Understanding image structure from a new multi-scale representation of higher order derivative filters

We are proposing a biologically inspired multi-scale derivative filter in which the higher order derivatives are expressed as a linear combination of a smoothing function at various scales. One of the functions in the summation has been approximated to a Dirac-delta function to finally yield the new filter. This modification has some support from the point of view of authentic edge detection as well as from neurophysiological and psychophysical experiments at the retinal level. Besides, it improves the quality of the filter in a number of ways. The proposed filter can be optimized at any desired scale. Hence it is very effective in extracting the features from a noisy picture. The filter is rotationally symmetric. Zero-crossing map of any picture filtered with the proposed model gives a half-toning effect to the retrieved image and hence preserves the intensity information in the image even in the edge map.