Early and accurate identification of Parkinsonian syndromes (PS) involving presynaptic degeneration from nondegenerative variants such as scans without evidence of dopaminergic deficit (SWEDD) and tremor disorders is important for effective patient management as the course, therapy, and prognosis differ substantially between the two groups. In this study, we use single photon emission computed tomography (SPECT) images from healthy normal, early PD, and SWEDD subjects, as obtained from the Parkinson's Progression Markers Initiative (PPMI) database, and process them to compute shape- and surface-fitting-based features. We use these features to develop and compare various classification models that can discriminate between scans showing dopaminergic deficit, as in PD, from scans without the deficit, as in healthy normal or SWEDD. Along with it, we also compare these features with striatal binding ratio (SBR)-based features, which are well established and clinically used, by computing a feature-importance score using random forests technique. We observe that the support vector machine (SVM) classifier gives the best performance with an accuracy of 97.29%. These features also show higher importance than the SBR-based features. We infer from the study that shape analysis and surface fitting are useful and promising methods for extracting discriminatory features that can be used to develop diagnostic models that might have the potential to help clinicians in the diagnostic process.