MULTISCALE IMAGE PROCESSING USING TRIANGULATED MESHES Maarten Jansen

MULTISCALE IMAGE PROCESSING USING TRIANGULATED MESHES Maarten Jansen, Hyeokho Choi, Sridhar Lavu, and Richard Baraniuk Rice University Non Linear Approximation in 1 D Problem: Edges • Wavelets • Horizon class functions – normal meshes – wavelets level 4 Approximation Error Results • Normal meshes level 5 • Edges / line singularities contain what and where information • Piecewise smooth functions – both • Wavelets suffer from poor decay Key Ideas 2 D Image Example Normal Meshes - 2 D Horizon Class Image Same level approximation • Image viewed as a 3 D surface mesh level 1 level 2 Level 5 • Treat images as 3 D surfaces level 3 • Projection of the normal mesh on the 2 D plane • Normal offsets level 1 level 2 level 3 Level 6 • Multiscale triangular representation Normal mesh transform Approximation Error Results Normal Meshes in 1 D Wavelet transform Conclusions • Narrow triangles • Normal meshes outperform 2 D wavelets • multiscale triangulation • normal offset • “where” and “what” information in one coefficient level 4 level 5 • • Future work • Principle in 1 D – normal offsets • Adaptive • Normal direction – points towards the edge • Compression and denoising applications level 4 level 5