Axial representations of shape
Computer Vision, Graphics, and Image Processing
Computer Vision, Graphics, and Image Processing
On characterizing ribbons and finding skewed symmetries
Computer Vision, Graphics, and Image Processing
The image processing handbook (2nd ed.)
The image processing handbook (2nd ed.)
Zoom-invariant vision of figural shape: the mathematics of cores
Computer Vision and Image Understanding
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A Blum ribbon is a figure whose boundary is the envelope of afamily of circles the centers of which lie along a singleunbranched curve called its medial axis. Define a Blum ribbon tobe simple if its medial axis is the line segment joining points(0,0) and (1,0). Any Blum ribbon can be made simple by flexingthe medial axis, rotating, then dilating, all of which are basictransformations in Blum‘s geometry of shape. The Lie groupSL(2, R) acts on circles centered on the x-axis bylinear fractional transformations. By means of this action it ispossible to associate to any simple Blum ribbon a curve inSL(2, R). A distance between corresponding points lyingon such curves is defined using the bi-invariant metric onSL(2, R). Resulting scale-invariant metrics on the setof figures defined as Blum ribbons are described and it is shownthat these metrics can provide effective measures of shapedifference.