The Frei–Chen operator, sometimes called Frei and Chen operator, is used in image processing for edge detection. It was proposed by Werner Frei and Chung-Ching Chen, researchers at USC's Image Processing Institute, in 1977. The idea is to use a set of orthogonal basis vectors related to distinctive image features, which enable the algorithm to extract boundary elements effectively.
Formulation The operator uses nine 3×3 kernels which are convolved with the original image to calculate the gradient.
We define the nine kernels as:
The pair is the isotropic average gradient The pair is used to detect ripples The pair is used to detect lines The pair is the discrete laplacian operator , the averaging operator, added to complete the basis are used for edges subspace, used for lines subspace and is used to compute averages
Let be the image sub-area, and be the angle (in space), is the number of orthogonal edge basis vectors spanning the edge subspace.
The larger , the poorer the fit between B and an element of the edge subspace.
The strategy is to classify image sub-area as containing and edge element only if is small which is done by thresholding.
Simple description The image is convolved with each of the kernel. Thus, 9 results are obtained.
Vectors are used for edge subspace identification. Hence numerator in the formula will be . Similarly, for line subspace identification, the numerator will be .
Using formula, we compute , if it is above a certain threshold , we say that an edge is detected in the image sub-area.
Example comparisons Here, the Frei–Chen operator, along with three different gradient operators is used to detect edges in the test image.
See also
Digital image processing
References