Abstract
One of the primary goals of low-level vision is to segment the domain D of an image I into the parts D i on which distinct surface patches, belonging to distinct objects in the scene, are visible, Although this sometimes requires high level knowledge about the shape and surface appearance of various classes of objects, there are many low-level clues about the appearance of the individual surface patches and the boundaries between them. For example, the surface patches usually have characteristic albedo patterns, textures, on them, and these textures often change sharply as you cross a boundary between two patches. Therefore, one approach to the segmentation problem has been to try to merge all the low-level clues for splitting and merging different parts of the domain D and come up with probability measures p({D i }) of how likely a given segmentation {D i } is on the basis of all available low-level information, and what is the most likely segmentation. Alternately, one sets E({D i }) = − log(p({Di})), which one calls the ‘energy’ of the segmentation, and seeks the segmentation with the minimum energy, In general, these models have two parts: a prior model of possible scene segmentations, possibly including variables to describe other scene structures that are relevant (e.g. depth relationships), and a data model of what images are consistent with this prior model of the scene. If we write w for the variables used to describe the scene, e.g. the subsets D i or the set of all their boundary points Γ, then the prior model is some probability space (Ω w,d p), where Ω w,d , is the set of all possible values of w. The model is specified by giving the probability distribution p(w) on all these values. The data model is a larger probability space (Ω w,d , p), where Ω w,d is the set of all possible values of w and of all possible observed images I.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Mumford, D. (1994). Bayesian Rationale for the Variational Formulation. In: ter Haar Romeny, B.M. (eds) Geometry-Driven Diffusion in Computer Vision. Computational Imaging and Vision, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1699-4_5
Download citation
DOI: https://doi.org/10.1007/978-94-017-1699-4_5
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4461-7
Online ISBN: 978-94-017-1699-4
eBook Packages: Springer Book Archive