While deep neural networks possess the capability to perform semantic segmentation, producing a single deterministic output limits reliability in safety-critical applications, caused by uncertainty and annotation variability. To address this, stochastic segmentation models using Conditional Variational Autoencoders (CVAE), Bayesian networks, and diffusion have been explored. However, existing approaches suffer from limited latent expressiveness and interpretability. Furthermore, our experiments showed that models like Probabilistic U-Net rely excessively on high latent variance, leading to posterior collapse. This work propose a novel framework by integrating Gaussian Mixture Model (GMM) with Normalizing Flow (NF) in CVAE for stochastic segmentation. GMM structures the latent space into meaningful semantic clusters, while NF captures feature deformations with quantified uncertainty. Our method stabilizes latent distributions through constrained variance and mean ranges. Experiments on LIDC, Crack500, and Cityscapes datasets show that our approach outperformed state-of-the-art in curvilinear structure and medical image segmentation.

Coprime arrays are a class of sensor arrays that play a crucial role in various signal processing tasks because of their desirable properties such as sparsity and increased degrees of freedom (DOF) of coarrays. In this contribution, a new class of three-dimensional (3D) arrays is constructed from pure cubic fields. By studying the properties of cubic integers, we convert the problem of finding two coprime 3-by-3 integer matrices to that of two coprime integers in the ring of integers of a cubic field, which significantly reduces the design complexity and expands the design space of these matrices. The proposed construction offers naturally commutative matrices and includes generalized circulant matrices as a special case (under certain restriction of a parameter). The surged DOF is guaranteed by the generalized Chinese Remainder Theorem (CRT) for rings and ideals.