Contact Info
Department of Applied Mathematics
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 519-888-4567, ext. 32700
Fax: 519-746-4319
PDF files require Adobe Acrobat Reader
Daniel Otero, PhD Candidate
Department of Applied Mathematics, University of Waterloo
Function-valued mappings and SSIM-based optimization: two alternative approaches to imaging
In this talk we present two novel approaches to carry out image processing tasks, namely, function-valued mappings (FVMs) and structural similarity index measure (SSIM)-based optimization. With FVMs, also known as Banach-valued functions in the literature, we propose a different way of representing complex datasets, e.g., hyperspectral and diffusion magnetic resonance images, which are usually represented as vector-valued functions. The infinite dimensionality of the range of FVMs offers interesting possibilities for modelling different kinds of datasets, as well as making possible the generalization of the classical fractal and Fourier transforms. As for SSIM-based optimization, we present a general framework for solving optimization problems in which the SSIM is employed as a fidelity term. This framework allows us to solve optimization problems involving the SSIM that had not been addressed before, and also provides an alternative way of performing some of the well known Euclidian-based image processing tasks: e.g., sparse reconstruction, denoising, zooming, etc.. Potential and current developed applications of these two approaches to imaging are also discussed.
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Contact Info
Department of Applied Mathematics
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 519-888-4567, ext. 32700
Fax: 519-746-4319
PDF files require Adobe Acrobat Reader
The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is co-ordinated within the Office of Indigenous Relations.