Convolutional neural network (CNN) is a powerful tool for many data applications. However, its high dimension nature, large network size and computational complexity, and the need of large amount of training data make it challenging to be used in edge computing applications, which are becoming increasingly popular, relevant and important. In this paper, we propose a descriptor based approach to accelerate convolutional neural network training, reduce input dimension and network size, which greatly facilitates the use of CNN for edge computating and even cloud computing. By using image descriptors to extract features from original images, we report a simpler convolutional neural network with fast training speed, low memory usage and outstanding accuracy without the need for a pre-trained network as opposed to the state of art. In indoor localization, our SURF descriptors accelerated CNN (SurfCNN) can reach an average position error of 0.28 m and orientation error of 9.2 •. Compared to the conventional CNN that uses original images as input, our algorithm reduces the dimension of the input features by a factor of 48 without impairing the accuracy. Further, at an extreme feature reduction of 14,440 times, our model still retains an average position error retained at 0.41 m and orientation error at 14 • .