Lattice codes have been evaluated in the watermarking literature based on their behavior in the presence of additive noise. In contrast with spread spectrum methods, the host image does not interfere with the watermark. Such evaluation is appropriate to simulate the effects of operations like compression, which are effectively noise-like for lattice codes. Lattice codes do not perform nearly as well when processing that fundamentally alters the characteristics of the host image is applied. One type of modification that is particularly detrimental to lattice codes involves changing the amplitude of the host. In a previous paper on the subject, we describe a modification to lattice codes that makes them invariant to a large class of amplitude modifications; those that are order preserving. However, we have shown that in its pure form the modification leads to problems with embedding distortion and noise immunity that are image dependent. In the current work we discuss an improved method for handling the aforementioned problem. Specifically, the set of quantization bins that is used for the lattice code is governed by a finite state machine. The finite state machine approach to quantization bin assignment requires side information in order for the quantizers to be recovered exactly. Our paper describes in detail two methods for recovery when such an approach is used.
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