Gauss' Law in Image Processing and Analysis via Fast Numerical Calculation of Vector Fields
✍ Scribed by L. da Fontoura Costa
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 640 KB
- Volume
- 5
- Category
- Article
- ISSN
- 1077-2014
No coin nor oath required. For personal study only.
✦ Synopsis
his paper describes a numerical approach to the expedite calculation of vector ®elds in two-dimensional (2D) spaces and how it has allowed the eective application of Gauss' law in image analysis and computer vision. The adopted technique for calculation of vector ®elds consists of decomposing than in terms of two scalar sub®elds, which can then be obtained in terms of convolutions of the image with large templates, an operation that is eectively performed by the fast Fourier transform. The performance of the technique has been quanti®ed in terms of RMS error and execution time, yielding encouraging results. The application of Gauss' law to digital images has also been addressed. Eects implied by the spatial quantization inherent to digital images, which can severely constrain the representation of the circulation path considered in the Gauss' law, were experimentally investigated, and it has been veri®ed that biased results can be obtained for short circulation paths. A process for generating calibration curves helping to circumvent such a problem has also been described. The application of the developed framework in image analysis, more speci®cally for construction of quadtrees, is described, assessed, and illustrated with respect to real images. The extension of the techniques to general circulation paths is also brie¯y outlined.