Reversible image rotations with modulo transforms

This paper proposes a new paradigm for the construction of reversible two point transforms or planar rotations. We show that the transform coefficients for integer to integer mappings through an integer rotation matrix are redundant in modular arithmetic. This redundancy can be exploited by quantizing transform coefficients in a critical manner, producing reversible and unit determinant transforms. For a subset of such critically quantized transforms, the quantization process can be performed by rounded integer division along each dimension. Such transforms are formed by a subset of Pythagorean triads, and can be used to implement reversible image rotations from a countable set of rotation angles. The subjective quality of the rotation so obtained compares favorably with the three shear or lifting algorithm.