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Edge enhancement, using transform of subtracted smoothing image

F. Cheevasuvit, K. Dejhan,A. Somboonkaew
Faculty of Engineering, King Mongkut’s Institute of Technology
Ladkrabang, Ladkrabag, Bangkok 10520, Thailand.


Abstract
The detail of edges in an image can be obtained by subtracting a smoothed image from the original. Since the resultant subtracted image contains not only the real edges, but also the spurious edges. The eliminate these spurious edges, the inverse Butterworth transform function has been proposed in this paper to transform the subtracted image. Therefore, an edge enhancement image can be performed by adding back the transformed image to the original.

Introduction
The satellite images always have low contrast, by consequence, the difficulty will be appeared in image interpretation. Therefore, the edge enhancement technique has been used to overcome this problem. The aim of edge enhancement. is to modify the appearance of an image to make it visually more attractive or to improve the visibility of certain features [1]. The edge enhancement technique leads to enhance all high spatial frequency detail in an image including edges, lines and points of high gradients [2]. The subtractive smoothing method has been used as the simplest way to obtain high spatial frequency image. By this method the detail of edges in the image can be performed by subtracting a smoothed image from the original. Some smoothing templates as shown in Fig. I will be selected for the convolution operation which will give a smoothed image. The smoothing process smoothes the detail in the image and also reduces the image contrast. These effects will cause the attenuation of high spatial frequency components. in the image. Therefore, the resultant smoothed image becomes blurred.


Then, the subtraction of smoothed image from the original gives an image with only edge detail. Thus, the edge enhancement image can be achieved by adding back the subtracted image back to the original. The block diagram of edge enhancement process as mentioned above can be shown as in the Fig. 2, while the Fig. 3 presents the resultant example result of edge enhancement image.


Fig. 2 Block diagram of edge enhancement by subtractive smoothing

Since the subtracted image contains not only the real edges but also the spurious edges. These spurious edges will increase the brightness of the enhanced image. Therefore, the high efficacious interpretation can not obtain unless the spurious edges are removed. To eliminate the spurious edges, the inverse Butterworth transform function has been proposed which described in the next paragraph.


Fig. 3 Example of edge enhancement , image for LANDSAT Band 7 over the Bangkok area.

Inverse Butterworth transform function
The spurious edges, in general , will appear in the homogeneous region of the original image. So the spurious edge pixel has a low value in the subtracted image, while the real edge pixel has a higher value. To remove the spurious edges, the inverse Butterworth function has been proposed. This subtracted value will be magnified. The Butterworth function can be written as the following equation.


Where j is a subtracted value Go is the cutoff value and k is the flatness order. The inverse Butterworth function can be obtained by equation (2)



This function will be used as a look up table for removing the spurious edges and magnified the real edges. The characteristic of these function are shown in Fig. 4.


Fig 4. Characteristic of the trasform functions

from equation (1) and (2), we found that as the flatness value (k) increases the more sperious edge will be removed . While the value of Go will be effected to the transform slope.

This inverse Butterworth transform function will be applied to the subtracted image. Therefore, the edge enhancement can be performed by adding back the transform subtracted image to the original image. The proposed technique can be shown as the block diagram of fig. 5, while the example result of edge enhancement image is shown in Fig. 6.


Fig. 5 Block diagram for removing the spurious edges.


Fig. 6 Edge enhancement by transform subtractive smoothing.

Conclusion
The inverse Butterworth transform function has been proposed for removing the spurious edges in the subtracted image while the real edges still preserving. The edge enhancement image is then performed by adding the transform subtracted image back to the original . This algorithm implements a high spatial frequency components boosting. Therefore, by using this enhanced image, the interpretation can be accomplished with efficiency and the analysis of image will be easier for a human observer

Reference
  1. R. Lewis, “Practical Digital Image Processing”, Ellis Horwood Limited, Simon & Schuster International Group, 1990.
  2. J.A. Richards, “Remote Sensing Digital Image Analysis: An introduction”, Springer-Verlag, 1986.
  3. R.A. Schowengerdt. “Techniques for Image Processing and Classification in Remote Sensing”, Academic Press, Inc., 1983.
  4. R.M. Hord. “Digital Image Processing of Remotely Sensed Data”, Academic Press, Inc., 1982.