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Segmentation in Scale Space


Rolf D. Henkel

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Scale Space

It follows from these considerations that we can not circumvent the simultaneous application of global and local analysis. One hint how to combine both approaches can be obtained from biological vision systems. In these systems, a scene is examined with neurons having different sized receptive fields. For example, one finds within the tectum opticum of salamander many neurons with small, some neurons with larger receptive fields, and even a few neurons sensitive to the total visual field of the salamander [13]. Yet another hint comes from theoretical considerations about the scales of the image formation process. Trivially, an upper limit of resolution is given by the receptor spacing, and a lower limit of resolution by the size of the observation window. One nice way to interpolate between these different scales is to utilize the two-dimensional diffusion equation [3]. Starting from the data f(x,y), one creates a family of images f(x,y;t), where t measures scale, by setting f(x,y;t=0) = f(x,y) and using the diffusion equation

equation28

to obtain the images at coarser scales.

This diffusion process has a natural analog in the sampling of input space by neurons with different sized receptive fields. The solution f(x,y;t) of the diffusion equation at scale t can be obtained from f(x,y;t=0) through convolution with the gaussian kernel

equation32

Thus neurons with different receptive field sizes can be interpreted as sampling scale space at certain discrete points tex2html_wrap_inline359 .



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