MULTISCALE IMAGE PROCESSING USING TRIANGULATED MESHES

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