MRI image segmentation using machine learning networks and level set approaches

<span>The segmented brain tissues from magnetic resonance images (MRI) always pose substantive challenges to the clinical researcher community, especially while making precise estimation of such tissues. In the recent years, advancements in deep learning techniques, more specifically in fully convolution neural networks (FCN) have yielded path breaking results in segmenting brain tumour tissues with pin-point accuracy and precision, much to the relief of clinical physicians and researchers alike. A new hybrid deep learning architecture combining SegNet and U-Net techniques to segment brain tissue is proposed here. Here, a skip connection of the concerned U-Net network was suitably explored. The results indicated optimal multi-scale information generated from the SegNet, which was further exploited to obtain precise tissue boundaries from the brain images. Further, in order to ensure that the segmentation method performed better in conjunction with precisely delineated contours, the output is incorporated as the level set layer in the deep learning network. The proposed method primarily focused on analysing brain tumor segmentation (BraTS) 2017 and BraTS 2018, dedicated datasets dealing with MRI brain tumour. The results clearly indicate better performance in segmenting brain tumours than existing ones.</span>

Semigroup Structures and Commutative Ideals of BCK-Algebras Based on Crossing Cubic Set Structures

First, semigroup structure is constructed by providing binary operations for the crossing cubic set structure. The concept of commutative crossing cubic ideal is introduced by applying crossing cubic set structure to commutative ideal in BCK-algebra, and several properties are investigated. The relationship between crossing cubic ideal and commutative crossing cubic ideal is discussed. An example to show that crossing cubic ideal is not commutative crossing cubic ideal is given, and then the conditions in which crossing cubic ideal can be commutative crossing cubic ideal are explored. Characterizations of commutative crossing cubic ideal are discussed, and the relationship between commutative crossing cubic ideal and crossing cubic level set is considered. An extension property of commutative crossing cubic ideal is established, and the translation of commutative crossing cubic ideal is studied. Conditions for the translation of crossing cubic set structure to be commutative crossing cubic ideal are provided, and its characterization is processed.