We describe a method to compute the Euler number of a binary digital image based on a codification of contour pixels of the image’s shapes. The overall procedure evolves from a set of lemmas and theorems, their demonstration and their numerical validation. The method is supported through an experimental set which analyzes some digital images and their outcome to demonstrate the applicability of the procedure. The paper also includes a discussion about present and futures steps on this research

The authors propose two equations based on the pixel geometry and connectivity properties, which can be used to compute, efficiently, the Euler number of a binary digital image with either thick or thin boundaries. Although computing this feature, the authors’ technique extracts the underlying topological information provided by the shape pixels of the given image. The correctness of computing the Euler number using the new equations is also established theoretically. The performance of the proposed method is compared against other available alternatives. Experimental results on a large image database demonstrate that the authors technique for computing the Euler number outperforms the earlier approaches significantly in terms of the number of basic arithmetic operations needed per pixel. Both equations are specialised only for 4‐connectivity cases.

Breast cancer is a disease that has emerged as the second leading cause of cancer deaths in women worldwide. The annual mortality rate is estimated to continue growing. Cancer detection at an early stage could significantly reduce breast cancer death rates long-term. Many investigators have studied different breast diagnostic approaches, such as mammography, magnetic resonance imaging, ultrasound, computerized tomography, positron emission tomography and biopsy. However, these techniques have limitations, such as being expensive, time consuming and not suitable for women of all ages. Proposing techniques that support the effective medical diagnosis of this disease has undoubtedly become a priority for the government, for health institutions and for civil society in general. In this paper, an associative pattern classifier (APC) was used for the diagnosis of breast cancer. The rate of efficiency obtained on the Wisconsin breast cancer database was 97.31%. The APC’s performance was compared with the performance of a support vector machine (SVM) model, back-propagation neural networks, C4.5, naive Bayes, k-nearest neighbor (k-NN) and minimum distance classifiers. According to our results, the APC performed best. The algorithm of the APC was written and executed in a JAVA platform, as well as the experimental and comparativeness between algorithms.

Coronavirus disease 2019 (COVID-19) is a highly communicable viral infection caused by the Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV2), which has spread rapidly throughout the world. From a computer science point of view, research efforts have focused on the use of approaches such as machine learning and curve fitting to predict or simulate disease behavior. However, the mathematical characterization of the spread of COVID-19 is a topic that has not yet been explored by these techniques. In this work, we propose a novel metaheuristic framework called META-COVID19, which merges the Generalized Boltzmann distribution and the family of Jacobi polynomials to automatically characterize the COVID-19 spread without prior knowledge of the data and without involving a human expert. In general terms, the algorithm receives as input a time series of daily reported cases and the output is a polynomial mathematical model. Our framework only needs a single parameter, which is the number of Jacobi polynomials to analyze during the iterative process, and it is capable of proposing polynomials whose adjustment error is close to 1E-3. Finally, we show the applicability of the polynomial models found by META-COVID19, through a theoretical mathematical analysis in order to know attributes of the spread of COVID-19 in different periods of time, allowing to generate better strategies to face it in the future.

A goodness compactness measure is necessary in computer medical diagnosis, shape analysis and computer vision processes. A compactness measure called the normalised E ‐factor (NEF) is introduced. It is shown that this measure is simple and robust to translations, rotations and scale changes and that it satisfies the set of criteria for a good compactness measure. Through a series of experiments it is shown that the normalised E ‐factor is useful for shape description, measuring digital compactness with or without holes and that it overcomes some drawbacks that are present in the classical and normalised discrete compactness measures.