Currently, the Morpho-Constitutional Analysis (MCA) is the de facto approach for the etiological diagnosis of kidney stone formation, and it is an important step for establishing personalized treatment to avoid relapses. More recently, research has focused on performing such tasks intra-operatively, an approach known as Endoscopic Stone Recognition (ESR). Both methods rely on features observed in the surface and the section of kidney stones to separate the analyzed samples into several sub-groups. However, given the high intra-observer variability and the complex operating conditions found in ESR, there is a lot of interest in using AI for computer-aided diagnosis. However, current AI models require large datasets to attain a good performance and for generalizing to unseen distributions. This is a major problem as large labeled datasets are very difficult to acquire, and some classes of kidney stones are very rare. Thus, in this paper, we present a method based on diffusion as a way of augmenting pre-existing ex-vivo kidney stone datasets. Our aim is to create plausible diverse kidney stone images that can be used for pre-training models using ex-vivo data. We show that by mixing natural and synthetic images of CCD images, it is possible to train models capable of performing very well on unseen intra-operative data. Our results show that is possible to attain an improvement of 10% in terms of accuracy compared to a baseline model pre-trained only on ImageNet. Moreover, our results show an improvement of 6% for surface images and 10% for section images compared to a model train on CCD images only, which demonstrates the effectiveness of using synthetic images.

DNA microarrays is a technology that can be used to diagnose cancer and other diseases. To automate the analysis of such data, pattern recognition and machine learning algorithms can be applied. However, the curse of dimensionality is unavoidable: very few samples to train, and many attributes in each sample. As the predictive accuracy of supervised classifiers decays with irrelevant and redundant features, the necessity of a dimensionality reduction process is essential. The main idea is to retain only the genes that are the most influential in the classification of the disease. In this paper, a new methodology based on Principal Component Analysis and Logistics Regression is proposed. Our method enables the selection of particular genes that are relevant for classification. Experiments were run using eight different classifiers on two benchmark datasets: Leukemia and Lymphoma. The results show that our method not only reduces the number of required attributes, but also increase the classification accuracy in more than 10% in all the cases we tested.

In this paper we apply the classic theory of harmonic analysis and the conformal geometric algebra (CGA) to evaluate the Fourier transform on the unit sphere S2and on the rotation group SO(3). Since the images taken by omnidirectional sensors can be mapped to the sphere, the problem of attitude estimation of a 3D camera rotation can be treated as a problem of estimating rotations between spherical images. Usually, this rotation estimation problem has been solved using the Radon transform with point correlation or with line correlation. Using a catadioptric system with a parabolic mirror, 3D lines will be projected as great circles on S2and then projected as circles on the image plane. CGA is a mathematical framework where its basic entities, spheres, circles, lines and planes can be used with incidence algebra operations to improve the line correlation in the Radon transform as a dual-circle correlation. Thus, harmonic analysis theory and conformal geometric algebra will be joined in this paper to improve the search of a 3D rotation correspondence between two omnidirectional images.

Because of their large field of view, omnidirectional images can assist with localization tasks to robotic navigation algorithms. Since the images taken by omnidirectional sensors can be mapped to the sphere, the problem of attitude estimation of a 3D camera rotation can be treated as a problem of estimating rotations between spherical images. Usually, this rotation estimation problem has been solved using point correspondences or gradient information of the points of the images, with the respective computational time consuming of those point algorithms. We present an effective solution to the attitude estimation problem using line information of the images through the Radon transform, because line algorithms are less time consuming that those using points. In the formulation of the Radon transform we include a similarity function on the cross product of two images which assigns a weight to all lines pairs, and where this similarity function is integrated over all lines pairs that satisfy a constraint for lines. That is, we formulate the problem to obtain the Euler angles of the 3D camera rotation as a correlation of functions defined on the product of spheres S2times S2which are acted upon by elements of the direct product groups of rotations SO(3) timesSO(3). Because of the spherical treatment of the data, our approach utilizes the spherical fourier transform and spherical harmonics to produce a solution in the Fourier domain.

We present an approach to ruled surfaces and complex 3D-curves using conformal geometric algebra. As robots and mechanisms move, any line attached to them will trace out a ruled surface. In robotics, the arm of a robot usually needs to follow a curve over a ruled surface or over the intersection of some of them. In this paper we present the way to model and to resolve these problems using algebra of incidence and rigid-motion transformations in the context of the conformal geometric algebra