped by perfect k-coloring of r-monohedral tillings. Then we studied the different cases of perfect foldings of 4-monohedral and 3-monohedral tillings of E 2 . Also the permutations describe each folding are obtained.
M.S El-Ghoul,M.E. Basher 충청수학회 2005 충청수학회지 Vol.18 No.2
In this paper, we introduced the tiling, for closed plane curves $\alpha (s)$, and we discussed the properties of tiling. Also if $\alpha (s)$ was arbitrary plane closed curve equipped by tiling $\Im $ then we studied the effect of retraction and tiling retraction on it.