Paul Fieguth is the Vice-Dean of the Faculty of Engineering, Professor, and Department Chair of the Department of Systems Design Engineering. He is also a co-director of the [Vision and Imaging Processing Lab](https://uwaterloo.ca/vision-image-processing-lab/) at the University of Waterloo. <...
Paul Fieguth is the Vice-Dean of the Faculty of Engineering, Professor, and Department Chair of the Department of Systems Design Engineering. He is also a co-director of the [Vision and Imaging Processing Lab](https://uwaterloo.ca/vision-image-processing-lab/) at the University of Waterloo.
His main areas of research lie in multiscale statistical modelling and remote sensing. In particular, Professor Fieguth concentrates on the theory development and understanding of hierarchical / scale recursive estimation algorithms for multi-resolution stochastic processes. Such algorithms use a statistically meaningful strategy to break large estimation problems into smaller pieces, leading to vast improvements in efficiency.
Certainly a very pressing challenge is the amount of image data being collected -- satellite pictures, microscopic images, Google Streetview. There are many image processing algorithms available for regular images, such as portraits from digital cameras, however for scientific imagery, such as satellite images of a forest, microscopic pictures of a cracks in concrete, or medical images of the body from an MRI, more specialized techniques of image processing are required.
Professor Fieguth's interests are to formulate mathematical models, such as the temperature of the earth's atmosphere or the expected topology of the brain, and to combine such models with measured data. Such mathematical operations are tremendously valuable for two reasons:
First, because they allow us to infer subtle results from the data, and second, because they allow us to test whether a given mathematical model makes sense or not, a crucial step in advancing our understanding. The problem, however, is that it is very difficult to solve these equations in a computer for large two- or three-dimensional problems. His research seeks to develop efficient alternatives to modeling and algorithms, currently focusing on two specific strategies:
1. Look at the problem over a variety of scales, coupling a coarse-scale model looking at large objects with a fine-scale model looking at details and textures. Such an idea sounds very simple or intuitive, since the human visual system very much works this way, but is extremely challenging, in practice, because most mathematical models do not allow themselves to be split up.
2. Allow the model to connect not just neighbouring pixels, but also pixels further apart. This goal seems obvious, however virtually all spatial statistical models have focused on highly local interactions. Professor Fieguth's research explores models in which every pixel is connected globally, or possibly to a randomly scattered set of pixels where the statistics of the set are a function of the underlying image.