Identifying COVID-19 on chest radiographic images (CXR) remains an essential task in patient tracking and follow-up. Several initiatives have worked on this task, and although the results presented so far are encouraging, few are reflected in applications adopted in clinical environments. Thus, understanding that there is still a field of research in this area, this work presents a method based on feature extraction by using Binary Patterns of Phase Congruency (BPPC) on segmented CXR images. This work aims to be a mild and fast alternative for the automatic detection of COVID-19 and its severity levels while requiring few computational resources. To do this, radiomic features are extracted from CXR images, a selection process based on SVM is used, and two models of shallow Feedforward networks are built. The presented results far surpass previous works, with an average accuracy for COVID-19 detection of 98.24% and 94.74% in identifying PCR+ images taken from people without infection marks and Normal diagnosis. A second model is also presented, in which the task is to classify CXR images of COVID-19 in different severity levels, and the presented AUC is 98.05%. The solution's high performance makes it a viable option as a computer-aided diagnostic tool, representing a significant gain in the speed and accuracy of COVID-19 diagnosis and in identifying the severity of the disease.