  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.
