טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentNisenboim Alexander
SubjectModel Based Shape from Shading for Microelectronics
Inspection Applications
DepartmentDepartment of Applied Mathematics
Supervisor Professor Alfred Bruckstein


Abstract


  The problem of recovering a 3D object’s shape from a single shaded image, namely the Shape from Shading (SFS) problem, has intrigued the computer vision researchers for almost 30 years. The research in this area was mostly inspired by the fact that our brain has an outstanding ability to perceive the depth of the observed scene from 2D images on the retina. Shading is only one of the clues used by our brain to do the job. However, one of the most interesting problems in the theory of human early vision is exactly how much information we are able to recover from shading. It is interesting that despite the lack of our understanding of this cognitive feature and major difficulties of our mathematical modeling attempts, nowadays there is a practical need to address important SFS-based applications in some branches of the computer industry. Model based Shape From Shading (SFS) is a new promising paradigm introduced by J.Attick et al, in 1996. In present work we adopt this approach to attack the   problem of recovering wafer shape from a single image taken by a Scanning Electron Microscope (SEM). This problem arises naturally in the microelectronics inspection industry. A low dimensional model of wafer surfaces has been developed and the SFS problem was rephrased as one of optimal parameter estimation. Wavelet techniques were employed to calculate an initial guess to start the minimization process. Finally, a Levenberg-Marguardt optimization procedure has been adopted to address the ill-posedness issue of the SFS problem and to insure stable numerical convergence. The proposed algorithm has been tested on synthetic images under both Lambertian and SEM imaging models.