Scale Space

Often the linear scale space is built as a preprocessing step in image processing. This scale space is based on the linear diffusion equation. The aim is to generate versions of the image at different scales. At these scales different levels of detail become explicit. Recently more versatile scale spaces have been studied: The scale space based on non-linear diffusion, the data sieve based on median filters with growing support, and several morphological scale spaces based on erosions and dilations.

The following examples illustrate the use of the scale space for edge detection. On each scale the zerocrossings of the Laplaciaan filtered image weighted with the output of the Sobel operator are calculated. The resulting images of scale space are shown by displaying one image after the other in an MPEG-encoded sequence. The scale increases as the sequence evolves. In the scale space based on linear diffusion calculated on the image lena the noise is filtered out as the scale increases but the edges also faint. In the scale space based on non-linear diffusion calculated on the same image the noise is also filtered out as the scale increases and strong edges are preserved.


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