We introduce a novel computational framework to enable automated identification of texture and shape features of lesions on 18F-FDG-PET images through a graph-based image segmentation method. The proposed framework predicts future morphological changes of lesions with high accuracy. The presented methodology has several benefits over conventional qualitative and semi-quantitative methods, due to its fully quantitative nature and high accuracy in each step of (i) detection, (ii) segmentation, and (iii) feature extraction. To evaluate our proposed computational framework, thirty patients received 2 18F-FDG-PET scans (60 scans total), at two different time points. Metastatic papillary renal cell carcinoma, cerebellar hemongioblastoma, non-small cell lung cancer, neurofibroma, lymphomatoid granulomatosis, lung neoplasm, neuroendocrine tumor, soft tissue thoracic mass, nonnecrotizing granulomatous inflammation, renal cell carcinoma with papillary and cystic features, diffuse large B-cell lymphoma, metastatic alveolar soft part sarcoma, and small cell lung cancer were included in this analysis. The radiotracer accumulation in patients' scans was automatically detected and segmented by the proposed segmentation algorithm. Delineated regions were used to extract shape and textural features, with the proposed adaptive feature extraction framework, as well as standardized uptake values (SUV) of uptake regions, to conduct a broad quantitative analysis. Evaluation of segmentation results indicates that our proposed segmentation algorithm has a mean dice similarity coefficient of 85.75±1.75%. We found that 28 of 68 extracted imaging features were correlated well with SUVmax (p<0.05), and some of the textural features (such as entropy and maximum probability) were superior in predicting morphological changes of radiotracer uptake regions longitudinally, compared to single intensity feature such as SUVmax. We also found that integrating textural features with SUV measurements significantly improves the prediction accuracy of morphological changes (Spearman correlation coefficient=0.8715, p<2e-16).