Document Type : Original Manuscript
Department of Computer Engineering, Rasht Branch, Islamic Azad University, Rasht, Iran
Convolutional neural networks show outstanding performance in many image processing problems, such as image recognition, object detection and image segmentation. Semantic segmentation is a very challenging task that requires recognizing, understanding what's in the image in pixel level. The goal of this research is to develop on the known mathematical properties of the soft-max function and demonstrate how they can be exploited to conclude the convergence of learning algorithm in a simple application of image recognition in supervised learning. So, we utilize results from convex analysis theory which associated with hierarchical architecture to derive additional properties of the soft-max function not yet covered in the existing literature for Multi-Class Classification problems. The proposed MC-DEEP model represents an average accuracy of 90.25% in different layers setting with 95% confidence interval in best initial settings in deep convolutional layers which applied on MNIST dataset. The results show that the regularized networks not only could provide better segmentation results with regularization effect than the original ones but also have certain robustness to noise.