Binary-valued wavelet decompositions of binary images

We introduce a binary-valued wavelet decomposition of binary images. Based on simple modulo-2 operations, the transform is computationally simple and immune to quantization effects. The new transform behaves like its real-valued counterpart. In particular, it yields an output similar to the thresholded output of a real wavelet transform operating on the underlying binary image. Using a new binary field transform to characterize binary filters, binary wavelets are constructed in terms of 2-band perfect reconstruction filter banks. We include lossless image coding results to illustrate the compactness of the representation.