Journal
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
Volume 29, Issue 8, Pages 1355-1366Publisher
IEEE COMPUTER SOC
DOI: 10.1109/TPAMI.2007.1066
Keywords
scale space; image derivatives; feature analysis; noise; natural images
Funding
- Engineering and Physical Sciences Research Council [EP/D030978/1] Funding Source: researchfish
- EPSRC [EP/D030978/1] Funding Source: UKRI
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Characterization of second order local image structure by a 6D vector ( or jet) of Gaussian derivative measurements is considered. We consider the affect on jets of a group of transformations - affine intensity-scaling, image rotation and reflection, and their compositions - that preserve intrinsic image structure. We show how this group stratifies the jet space into a system of orbits. Considering individual orbits as points, a 3D orbifold is defined. We propose a norm on jet space which we use to induce a metric on the orbifold. The metric tensor shows that the orbifold is intrinsically curved. To allow visualization of the orbifold and numerical computation with it, we present a mildly-distorting but volume-preserving embedding of it into euclidean 3-space. We call the resulting shape, which is like a flattened lemon, the second order local-image-structure solid. As an example use of the solid, we compute the distribution of local structures in noise and natural images. For noise images, analytical results are possible and they agree with the empirical results. For natural images, an excess of locally 1D structure is found.
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