Chapter 3
2D Moment Invariants to Translation, Rotation, and Scaling
Jan Flusser,
Tomáš Suk,
Barbara Zitová,
Jan Flusser
Institute of Information Theory and Automation, Czech Academy of Sciences, Prague, Czech Republic
Search for more papers by this authorTomáš Suk
Institute of Information Theory and Automation, Czech Academy of Sciences, Prague, Czech Republic
Search for more papers by this authorBarbara Zitová
Institute of Information Theory and Automation, Czech Academy of Sciences, Prague, Czech Republic
Search for more papers by this authorBook Author(s):Jan Flusser,
Tomáš Suk,
Barbara Zitová,
Jan Flusser
Institute of Information Theory and Automation, Czech Academy of Sciences, Prague, Czech Republic
Search for more papers by this authorTomáš Suk
Institute of Information Theory and Automation, Czech Academy of Sciences, Prague, Czech Republic
Search for more papers by this authorBarbara Zitová
Institute of Information Theory and Automation, Czech Academy of Sciences, Prague, Czech Republic
Search for more papers by this authorSummary
This chapter introduces 2D moment invariants with respect to the simplest spatial in-plane transformations, translation, rotation, and scaling (TRS). The TRS model is a sufficient approximation of the actual image deformation if the scene is flat and almost perpendicular to the optical axis. The chapter begins with a few basic definitions and with an introduction to moments and focuses on design of the invariants. It presents a general approach to deriving rotation invariants, which uses circular moments. The chapter also presents a general method of deriving complete and independent sets of rotation invariants of any orders. This method employs complex moments of the image. It highlights the relationship between the Hu invariants and the proposed invariants. The chapter shows that the Hu invariants are incomplete and mutually dependent, which can explain some practical problems connected with their usage. It investigates the behavior of rotation invariants under mirror reflection of the image.
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