Ph.D. Open Thesis Defense
Name: Yamuna N. Swamy
S. R. Number: : 5510-120-092-07325
Title: Studies on Kernel Based Edge Detection and Hyper Parameter Selection in Image Restoration and Diffuse Optical Image Reconstruction
Date & Time: July 27, 2017 (Thursday), 12:00 P.M.
Venue: Room No 102 (Seminar Hall), CDS
Computational imaging has been playing an important role in understanding and analyzing the captured images. Both image segmentation and restoration has been integral parts of computational imaging. The studies performed in this thesis has been focussed toward developing novel algorithms for image segmentation and restoration. Study related to usage of Morozov Discrepancy Principle in Diffuse Optical Imaging was also presented here to show that hyperparameter selection could be performed with ease.
The Laplacian of Gaussian (LoG) and Canny operators use Gaussian smoothing before applying the derivative operator for edge detection in real images. The LoG kernel was based on second derivative and is highly sensitive to noise when compared to the Canny edge detector. A new edge detection kernel, called as Helmholtz of Gaussian (HoG), which provides higher diffusivity is developed in this thesis and it was shown that it is more robust to noise. The formulation of the developed HoG kernel is similar to LoG. It was also shown both theoretically and experimentally that LoG is a special case of HoG. This kernel when used as an edge detector exhibited superior performance compared to LoG, Canny and wavelet based edge detector for the standard test cases both in one- and two-dimensions.
The linear inverse problem encountered in restoration of blurred noisy images is typically solved via Tikhonov minimization. The outcome (restored image) of such minimization is highly dependent on the choice of regularization parameter. In the absence of prior information about the noise levels in the blurred image, finding this regularization/hyper parameter in an automated way becomes extremely challenging. The available methods like Generalized Cross Validation (GCV) may not yield optimal results in all cases. A novel method that relies on minimal residual method for finding the regularization parameter automatically was proposed here and was systematically compared with the GCV method. It was shown that the proposed method performance was superior to the GCV method in providing high quality restored images in cases where the noise levels are high.
Diffuse optical tomography uses near infrared (NIR) light as the probing media to recover the distributions of tissue optical properties with an ability to provide functional information of the tissue under investigation. As NIR light propagation in the tissue is dominated by scattering, the image reconstruction problem (inverse problem) is nonlinear and ill-posed, requiring usage of advanced computational methods to compensate this. An automated method for selection of regularization/hyper parameter that incorporates Morozov discrepancy principle(MDP) into the Tikhonov method was proposed and shown to be a promising method for the Dynamic Diffuse Optical Tomography.
ALL ARE WELCOME