Frei-Chen operator

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

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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

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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

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Here, frie-chen operator, along with three different gradient operators is used to detect edges in the test image.

See also

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References

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  1. ^ 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.