A Review of the Minimum Maximum Criterion for Optimal Bit Allocation Among Dependent Quantizers

In this paper, we review a general framework for the optimal bit allocation among dependent quantizers based on the minimum maximum (MINMAX) distortion criterion. Pros and cons of this optimization criterion are discussed and compared to the well-known Lagrange multiplier method for the minimum average (MINAVE) distortion criterion. We argue that, in many applications, the MINMAX criterion is more appropriate than the more popular MINAVE criterion. We discuss the algorithms for solving the optimal bit allocation problem among dependent quantizers for both criteria and highlight the similarities and differences. We point out that any problem which can be solved with the MINAVE criterion can also be solved with the MINMAX criterion, since both approaches are based on the same assumptions. We discuss uniqueness of the MINMAX solution and the way both criteria can be applied simultaneously within the same optimization framework. Furthermore, we show how the discussed MINMAX approach can be directly extended to result in the lexicographically optimal solution. Finally, we apply the discussed MINMAX solution methods to still image compression, intermode frame compression of H.263, and shape coding applications.