Prewitt
Encyclopedia
The Prewitt operator is used in image processing
, particularly within edge detection
algorithms. Technically, it is a discrete differentiation operator, computing an approximation of the gradient
of the image intensity function. At each point in the image, the result of the Prewitt operator is either the corresponding gradient vector or the norm of this vector. The Prewitt operator is based on convolving the image with a small, separable, and integer valued filter in horizontal and vertical direction and is therefore relatively inexpensive in terms of computations. On the other hand, the gradient approximation which it produces is relatively crude, in particular for high frequency variations in the image.
of the image intensity at each point, giving the direction of the largest possible increase from light to dark and the rate of change in that direction. The result therefore shows how "abruptly" or "smoothly" the image changes at that point, and therefore how likely it is that that part of the image represents an edge, as well as how that edge is likely to be oriented. In practice, the magnitude (likelihood of an edge) calculation is more reliable and easier to interpret than the direction calculation.
Mathematically, the gradient
of a two-variable function (here the image intensity function) is at each image point a 2D vector with the components given by the derivative
s in the horizontal and vertical directions. At each image point, the gradient vector points in the direction of largest possible intensity increase, and the length of the gradient vector corresponds to the rate of change in that direction. This implies that the result of the Prewitt operator at an image point which is in a region of constant image intensity is a zero vector and at a point on an edge is a vector which points across the edge, from darker to brighter values.
with the original image to calculate approximations of the derivatives - one for horizontal changes, and one for vertical. If we define
as the source image, and 
and 
are two images which at each point contain the horizontal and vertical derivative approximations, the latter are computed as:
Image processing
In electrical engineering and computer science, image processing is any form of signal processing for which the input is an image, such as a photograph or video frame; the output of image processing may be either an image or, a set of characteristics or parameters related to the image...
, particularly within edge detection
Edge detection
Edge detection is a fundamental tool in image processing and computer vision, particularly in the areas of feature detection and feature extraction, which aim at identifying points in a digital image at which the image brightness changes sharply or, more formally, has discontinuities...
algorithms. Technically, it is a discrete differentiation operator, computing an approximation of the gradient
Image gradient
An image gradient is a directional change in the intensity or color in an image. Image gradients may be used to extract information from images....
of the image intensity function. At each point in the image, the result of the Prewitt operator is either the corresponding gradient vector or the norm of this vector. The Prewitt operator is based on convolving the image with a small, separable, and integer valued filter in horizontal and vertical direction and is therefore relatively inexpensive in terms of computations. On the other hand, the gradient approximation which it produces is relatively crude, in particular for high frequency variations in the image.
Simplified description
In simple terms, the operator calculates the gradientImage gradient
An image gradient is a directional change in the intensity or color in an image. Image gradients may be used to extract information from images....
of the image intensity at each point, giving the direction of the largest possible increase from light to dark and the rate of change in that direction. The result therefore shows how "abruptly" or "smoothly" the image changes at that point, and therefore how likely it is that that part of the image represents an edge, as well as how that edge is likely to be oriented. In practice, the magnitude (likelihood of an edge) calculation is more reliable and easier to interpret than the direction calculation.
Mathematically, the gradient
Gradient
In vector calculus, the gradient of a scalar field is a vector field that points in the direction of the greatest rate of increase of the scalar field, and whose magnitude is the greatest rate of change....
of a two-variable function (here the image intensity function) is at each image point a 2D vector with the components given by the derivative
Derivative
In calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a...
s in the horizontal and vertical directions. At each image point, the gradient vector points in the direction of largest possible intensity increase, and the length of the gradient vector corresponds to the rate of change in that direction. This implies that the result of the Prewitt operator at an image point which is in a region of constant image intensity is a zero vector and at a point on an edge is a vector which points across the edge, from darker to brighter values.
Formulation
Mathematically, the operator uses two 3×3 kernels which are convolvedConvolution
In mathematics and, in particular, functional analysis, convolution is a mathematical operation on two functions f and g, producing a third function that is typically viewed as a modified version of one of the original functions. Convolution is similar to cross-correlation...
with the original image to calculate approximations of the derivatives - one for horizontal changes, and one for vertical. If we define
as the source image, and and are two images which at each point contain the horizontal and vertical derivative approximations, the latter are computed as:Example
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See also
- Sobel operator
- Roberts CrossRoberts CrossThe Roberts' Cross operator is used in image processing and computer vision for edge detection. It was one of the first edge detectors and was initially proposed by Lawrence Roberts in 1963...
- edge detectionEdge detectionEdge detection is a fundamental tool in image processing and computer vision, particularly in the areas of feature detection and feature extraction, which aim at identifying points in a digital image at which the image brightness changes sharply or, more formally, has discontinuities...
- feature detection (computer vision)
- digital image processingDigital image processingDigital image processing is the use of computer algorithms to perform image processing on digital images. As a subcategory or field of digital signal processing, digital image processing has many advantages over analog image processing...
- computer visionComputer visionComputer vision is a field that includes methods for acquiring, processing, analysing, and understanding images and, in general, high-dimensional data from the real world in order to produce numerical or symbolic information, e.g., in the forms of decisions...
- feature extractionFeature extractionIn pattern recognition and in image processing, feature extraction is a special form of dimensionality reduction.When the input data to an algorithm is too large to be processed and it is suspected to be notoriously redundant then the input data will be transformed into a reduced representation...
- Image gradientImage gradientAn image gradient is a directional change in the intensity or color in an image. Image gradients may be used to extract information from images....