In this paper, we extend the gradient vector flow field for robust variational segmentation of vector-valued images. Rather than using scalar edge information, we define a vectorial edge map derived from a weighted local structure tensor of the image that enables the diffusion of the gradient vectors in accurate directions through the 4D gradient vector flow equation. To reduce the contribution of noise in the structure tensor, image channels are weighted according to a blind estimator of contrast. The method is applied to biological volume delineation in dynamic PET imaging, and validated on realistic Monte Carlo simulations of numerical phantoms as well as on real images.

Finding the best configuration of a neural network’s hyper-parameters may take too long to be feasible using an exhaustive search, especially when the cardinality of the search space has a big combinatorial number of possible solutions with various hyper-parameters. This problem is aggravated when we also need to optimize the parameters of the neural network, such as the weight of the hidden neurons and biases. Extreme learning machines (ELMs) are part of the random weights neural network family, in which parameters are randomly initialized, and the solution, unlike gradient-descent-based algorithms, can be found analytically. This ability is especially useful for metaheuristic analysis due to its reduced training times allowing a faster optimization process, but the problem of finding the best hyper-parameter configuration is still remaining. In this paper, we propose a modification of the artificial bee colony (ABC) metaheuristic to act as parameterizers for a regularized ELM, incorporating three methods: an adaptive mechanism for ABC to balance exploration (global search) and exploitation (local search), an adaptation of the opposition-based learning technique called opposition local-based learning (OLBL) to strengthen exploitation, and a record of access to the search space called forbidden redundant indexes (FRI) that allow us to avoid redundant calculations and track the explored percentage of the search space. We set ten parameterizations applying different combinations of the proposed methods, limiting them to explore up to approximately 10% of the search space, with results over 98% compared to the maximum performance obtained in the exhaustive search in binary and multiclass datasets. The results demonstrate a promising use of these parameterizations to optimize the hyper-parameters of the R-ELM in datasets with different characteristics in cases where computational efficiency is required, with the possibility of extending its use to other problems with similar characteristics with minor modifications, such as the parameterization of support vector machines, digital image filters, and other neural networks, among others.

This work presents an extension of morphological operators for color images. The morphological operations require that the set items to be analyzed are completely ordered, thus it is necessary to find a maximum and a minimum values in order to obtain such an ordering. In this paper a new lexicographical and distance criteria for the pixels ordering in color images are proposed. These criteria have allowed color images morphological operations to be defined, which are consistent with the properties for grayscale images morphological operations.

Dynamic PET imaging enables the study of radiotracers concentration kinetics along time. However, PET images suffer from limited spatial resolution, low signal-to-noise ratio, and time dependent contrast between tissues, making segmentation of biological volumes difficult. Deformable models are of great interest due to their inherent boundary continuity, but their applications to PET images still remains challenging due to high sensitivity to noise. To address these limitations, we propose a method to perform 3-D+time dynamic PET image segmentation using parametric active surfaces based on a gradient of the vectorial image. This method takes advantage of both spatial and temporal consistency of the signal along the acquisition. We validate our method using GATE Monte Carlo simulations and compare it with single frame based active surface models. We show significant improvement of several figures of merit.