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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.