2011 | OriginalPaper | Chapter
Quadratic Optimization and Contour Grouping
Activate our intelligent search to find suitable subject content or patents.
Select sections of text to find matching patents with Artificial Intelligence. powered by
Select sections of text to find additional relevant content using AI-assisted search. powered by
This chapter presents a new and exciting application of quadratic optimization methods to the problem of contour grouping in computer vision. It turns out that this problem leads to finding the local maxima of a Hermitian matrix depending on a parameter. We are thus led to the problem of finding the derivative of an eigenvalue and the derivative of some eigenvector associated with this eigenvalue, in the case of a normal matrix. The problem also leads naturally to the consideration of the field of values of a matrix, a concept studied as early as 1918 by Toeplitz and Hausdorff. We prove that the field of values is convex, a theorem due to Toeplitz and Hausdorff. This fact is helpful in improving the search for local maxima.