DEEP FULLY RESIDUAL CONVOLUTIONAL NEURAL NETWORK FOR SEMANTIC IMAGE SEGMENTATION

Department of Computer Science and EngineeringThe goal of semantic image segmentation is to partition the pixels of an image into semantically meaningful parts and classifying those parts according to a predefined label set. Although object recognition models achieved remarkable performance recently and they even surpass human???s ability to recognize objects, but semantic segmentation models are still behind. One of the reason that makes semantic segmentation relatively a hard problem is the image understanding at pixel level by considering global context as oppose to object recognition. One other challenge is transferring the knowledge of an object recognition model for the task of semantic segmentation. In this thesis, we are delineating some of the main challenges we faced approaching semantic image segmentation with machine learning algorithms. Our main focus was how we can use deep learning algorithms for this task since they require the least amount of feature engineering and also it was shown that such models can be applied to large scale datasets and exhibit remarkable performance. More precisely, we worked on a variation of convolutional neural networks (CNN) suitable for the semantic segmentation task. We proposed a model called deep fully residual convolutional networks (DFRCN) to tackle this problem. Utilizing residual learning makes training of deep models feasible which ultimately leads to having a rich powerful visual representation. Our model also benefits from skip-connections which ease the propagation of information from the encoder module to the decoder module. This would enable our model to have less parameters in the decoder module while it also achieves better performance. We also benchmarked the effective variation of the proposed model on a semantic segmentation benchmark. We first make a thorough review of current high-performance models and the problems one might face when trying to replicate such models which mainly arose from the lack of sufficient provided information. Then, we describe our own novel method which we called deep fully residual convolutional network (DFRCN). We showed that our method exhibits state of the art performance on a challenging benchmark for aerial image segmentation.clos

Tensor Products of Some Special Rings

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Gorenstein homological dimensions and Auslander categories

In this paper, we study Gorenstein injective, projective, and flat modules over a Noetherian ring $R$. For an $R$-module $M$, we denote by ${\rm Gpd}_RM$ and ${\rm Gfd}_R M$ the Gorenstein projective and flat dimensions of $M$, respectively. We show that ${\rm Gpd}_RM<\infty$ if and only if ${\rm Gfd}_RM<\infty$ provided the Krull dimension of $R$ is finite. Moreover, in the case that $R$ is local, we correspond to a dualizing complex ${\bf D}$ of $\hat{R}$, the classes $A'(R)$ and $B'(R)$ of $R$-modules. For a module $M$ over a local ring $R$, we show that $M\in A'(R)$ if and only if ${\rm Gpd}_RM<\infty$ or equivalently ${\rm Gfd}_RM<\infty$. In dual situation by using the class $B'(R)$, we provide a characterization of Gorenstein injective modules.Comment: 15 page