  Image forensics is a rising topic as the trustworthy multimedia content is
critical for modern society. Like other vision-related applications, forensic
analysis relies heavily on the proper image representation. Despite the
importance, current theoretical understanding for such representation remains
limited, with varying degrees of neglect for its key role. For this gap, we
attempt to investigate the forensic-oriented image representation as a distinct
problem, from the perspectives of theory, implementation, and application. Our
work starts from the abstraction of basic principles that the representation
for forensics should satisfy, especially revealing the criticality of
robustness, interpretability, and coverage. At the theoretical level, we
propose a new representation framework for forensics, called Dense Invariant
Representation (DIR), which is characterized by stable description with
mathematical guarantees. At the implementation level, the discrete calculation
problems of DIR are discussed, and the corresponding accurate and fast
solutions are designed with generic nature and constant complexity. We
demonstrate the above arguments on the dense-domain pattern detection and
matching experiments, providing comparison results with state-of-the-art
descriptors. Also, at the application level, the proposed DIR is initially
explored in passive and active forensics, namely copy-move forgery detection
and perceptual hashing, exhibiting the benefits in fulfilling the requirements
of such forensic tasks.
