The novel coronavirus disease (SARS-CoV-2 or COVID-19) is spreading across the world and is affecting public health and the world economy. Artificial Intelligence (AI) can play a key role in enhancing COVID-19 detection. However, lung infection by COVID-19 is not quantifiable due to a lack of studies and the difficulty involved in the collection of large datasets. Segmentation is a preferred technique to quantify and contour the COVID-19 region on the lungs using computed tomography (CT) scan images. To address the dataset problem, we propose a deep neural network (DNN) model trained on a limited dataset where features are selected using a region-specific approach. Specifically, we apply the Zernike moment (ZM) and gray level co-occurrence matrix (GLCM) to extract the unique shape and texture features. The feature vectors computed from these techniques enable segmentation that illustrates the severity of the COVID-19 infection. The proposed algorithm was compared with other existing state-of-the-art deep neural networks using the Radiopedia and COVID-19 CT Segmentation datasets presented specificity, sensitivity, sensitivity, mean absolute error (MAE), enhance-alignment measure (EM_φ), and structure measure (S_m) of 0.942, 0.701, 0.082, 0.867, and 0.783, respectively. The metrics demonstrate the performance of the model in quantifying the COVID-19 infection with limited datasets.