Organization of: Scale-Space Theory in Computer Vision

Scale-Space Theory in Computer Vision deals with the fundamental problems that are associated with the use of scale-space analysis in early processing of visual information. More specifically some of the main questions it addresses are the following:
  • How should the scale-space model be implemented computationally? The scale-space theory has been formulated for continuous signals, while realistic signals are discrete.
  • Can the scale-space representation be used for extracting information? How should this be done?
  • The scale-space representation in itself contains no information about preferred scales. In fact, without any a priori scale information all levels of scale must be treated similarly. Is it possible to determine a sparse set of appropriate scales for further processing?
  • How can the scale-space concept interact with and cooperate with other processing modules?
  • What can happen in scale-space? What is the behaviour of structure in scale-space? How do features evolve under scale-space smoothing? What types of bifurcation events can take place?
  • Can cues to three-dimensional surface shape be computed directly from visual front-end operations?
The presentation is divided into four parts.

Part I starts by considering the basic theory of scale-space representation. A number of fundamental results on scale-space and related multi-scale representations are reviewed. The problem of how to formulate a scale-space theory for discrete signals is treated, as is the problem of how to compute image features within the Gaussian derivative framework.

Then, in Part II a representation called the scale-space primal sketch is presented, which is a formal representation of structures at multiple scales in scale-space aimed at the making information in the scale-space representation explicit. The theory behind its construction is analysed, and an algorithm is presented for computing the representation.

In Part III it is demonstrated how this representation can be integrated with other visual modules. Qualitative scale and region information extracted from the scale-space primal sketch can be used for guiding other low-level processes and simplifying their tasks.

Finally, in Part IV it is shown how the suggested method for scale selectioncan be extended to other aspects of image structure, and how three-dimensional shape cues can be computed within the Gaussian derivative framework. Such information can then be used for adapting the shape of the smoothing kernel, to reduce the shape distorting effects of the scale-space smoothing, and thus increase the accuracy in the computed surface orientation estimates.

Responsible for this page: Tony Lindeberg