Numerical Recipes / Multidimensional Root Search (using newt): How to Minimize Maximum Error

This question is related to the book "numerical recipes in C ++", so it will be reserved for people who know a little about it, as well as multidimensional optimization.

I am writing a program that should search for a multidimensional root, and to solve it I use the multidimensional method of finding newton roots, namely the "newt" procedure.

For those who are interested in details, I am trying to adjust the deformable three-dimensional model to the stereoscopic view of the object, based on several features (features that are visible with two cameras).

To do this, I use the newt procedure with the following:

  • 11 Input parameters: my deformable model can be modeled with 11 parameters (consisting of 5 geometric parameters and 6 degrees of freedom for placing a 3D object):
  • 14 Output parameters for which I need to find the root: based on the points of the function that are identified by the camera and given a set of “input parameters”, I can calculate the set of distances between the points of the object visible to the camera and their theoretical position. I have 7 of these points, so this gives me 14 parameters (7 distances 2 times, since I calculate the distances on both cameras).

, (14), (11): , "newt", , , 11 , 3 .

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:

  • 14 11 ( , , , ). 100% .
  • :
    • mnewt
    • 14
    • mnewt
    • -

- , , , , ?

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F(x) f(x)=0, x - m- , f n- . , m < n ( 11 14).

, x. , x^T A x + c f(x)^T f(x) x, c. A nxn . x, f(x)=0, .

., , .

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