Refine: Iterative Search

Abstract

The role of search is to find the optimal set of pose parameters S* which minimize the error function of a given scene:

$$ \forall b:\varepsilon ({S^*}) < \varepsilon ({S^b})\;where\;{S^*} \ne {S^b} $$

(5.1)

Chapter 4 formulated an error function ε which is characterized by the following conditions:

• 1. The error function parameters are continuous and real valued. The number of possible scene configurations is therefore infinite.

• 2. An explicit analytic function for the error does not exist: no derivative of the function with respect to the pose parameters can be computed and traditional gradient descent methods, such as Newton-Raphson, are not appropriate.

• 3. The error surface for a given scene is not smooth and contains local minima.

• 4. Since pose parameters interact, search cannot optimize one parameter in isolation. For instance, solving for the depth of an object is not appropriate if the orientation is incorrect.

These characteristics imply search is difficult. Since traditional optimization techniques based upon analytic function optimization cannot be applied, heuristic techniques are examined.