In
computer vision
Computer vision is an interdisciplinary scientific field that deals with how computers can gain high-level understanding from digital images or videos. From the perspective of engineering, it seeks to understand and automate tasks that the hum ...
, the Marr–Hildreth algorithm is a method of
detecting edges in
digital image
A digital image is an image composed of picture elements, also known as ''pixels'', each with ''finite'', '' discrete quantities'' of numeric representation for its intensity or gray level that is an output from its two-dimensional functions ...
s, that is, continuous curves where there are strong and rapid variations in image brightness.
The Marr–Hildreth edge detection method is simple and operates by convolving the image with the
Laplacian
In mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a scalar function on Euclidean space. It is usually denoted by the symbols \nabla\cdot\nabla, \nabla^2 (where \nabla is the ...
of the
Gaussian function
In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function of the base form
f(x) = \exp (-x^2)
and with parametric extension
f(x) = a \exp\left( -\frac \right)
for arbitrary real constants , and non-zero . It is n ...
, or, as a fast approximation by
difference of Gaussians In imaging science, difference of Gaussians (DoG) is a feature enhancement algorithm that involves the subtraction of one Gaussian blurred version of an original image from another, less blurred version of the original. In the simple case of grays ...
. Then,
zero crossing
A zero-crossing is a point where the sign of a mathematical function changes (e.g. from positive to negative), represented by an intercept of the axis (zero value) in the graph of the function. It is a commonly used term in electronics, mathemat ...
s are detected in the filtered result to obtain the edges. The Laplacian-of-Gaussian image operator is sometimes also referred to as the
Mexican hat wavelet
In mathematics and numerical analysis, the Ricker wavelet
:\psi(t) = \frac \left(1 - \left(\frac\right)^2 \right) e^
is the negative normalizing constant, normalized second derivative of a Gaussian function, i.e., up to scale and normalization, t ...
due to its visual shape when turned upside-down.
David Marr and
Ellen C. Hildreth are two of the inventors.
Limitations
The Marr–Hildreth operator suffers from two main limitations. It generates responses that do not correspond to edges, so-called "false edges", and the localization error may be severe at curved edges. Today, there are much better edge detection methods, such as the
Canny edge detector
The Canny edge detector is an edge detection operator that uses a multi-stage algorithm to detect a wide range of edges in images. It was developed by John F. Canny in 1986. Canny also produced a ''computational theory of edge detection'' explain ...
based on the search for local directional maxima in the gradient magnitude, or the differential approach based on the search for zero crossings of the differential expression that corresponds to the second-order derivative in the gradient direction (both of these operations preceded by a Gaussian smoothing step). For more details, see the article on
edge detection
Edge detection includes a variety of mathematical methods that aim at identifying edges, curves in a digital image at which the image brightness changes sharply or, more formally, has discontinuities. The same problem of finding discontinuitie ...
.
See also
*
Blob detection
In computer vision, blob detection methods are aimed at detecting regions in a digital image that differ in properties, such as brightness or color, compared to surrounding regions. Informally, a blob is a region of an image in which some propert ...
*
CVIPtools
CVIPtools (Computer Vision and Image Processing Tools) is an Open Source image processing software. It is free for use with Windows, and previous versions are available for UNIX. It is an interactive program for image processing and computer visio ...
References
{{DEFAULTSORT:Marr-Hildreth algorithm
Feature detection (computer vision)