In sketching a shape to be found in the database, a major problem is getting the relative geometry of pieces of a shape correct. The relative sizes and positions of pieces will usually be wrong, e.g., wheel sizes and locations, windshield location with respect to car front and back, etc. In searching the database for a match, this relative geometry inaccuracy cannot be compensated for by using affine-invariant match methods because the distortion is not global to the entire shape, it is semi-local and different for different pieces of a shape. Since, in general, we cannot count on the database preparation algorithms and the database querist to have the same concept of shape pieces and piece variability nor can we count on the querist being trained to use the database search conventions, we assume that the querist should be able to specify intra-shape piece variability in a convenient natural way. For exemple, a user is to sketch the hood and windshield region of a car, but is not sure of the height of the windshield -roof with respect to the car body, nor of the exact placing of the windshield nor the length of the roof. Consequently, the querist sketches two shapes with each shape being an extreme, and assumes the true shape is somewhere between.
The matching algorithm would then index into the database based not on Sketch 1 alone nor on Sketch 2 alone, but rather based on some function of these. Our first inclination is to use the line in coefficient space that is determined by these two points. Then the best point on the line is the projection, of the 3L IP fit to the true car data, onto the line. This is a trivial single-computation linear projection. To extend this to permit greater variability, 3 or more sketches of extreme shapes and the subspace they define will be studied for the purpose.
Morphing between two 4th degree implicit polinomials with linear and none-linear interpolations of polynomial coefficients.
Last updated: June 3, 1998
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