The second order local-image-structure solid.
IEEE Transactions on Pattern Analysis and Machine Intelligence
1355 - 1366.
Available under License : See the attached licence file.
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.
|Title:||The second order local-image-structure solid|
|Open access status:||An open access version is available from UCL Discovery|
|Additional information:||© 2007 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.|
|Keywords:||scale space, image derivatives, feature analysis, noise, natural images, PRIMARY VISUAL-CORTEX, NATURAL IMAGES, DIFFERENTIAL STRUCTURE, SCALE-SPACE, STATISTICS, CONTRAST, DIVERGENCE, SURFACE, FILTERS|
|UCL classification:||UCL > School of BEAMS > Faculty of Engineering Science > Computer Science|
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