Identification of Partially Obscured Objects in Two Dimensions By Matching of No
Identification of Partially Obscured Objects in Two Dimensions By Matching of No
Jacob T Schwartz
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Moreover, if the observed points did lie exactly on the surface P(Ex)=0, then the minimizing Q in (1*) would clearly be Q(x) = P(Ex), so that once having the coefficients of Q we could expect to calculate E in straightforward fashion. (Suppose, for example, that the polynomial P is of even order. The rotational part R of E acts independently of £'s translational part on the highest order terras of P. If P is quadratic, R can be determined from Q by finding the principal axes of (2's purely quad...ratic part and matching them with the corresponding axes for P. If P is of higher degree, we can apply the Laplacian operator A, which is rotationally invariant, to the highest order terras of both P and Q just often enough to produce two quadratic polynomials, and then match principal axes as before. Next suppose that the principal terms of P are cubic. In this case, we can associate an orthogonal set of 'principal axes' with P in the following way. Take AP, which is linear, and take the vector v ; orthogonal to the plane ikP-0.
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