Quantification, or prevalence estimation, is the task of predicting the prevalence of each class within an unknown bag of examples. Most existing quantification methods in the literature rely on prior probability shift assumptions to create a quantification model that uses the predictions of an underlying classifier to make optimal prevalence estimates. In this work, we present an end-to-end neural network that uses Gaussian distributions in latent spaces to obtain invariant representations of bags of examples. This approach addresses the quantification problem using deep learning, enabling the optimization of specific loss functions relevant to the problem and avoiding the need for an intermediate classifier, tackling the quantification problem as a direct optimization problem. Our method achieves state-of-the-art results, both against traditional quantification methods and other deep learning approaches for quantification. The code needed to reproduce all our experiments is publicly available at https://github.com/AICGijon/gmnet.

Using the fibular flap as a model, this study aims to develop a three-dimensional visualization method for perforator vessels. This method integrates artificial intelligence algorithms, mixed reality technology, and polyetheretherketone (PEEK) fiducial markers to achieve precise localization and three-dimensional rendering of the vessels. The goal is to provide surgeons with an independent, controllable 3D vascular visualization system and to offer a reference for extending this method's application to multidisciplinary fields such as vascular intervention and neurosurgery. The study included three patients undergoing reconstructive surgery with fibular flaps. The technical procedure consisted of: (1) fabricating PEEK fiducial markers and affixing them to the designated flap donor site; (2) performing CT angiography and reconstructing the acquired two-dimensional data into a three-dimensional model incorporating the lower limb and the PEEK markers; (3) developing an artificial intelligence algorithm within the HoloLens 2 head-mounted holographic display to align the virtual 3D PEEK model with the physical markers on the patient, thereby achieving registration between the model and the human body. During surgery, we recorded the number of perforator vessels identified by the system versus the actual number found surgically, the distance between the projected and actual vessel exit points, and the time required for registration. Across the three patients, the system identified a total of five perforator vessels, which matched the surgical findings. The average distance between the localized and actual vessel exit points was 1.7 mm. The total registration time, from system activation to successful alignment, averaged 108 s, with the core registration process itself averaging 16 s. All flaps survived postoperatively with no related complications. In this study, an AI algorithm was developed and integrated into the HoloLens 2, which was able to identify the physical fiducial markers attached to the patient's body surface. Through the registration of these physical markers with their virtual counterparts, alignment between the human tissue and its three-dimensional model was achieved. This technical framework demonstrated potential versatility and adaptability, and may serve as a methodological reference for developing navigation systems in other surgical disciplines. However, its broader applicability requires validation through larger-scale future studies.