Ebook: Front-End Vision and Multi-Scale Image Analysis: Multi-Scale Computer Vision Theory and Applications, written in Mathematics

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.

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Front-End Vision and Multi-Scale Image Analysis is a tutorial in multi-scale methods for computer vision and image processing. It builds on the cross fertilization between human visual perception and multi-scale computer vision (`scale-space') theory and applications. The multi-scale strategies recognized in the first stages of the human visual system are carefully examined, and taken as inspiration for the many geometric methods discussed. All chapters are written in Mathematica, a spectacular high-level language for symbolic and numerical manipulations.

The book presents a new and effective approach to quickly mastering the mathematics of computer vision and image analysis. The typically short code is given for every topic discussed, and invites the reader to spend many fascinating hours `playing' with computer vision.

Front-End Vision and Multi-Scale Image Analysis is intended for undergraduate and graduate students, and all with an interest in computer vision, medical imaging, and human visual perception.

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Front-End Vision and Multi-Scale Image Analysis is a tutorial in multi-scale methods for computer vision and image processing. It builds on the cross fertilization between human visual perception and multi-scale computer vision (`scale-space') theory and applications. The multi-scale strategies recognized in the first stages of the human visual system are carefully examined, and taken as inspiration for the many geometric methods discussed. All chapters are written in Mathematica, a spectacular high-level language for symbolic and numerical manipulations.

The book presents a new and effective approach to quickly mastering the mathematics of computer vision and image analysis. The typically short code is given for every topic discussed, and invites the reader to spend many fascinating hours `playing' with computer vision.

Front-End Vision and Multi-Scale Image Analysis is intended for undergraduate and graduate students, and all with an interest in computer vision, medical imaging, and human visual perception.

Content:
Front Matter....Pages i-xviii
Apertures and the notion of scale....Pages 1-12
Foundations of scale-space....Pages 13-36
The Gaussian kernel....Pages 37-51
Gaussian derivatives....Pages 53-69
Multi-scale derivatives: implementations....Pages 71-89
Differential structure of images....Pages 91-136
Natural limits on observations....Pages 137-141
Differentiation and regularization....Pages 143-152
The front-end visual system — the retina....Pages 153-165
A scale-space model for the retinal sampling....Pages 167-177
The front-end visual system — LGN and cortex....Pages 179-195
The front-end visual system — cortical columns....Pages 197-213
Deep structure I. watershed segmentation....Pages 215-240
Deep structure II. catastrophe theory....Pages 241-256
Deep structure III. topological numbers....Pages 257-276
Deblurring Gaussian blur....Pages 277-284
Multi-scale optic flow....Pages 285-310
Color differential structure....Pages 311-327
Steerable kernels....Pages 329-343
Scale-time....Pages 345-360
Geometry-driven diffusion....Pages 361-391
Epilog....Pages 393-394
Back Matter....Pages 395-466