This paper is devoted to investigating the solutions of refinement equations of the form Ф（x）=∑α∈Z^s α（α）Ф（Mx-α）,x∈R^s,where the vector of functions Ф = （Ф1,… ,Фr）^T is in （L1（R^s））^r, α =（...This paper is devoted to investigating the solutions of refinement equations of the form Ф（x）=∑α∈Z^s α（α）Ф（Mx-α）,x∈R^s,where the vector of functions Ф = （Ф1,… ,Фr）^T is in （L1（R^s））^r, α =（α（α））α∈Z^s is an infinitely supported sequence of r × r matrices called the refinement mask, and M is an s × s integer matrix such that lim n→∞ M^-n =0, with m = detM. Some properties about the solutions of refinement equations axe obtained.展开更多
An approximate solution of the refinement equation was given by its mask, and the approximate sampling theorem for bivariate continuous function was proved by applying the approximate solution . The approximate sampli...An approximate solution of the refinement equation was given by its mask, and the approximate sampling theorem for bivariate continuous function was proved by applying the approximate solution . The approximate sampling function defined uniquely by the mask of the refinement equation is the approximate solution of the equation , a piece-wise linear function , and posseses an explicit computation formula . Therefore the mask of the refinement equation is selected according to one' s requirement, so that one may controll the decay speed of the approximate sampling function .展开更多
Traffic signs play a crucial role in managing traffic on the road,disciplining the drivers,thereby preventing injury,property damage,and fatalities.Traffic sign management with automatic detection and recognition is v...Traffic signs play a crucial role in managing traffic on the road,disciplining the drivers,thereby preventing injury,property damage,and fatalities.Traffic sign management with automatic detection and recognition is very much part of any Intelligent Transportation System(ITS).In this era of self-driving vehicles,calls for automatic detection and recognition of traffic signs cannot be overstated.This paper presents a deep-learning-based autonomous scheme for cognizance of traffic signs in India.The automatic traffic sign detection and recognition was conceived on a Convolutional Neural Network(CNN)-Refined Mask R-CNN(RM R-CNN)-based end-to-end learning.The proffered concept was appraised via an innovative dataset comprised of 6480 images that constituted 7056 instances of Indian traffic signs grouped into 87 categories.We present several refinements to the Mask R-CNN model both in architecture and data augmentation.We have considered highly challenging Indian traffic sign categories which are not yet reported in previous works.The dataset for training and testing of the proposed model is obtained by capturing images in real-time on Indian roads.The evaluation results indicate lower than 3%error.Furthermore,RM R-CNN’s performance was compared with the conventional deep neural network architectures such as Fast R-CNN and Mask R-CNN.Our proposed model achieved precision of 97.08%which is higher than precision obtained by Mask R-CNN and Faster RCNN models.展开更多
基金Supported by the National Natural Science Foundation of China (10071071)
文摘This paper is devoted to investigating the solutions of refinement equations of the form Ф（x）=∑α∈Z^s α（α）Ф（Mx-α）,x∈R^s,where the vector of functions Ф = （Ф1,… ,Фr）^T is in （L1（R^s））^r, α =（α（α））α∈Z^s is an infinitely supported sequence of r × r matrices called the refinement mask, and M is an s × s integer matrix such that lim n→∞ M^-n =0, with m = detM. Some properties about the solutions of refinement equations axe obtained.
基金the NSF of Henan Province (984051900)the NSF of Henan Education Committee (98110015)the Excellent Teacher Foundation of High School in Henan Province
文摘An approximate solution of the refinement equation was given by its mask, and the approximate sampling theorem for bivariate continuous function was proved by applying the approximate solution . The approximate sampling function defined uniquely by the mask of the refinement equation is the approximate solution of the equation , a piece-wise linear function , and posseses an explicit computation formula . Therefore the mask of the refinement equation is selected according to one' s requirement, so that one may controll the decay speed of the approximate sampling function .
文摘Traffic signs play a crucial role in managing traffic on the road,disciplining the drivers,thereby preventing injury,property damage,and fatalities.Traffic sign management with automatic detection and recognition is very much part of any Intelligent Transportation System(ITS).In this era of self-driving vehicles,calls for automatic detection and recognition of traffic signs cannot be overstated.This paper presents a deep-learning-based autonomous scheme for cognizance of traffic signs in India.The automatic traffic sign detection and recognition was conceived on a Convolutional Neural Network(CNN)-Refined Mask R-CNN(RM R-CNN)-based end-to-end learning.The proffered concept was appraised via an innovative dataset comprised of 6480 images that constituted 7056 instances of Indian traffic signs grouped into 87 categories.We present several refinements to the Mask R-CNN model both in architecture and data augmentation.We have considered highly challenging Indian traffic sign categories which are not yet reported in previous works.The dataset for training and testing of the proposed model is obtained by capturing images in real-time on Indian roads.The evaluation results indicate lower than 3%error.Furthermore,RM R-CNN’s performance was compared with the conventional deep neural network architectures such as Fast R-CNN and Mask R-CNN.Our proposed model achieved precision of 97.08%which is higher than precision obtained by Mask R-CNN and Faster RCNN models.
