Edge detection by Marr and Hildreth's Method

So for we discussed edge det. algos that produce one edge map from an i/p image.

Marr and Hildreth observed that significant intensity changes occur at different scales (resolutions) in an image. For eg blurry shadowy regions and sharply focused fine detail may be present in the same image. "Optimal" detection of significant intensity changes. It generally requires the use of operators that respond to several different scales.

Marr and Hildreth suggested that the original image be bandlimited at several cut of frequency and that an edge det algorithm be applied to each of the images. The resulting edge maps have edges corresponding to different res.

Marr and Hildreth suggested that the original image be bandlimited at several cut of frequency and that an edge det algorithm be applied to each of the images. The resulting edge maps have edges corresponding to different us. To bandlimit an image at different cut off frequencies the impulse response and frequency response of LPF proposed is Gaussian shaped and is given by,

where determines the cut off frequency; with larger corresponding to lower cut off frequency.

The choice of Gaussian shape is motivation by the fact that it is smooth and localized in both the spatial and frequency domains.

A smooth is less likely to introduce any changes that are not present in the original shape. A more localized is less likely to shift the location of edges.

Marr and Hildreth argue that edge maps of different scales contain important information about physically significant parameters. The visual world is made of elements such as contours, scratches & shadows which are highly localized at their own scale. This localization is also reflected in such physically important changes as reflectance change & illumination change. If the same edge is present in a set of edge maps of different scale it represents the presence of an image intensity change due to a single physical phenomena.

(continued in the next slide)