In this paper, a novel realization of two-dimensional nonseparable wavelet filter bank with adaptive filter parameters is proposed. Two-dimensional generalization of the previously presented 1-D scheme is based on nonseparable quincunx decimation. 2-D filters are designed directly rather then obtained from 1-D filters using the pyramid scheme. Described space variant wavelet filter bank has several advantages when compared to fixed banks. Basic convergence and regularity properties of the limit wavelet functions and scales are provided by fixed part of the filter bank. Variable part of the bank adapts to the analyzed signal. Realization is based on the lifting scheme, derived from a method of fixed 2-D wavelet filter bank design. Original 2-D interpolation of samples in the space domain is modified to an approximation scheme that can be recomputed at each step of decomposition. Adaptation criterion is calculated from wavelet coefficients. Wavelet filter banks with adaptive filter parameters can outperform fixed banks in a number of applications, but the suitable adaptation criterion is still to be found.