Frei-Chen operator
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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[1]. 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
[edit]The operator uses nine 3x3 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 orthgonal 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
[edit]The image is convoled 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
[edit]Here, frie-chen operator, along with three different gradient operators is used to detect edges in the test image.
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Grayscale test image of brick wall and bike rack
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Edge detection using Frie-Chen operator
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Edge detection using Roberts cross operator
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Edge detection using Prewitt operator
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Edge detection using Sobel operator
See also
[edit]References
[edit]- ^ Frei; Chung-Ching Chen (October 1977). "Fast Boundary Detection: A Generalization and a New Algorithm". IEEE Transactions on Computers. C-26 (10): 988–998. doi:10.1109/TC.1977.1674733. ISSN 0018-9340.