Transforms {Hilbert transform} can be for one-dimensional signals.
Features have parameters, such as length, angle, color, distance, radius, and angle. Parameters have continuous-value ranges, such as lengths from millimeters to meters, or discrete-value sets, such as color categories. Features have parameter values that make vectors. For example, if parameter number is four, features have four-vectors, such as (0, 0, 0, 0), (3, 0, 0, 0), or (4, 2, 1, 3).
space
Hough spaces have dimension number equal to parameter number. In the example, Hough space has four coordinates. Hough space points can represent features.
feature extraction
Objects whose feature vector lies near feature point have that feature.
feature extraction: accumulator
Feature extraction can use voting {Hough transform}, to accumulate weights at feature points in Hough space {accumulator space} (Paul Hough) [1962]. After voting, if weight passes threshold at feature point, image has feature.
lines
Parameterized standard line, circle, or ellipse test sets establish feature-point coordinates in accumulator space. For lines, accumulator space can use polar-coordinate radius and angle. Edge-detector algorithms can pre-process images to find edges. Hough transforms can group edge points into lines, circles, or ellipses for identification (Richard Duda and Peter Hart) [1972] (Dana H. Ballard) [1981].
Transforms {pyramid transform} can be for three-dimensional signals and takes high-resolution images and makes low-resolution images.
One-dimensional Hilbert transforms {Radon transform}, at specific orientations, can transform multi-dimensional signals.
Transforms {Riesz transform} can be for two-dimensional signals.
3-Computer Science-Systems-Computer Vision-Algorithms
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Date Modified: 2022.0225