COVID-19 is a disease caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) that can lead to complications such as acute respiratory distress syndrome, acute heart injury and secondary infections in a relatively high proportion of patients and, consequently, significant mortality. The definitive diagnosis of COVID-19 is performed by real-time Polymerase Chain Reaction (RT-PCR). However, as the result of RT-PCR, at least for now, has been made available within a longer period of time than the computed tomography (CT) report, this has taken on an important role in the detection of patients infected with COVID-19. A rough estimate of the extent of lung involvement by the disease is also important and considered an additional criterion for deciding on discharge or hospitalization. Recent research has adopted deep neural networks and other machine learning approaches to detect the presence of lung infection caused by COVID-19. However, the extent of lung involvement (volume) caused by the disease has been little investigated. In this work, we created an end-to-end computer vision system to automatically quantify the Percentage Of Infection (POI) in chest CT images of COVID-19 cases confirmed by the laboratory. Trying to obtain high accuracy, we evaluated the performance of three deep neural networks well known in the literature, trained with three different training strategies: (1) no transfer learning with randomly initialized weights; (2) transfer learning without fine-tuning with ImageNet weights; and (3) transfer learning with 100% fine-tuning. Data augmentation and dropout were used during networks training to reduce overfitting and increase the generalization capacity of the models. Our approach consists of segmenting a chest CT with the SLIC Superpixels method and classifying each segment (superpixel) into a specific class (COVID or non-COVID). We used the weights of the deep neural network best evaluated for accuracy in our computer vision system in order to classify the superpixels in the image and quantify the regions of COVID-19 infection, thus calculating the POI on chest CT. The results indicate that deep learning models can be successfully used to support radiologists in the quantitative diagnosis of lung infection caused by COVID-19, reaching an accuracy of up to 98.4% with Inception-Resnet-v2 architecture.