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Second, all local maxima that have height lower or equal to a given threshold are suppressed. The height f of the remaining maxima is decreased by h {\displaystyle h} . The h-maxima transform is defined as the reconstruction by dilation of f {\displaystyle f} from f − h {\displaystyle f-h} :
Fermat's theorem is central to the calculus method of determining maxima and minima: in one dimension, one can find extrema by simply computing the stationary points (by computing the zeros of the derivative), the non-differentiable points, and the boundary points, and then investigating this set to determine the extrema.
Feature enhancement in an image (St Paul's Cathedral, London) using Phase Stretch Transform (PST). Left panel shows the original image and the right panel shows the detected features using PST. The phase stretch transform or PST is a physics-inspired computational approach to signal and image processing. One of its utilities is for feature ...
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.
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.
Maritime scenes of optical aerial images from the visible spectrum. It contains color images in dynamic marine environments, each image may contain one or multiple targets in different weather and illumination conditions. Object bounding boxes and labeling. 7389 Images Classification, aerial object detection 2018 [162] [163] A.-J. Gallego et al.
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]