multiscale image processing using triangulated meshes
DESCRIPTION
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 - PowerPoint PPT PresentationTRANSCRIPT
Key Ideas
MULTISCALE IMAGE PROCESSING USING TRIANGULATED MESHESMaarten Jansen, Hyeokho Choi, Sridhar Lavu, and Richard Baraniuk
Rice University
2D Image Example
• Treat images as 3D surfaces
• Multiscale triangular representation
• Normal offsets
• Edges / line singularities contain what and where information
• Wavelets suffer from poor decay
• Principle in 1D– normal offsets
• Adaptive• Normal direction
– points towards the edge
• Wavelets
• Normal meshes
• Normal meshes outperform 2D wavelets
• multiscale triangulation • normal offset• “where” and “what” information in one coefficient
•Future work
• Compression and denoising applications
Conclusions
Normal mesh transform
Wavelet transform
• Horizon class functions– normal meshes
– wavelets
• Piecewise smooth functions– both
Leve
l 5Le
vel 6
Leve
l 5Le
vel 6
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
)( 2lengthOwidth
• Narrow triangles
•
level 4 level 5
level 4 level 5
21|||| nOff n
233log22|||| nn Off
2|||| nOff n
22|||| nn Off
1|||| nOff n
level 4 level 5
Problem: Edges
Normal Meshes in 1D
Non Linear Approximation in 1D
Normal Meshes - 2D Horizon Class Image
Approximation Error Results
Approximation Error Results