We introduce a new patch-based multi-resolution analysis of semi-regular mesh surfaces. This analysis brings patch-specific wavelet decomposition, quantization and encoding to the mesh compression process. Our underlying mesh partitioning relies on surface roughness (based on frequency magnitude variations), in order to produce patches, representative of semantic attributes of the object. With current compression methods based on wavelet decomposition, some regions of the mesh still have wavelet coefficients with a non negligible magnitude or polar angle (the angle with the normal vector), reflecting the high frequencies of the model. For each non-smooth region, our adaptive compression chain provides the possibility to choose the best prediction filter adjusted to its specificity. Our hierarchical analysis is based on a semi-regular mesh decomposition produced by second-generation wavelets. Apart from progressive compression, other types of applications can benefit from this adaptive decomposition, like error resilient compression, view-dependent reconstruction, indexation or watermarking. Selective refinement examples are given to illustrate the concept of ROI (Region Of Interest) decoding, which few people has considered, whereas it is possible with JPEG2000 for images.