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The Hough transform is a feature extraction technique used in image analysis, computer vision, pattern recognition, and digital image processing. [1] [2] The purpose of the technique is to find imperfect instances of objects within a certain class of shapes by a voting procedure.
The generalized Hough transform (GHT), introduced by Dana H. Ballard in 1981, is the modification of the Hough transform using the principle of template matching. [1] The Hough transform was initially developed to detect analytically defined shapes (e.g., line, circle, ellipse etc.). In these cases, we have knowledge of the shape and aim to ...
The circle Hough Transform (CHT) is a basic feature extraction technique used in digital image processing for detecting circles in imperfect images. The circle candidates are produced by “voting” in the Hough parameter space and then selecting local maxima in an accumulator matrix. It is a specialization of the Hough transform.
Alternative methods for scale-invariant object recognition under clutter / partial occlusion include the following. RIFT [38] is a rotation-invariant generalization of SIFT. The RIFT descriptor is constructed using circular normalized patches divided into concentric rings of equal width and within each ring a gradient orientation histogram is ...
Numerous methods exist to compute descent directions, all with differing merits, such as gradient descent or the conjugate gradient method. More generally, if P {\displaystyle P} is a positive definite matrix, then p k = − P ∇ f ( x k ) {\displaystyle p_{k}=-P\nabla f(x_{k})} is a descent direction at x k {\displaystyle x_{k}} . [ 1 ]
This gradient can then be manipulated directly to produce several different effects when the resulting image is solved for. For example, if a uniform constant scales the gradient, it results in a simple sharpening filter. A better sharpening filter can be made by only scaling the gradient in areas deemed important. [2]
A simple example is fitting a line in two dimensions to a set of observations. Assuming that this set contains both inliers, i.e., points which approximately can be fitted to a line, and outliers, points which cannot be fitted to this line, a simple least squares method for line fitting will generally produce a line with a bad fit to the data including inliers and outliers.
As with the conjugate gradient method, biconjugate gradient method, and similar iterative methods for solving systems of linear equations, the CGS method can be used to find solutions to multi-variable optimisation problems, such as power-flow analysis, hyperparameter optimisation, and facial recognition. [8]