Loss Function Modeling for Deep Neural Networks Applied to Pixel-level Tasks

Abstract

In recent years, deep convolutional neural networks has overcome several challenges in the Ąeld of Computer Vision and Image Processing. Particularly, pixel-level tasks such as image segmentation, restoration, generation, enhancement, and inpainting have shown signiĄcant improvements thanks to the advances of the technique. In general, training a neural network is similar to solving a complex optimization problem where the unknowns are the parameters of the model, and the goal is to transform vectors from the input domain to the output set. This optimization process can be seen as a directed search through an error surface where the optimal set of weights is the one that gives a minimal error over a data sample. Since reaching the global minimum is very difficult, the task is simpliĄed to Ąnd an acceptable solution for the task. However, because of the high dimensionality of the solution space, the non-convexity of the error surface, and the presence of many Ćat regions and saddle points in the surface, the process of training a neural network is generally addressed by carefully tuning the hyperparameters of the model and annotating a vast training dataset. The three core components of the cost function used for supervised training are the architecture, the data, and the loss function. Despite the emergence of many new architectures, Ąnding better networks to solve a task is difficult. The modeling of new loss functions is a more feasible approach to improve the optimization and, therefore, Ąnd better-performed models. This work proposes to use a given network, and concentrates on the designing of loss functions for pixel-level regression and pixel-level classiĄcation problems, namely, image segmentation, to improve results. The rationale behind proposed loss functions is that the incorporation of priors in the form of regularization terms helps to distinguish between similarly-performed models, like the ones found in Ćat regions. New pre-processing and post-processing techniques are also introduced in each case to assist in solving real-life problems. The applicability of pixel-level classiĄcation loss functions in instance segmentation task with full and weak supervision was studied using challenging biological image datasets with isolated and clustered cells for both 2D and 3D. A pixel-level regression loss function was applied to the multi-focus image fusion problem. Experimental results for instance segmentation and image restoration tasks suggest an improvement of the performance when compared to other competitive loss functions. 3D segmentation and multi-focus image fusion approaches showed low execution time.