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Laplacian edge enhancement emphasizes all edges present regardless of orientation. It is a sharpening process variant. Sharpening therefore adds the Laplacian output to the original image. Laplacian filters follow:
| –1 | –1 | –1 |
| –1 | 8 | –1 |
| –1 | –1 | –1 |
| 1 | –2 | 1 |
| –2 | 4 | –2 |
| 1 | –2 | 1 |
| 0 | –1 | 0 |
| –1 | 4 | –1 |
| 0 | –1 | 0 |
Sometimes image data is corrupted and lost, for example, during transmission from satellites to ground stations. The lost data often appears as visually obvious incorrect pixel intensities. In certain instances, it is possible to approximate corrupted pixel values using valid pixel values for pixels surrounding the corrupted pixel value. The basic problem is how to devise algorithms that automatically detect pixels that have corrupted values.
Usually in a pixel-by-pixel operation, an algorithm uses surrounding pixels to calculate a figure of merit which is compared to the pixel value under scrutiny. If the pixel value exceeds the figure of merit by some arbitrary measure, then the output value is computed using the surrounding input pixel values rather than the actual pixel value under scrutiny.
For example, at every input pixel position, one approach averages the eight adjacent pixels surrounding input pixels and calculates the standard deviation. This is the equivalent of a spatial low-pass filter with a central weight equal to zero. If the suspect pixel value is more than one standard deviation from the calculated mean, then the output value for that pixel position is the mean. Otherwise, it is the input pixel value.
Sometimes it is possible to capture multiple images of a scene before the scene changes or the camera moves. In such cases, it is possible to average valid pixel values point by point and divide by the number of pixel values summed. The corrupting noise varies randomly at each pixel position but the average tends towards the true pixel values. This is because random pixel intensity decreases cancel out to some degree when added to random intensity increases.
The median filter technique sorts each pixel position value with the various pixel values surrounding the point under scrutiny. It then selects the median (middle) value as the output value. The median filter works because noisy pixels tend to have values that are extremely high or low when compared with the neighboring values. The median (mid-range) of the pixel and neighboring values reject extreme values.
The techniques this chapter discusses cannot be used on individual RGB component planes without introducing noticeable color inaccuracies in the final image. To use the techniques on color images first requires separating the intensity information from the chromaticity information and performing the operation on the derived achromatic image.
After performing the enhancement operation on the achromatic pixel information, on a pixel-by-pixel basis, divide the original achromatic intensity value by the derived output intensity value and use the quotient to scale the individual original RGB components. This preserves color information while modifying the intensity values in accordance with the enhancement strategy. The VESAPCX.C sample program in Chapter 17 sharpens 24-bit images using this linear scaling technique.
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