The tree-structured wavelet transform has received a lot of attention and has found successful applications in signal denoising, image coding, image analysis, etc. In this paper, we present an analysis of the structural stability of the tree-structured wavelet transform, a topic which has not been addressed properly in previous research. We also present a texture classification algorithm based on a bottomup tree-structured wavelet transform. The proposed approach does not require ad-hoc parameters and demonstrates superior performance, as compared to the top-down approach proposed previously.