We propose a lossy data compression scheme based on an approximate two dimensional pattern matching (2D-PMC) extension of the Lempel-Ziv lossless scheme. We apply the scheme to image and video compression and report on our theoretical and experimental results. Theoretically, we show that the so called fixed database model leads to suboptimal compression. Furthermore, the compression ratio of this model is as low as the generalized entropy that we define in the paper. We use this model for our video compression scheme and present experimental results. For image compression we use a growing database model. The implementation of 2D-PMC is a challenging problem from the algorithmic point of view. We use a range of novel techniques and data structures such as k-d trees, generalized run length coding, adaptive arithmetic coding, and variable and adaptive maximum distortion level to achieve good compression ratios at high compression speeds.