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 human ...

, 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 ...

, or, as a fast approximation by difference of Gaussians. 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, mathem ...

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'' explai ...

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 ...

References

{{DEFAULTSORT:Marr-Hildreth algorithm Feature detection (computer vision)

Limitations

See also

References