Because of this, the zero-crossing segments from the different channels are not independent, and rules are deduced for combining them into a description of the image. (2) Intensity changes in images arise from surface discontinuities or from reflectance or illumination boundaries, and these all have the property that they are spatially localized. The intensity changes thus discovered in each of the channels are then represented by oriented primitives called zero-crossing segments, and evidence is given that this representation is complete. Thus, intensity changes at a given scale are best detected by finding the zero values of ∇ 2 G(x, y)* I(x, y) for image I, where G(x, y) is a two-dimensional Gaussian distribution and ∇ 2 is the Laplacian. An appropriate filter for this purpose at a given scale is found to be the second derivative of a Gaussian, and it is shown that, provided some simple conditions are satisfied, these primary filters need not be orientation-dependent. (1) Intensity changes, which occur in a natural image over a wide range of scales, are detected separately at different scales.
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