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In mathematical morphology, the h-maxima transform is a morphological operation used to filter local maxima of an image based on local contrast information. First, all local maxima are defined as connected pixels in a given neighborhood with intensity level greater than pixels outside the neighborhood.
In numerical analysis, a quasi-Newton method is an iterative numerical method used either to find zeroes or to find local maxima and minima of functions via an iterative recurrence formula much like the one for Newton's method, except using approximations of the derivatives of the functions in place of exact derivatives.
Once DoG images have been obtained, keypoints are identified as local minima/maxima of the DoG images across scales. This is done by comparing each pixel in the DoG images to its eight neighbors at the same scale and nine corresponding neighboring pixels in each of the neighboring scales.
A surface with two local maxima. (Only one of them is the global maximum.) If a hill-climber begins in a poor location, it may converge to the lower maximum. Hill climbing will not necessarily find the global maximum, but may instead converge on a local maximum. This problem does not occur if the heuristic is convex.
In mathematical optimization, the method of Lagrange multipliers is a strategy for finding the local maxima and minima of a function subject to equation constraints (i.e., subject to the condition that one or more equations have to be satisfied exactly by the chosen values of the variables). [1]
However, in some cases, it can be advantageous to apply a different threshold to different parts of the image, based on the local value of the pixels. This category of methods is called local or adaptive thresholding. They are particularly adapted to cases where images have inhomogeneous lighting, such as in the sudoku image on the right.
Global optimization is distinguished from local optimization by its focus on finding the minimum or maximum over the given set, as opposed to finding local minima or maxima. Finding an arbitrary local minimum is relatively straightforward by using classical local optimization methods. Finding the global minimum of a function is far more ...
It can be theoretically shown that a scale selection module working according to this principle will satisfy the following scale covariance property: if for a certain type of image feature a local maximum is assumed in a certain image at a certain scale , then under a rescaling of the image by a scale factor the local maximum over scales in the ...