Front-End Vision and Multi-Scale Image Analysis

1. Front Matter

   Pages i-xviii

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2. Apertures and the notion of scale

   Pages 1-12

3. Foundations of scale-space

   Pages 13-36

4. The Gaussian kernel

   Pages 37-51

5. Gaussian derivatives

   Pages 53-69

6. Multi-scale derivatives: implementations

   Pages 71-89

7. Differential structure of images

   Pages 91-136

8. Natural limits on observations

   Pages 137-141

9. Differentiation and regularization

   Pages 143-152

10. The front-end visual system — the retina

    Pages 153-165

11. A scale-space model for the retinal sampling

    Pages 167-177

12. The front-end visual system — LGN and cortex

    Pages 179-195

13. The front-end visual system — cortical columns

    Pages 197-213

14. Deep structure I. watershed segmentation

    • Erik Dam, Bart M. ter Haar Romeny

    Pages 215-240

15. Deep structure II. catastrophe theory

    • Erik Dam, Bart M. ter Haar Romeny

    Pages 241-256

16. Deep structure III. topological numbers

    • Bart M. ter Haar Romeny, Erik Dam

    Pages 257-276

17. Deblurring Gaussian blur

    Pages 277-284

18. Multi-scale optic flow

    • Bart ter Haar Romeny, Luc Florack, Avan Suinesiaputra

    Pages 285-310

19. Color differential structure

    • Jan-Mark Geusebroek, Bart M. ter Haar Romeny, Jan J. Koenderink, Rein van den Boomgaard, Peter Van Osta

    Pages 311-327

20. Steerable kernels

    Pages 329-343

Many approaches have been proposed to solve the problem of finding the optic flow field of an image sequence. Three major classes of optic flow computation techniques can discriminated (see for a good overview Beauchemin and Barron IBeauchemin19951): gradient based (or differential) methods; phase based (or frequency domain) methods; correlation based (or area) methods; feature point (or sparse data) tracking methods; In this chapter we compute the optic flow as a dense optic flow field with a multi scale differential method. The method, originally proposed by Florack and Nielsen [Florack1998a] is known as the Multiscale Optic Flow Constrain Equation (MOFCE). This is a scale space version of the well known computer vision implementation of the optic flow constraint equation, as originally proposed by Horn and Schunck [Horn1981]. This scale space variation, as usual, consists of the introduction of the aperture of the observation in the process. The application to stereo has been described by Maas et al. [Maas 1995a, Maas 1996a]. Of course, difficulties arise when structure emerges or disappears, such as with occlusion, cloud formation etc. Then knowledge is needed about the processes and objects involved. In this chapter we focus on the scale space approach to the local measurement of optic flow, as we may expect the visual front end to do. 17. 2 Motion detection with pairs of receptive fields As a biologically motivated start, we begin with discussing some neurophysiological findings in the visual system with respect to motion detection.

• computer vision
• Diffusion
• image analysis
• kernel
• knowledge
• Pattern Matching
• tracking

• Fac. Biomedical Engineering Dept. Image Analysis & Interpretation, Eindhoven University of Technology, MB Eindhoven, Netherlands

  Bart M. Romeny

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