Photometric transformations, such as brightness and contrast adjustment, can be applied to a face image repeatedly creating a set of near-duplicate images. Identifying the original image from a set of such near-duplicates and deducing the relationship between them are important in the context of digital image forensics... This is commonly done by generating an image phylogeny tree \textemdash \hspace{0.08cm} a hierarchical structure depicting the relationship between a set of near-duplicate images. In this work, we utilize three different families of basis functions to model pairwise relationships between near-duplicate images. The basis functions used in this work are orthogonal polynomials, wavelet basis functions and radial basis functions. We perform extensive experiments to assess the performance of the proposed method across three different modalities, namely, face, fingerprint and iris images; across different image phylogeny tree configurations; and across different types of photometric transformations. We also utilize the same basis functions to model geometric transformations and deep-learning based transformations. We also perform extensive analysis of each basis function with respect to its ability to model arbitrary transformations and to distinguish between the original and the transformed images. Finally, we utilize the concept of approximate von Neumann graph entropy to explain the success and failure cases of the proposed IPT generation algorithm. Experiments indicate that the proposed algorithm generalizes well across different scenarios thereby suggesting the merits of using basis functions to model the relationship between photometrically and geometrically modified images. (read more)