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Multi-scale feature detectionThe above-mentioned results serve as a formal and empirical justification for using Gaussian filtering followed by derivative computations as initial steps in early processing of image data. More important, a catalogue is provided of what smoothing kernels are natural to use, as well as a framework for relating filters of different types and at different scales. (Figure 4 shows a few examples of filter kernels from this filter bank.) Linear filtering, however, cannot be used as the only component in a vision system aimed at deriving symbolic representations from images; some non-linear processing steps must be introduced into the analysis. More concretely, some mechanism is required for combining the output of these Gaussian derivative operators of different orders and at different scales into more explicit descriptors of the image geometry.
An approach that has been advocated by Koenderink and his co-workers
is to describe image properties in terms of differential geometric
descriptors, i.e., different possibly non-linear
combinations of derivatives.
Since one would typically like image descriptors to possess
invariance properties under certain transformations
(typically, rotations, rescalings and affine or perspective deformations),
this naturally leads to the study of differential invariants [].
A major difference compared to traditional invariant theory, however,
is that the primitive derivative operators in this case are
smoothed derivatives computed from the scale-space representation.
Tony Lindeberg Tue Jul 1 14:57:47 MET DST 1997 |
