Gaussian scale space from insufficient image information

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Gaussian scale space is properly defined and well-developed for images completely knownand defined on the d dimensional Euclidean space Rd. However, as soon as image information is only partly available, say, on a subset V of Rd, the Gaussian scale space paradigm is not readily applicable and one has to resort to different approaches to come to a scale space on V. Examples are the theory dealing with scale space on Zd ¿ Rd, i.e., discrete scale space; the approach based on the heat equation satisfying certain boundary conditions; and the ad hoc approaches dealing with (hyper)rectangular images, e.g. zero-padding of the area outside of V, or periodic continuation of the image. We propose to solve the foregoing problem for general V from a Bayesian viewpoint. Assuming that the observed image is obtained by linearly sampling a real underlying image that is actually defined on the complete d dimensional Euclidean space, we can infer this latter image and from that image build the scale space. Re-sampling this scale space then gives rise to the scale space on V. Necessary for inferring the underlying image is knowledge on the linear apertures (or receptive field) used for sampling this image, and information on the prior over the class of all images.
Original languageEnglish
Title of host publicationScale Space Methods in Computer Vision : 4th International Conference, Scale Space 2003 Isle of Skye, UK, June 10–12, 2003 Proceedings
EditorsLewis D. Griffin, Martin Lillholm
Publication date2003
ISBN (Print)978-3-540-40368-5
Publication statusPublished - 2003
Externally publishedYes
Event4th International Conference on Scale Space Methods in Computer Vision - Isle of Skye, United Kingdom
Duration: 10 Jun 200312 Jun 2003
Conference number: 4


Conference4th International Conference on Scale Space Methods in Computer Vision
LandUnited Kingdom
ByIsle of Skye
SeriesLecture notes in computer science

ID: 5581219