Deep Discriminant Analysis in binary segmentation of images

Abstract

Image segmentation is a fundamental task in image processing, with applications ranging from medical imaging to autonomous systems. This thesis introduces a novel Deep Discriminant Analysis (DDA) loss, which integrates classical discriminant analysis principles into deep neural networks to increase class separability in segmentation tasks. The proposed loss encourages the network to produce wellseparated representations of foreground and background pixels in the learned feature space, leading to more discriminative and interpretable representations. The effectiveness of the DDA loss is first validated on synthetic and simple classi-cation problems, then evaluated on the challenging DIS5K dataset using a tailored U-Net architecture. Experimental results demonstrate consistent improvements over the standard Binary Cross-Entropy (BCE) loss, yielding faster convergence, higher separability, and superior segmentation metrics across multiple test subsets. All experiments are carried out using publicly available datasets and open-source frameworks, with careful consideration of reproducibility, computational efficiency, and ethical standards. These findings confirm that discriminant analysis principles can be effectively embedded within deep architectures, offering a practical enhancement to contemporary segmentation methods.