## Local Operators

Local operators enhance the image by providing a new value for each pixel in a manner that depends only on that pixel and others in a neighborhood around it. Many local operators are linear spatial filters implemented with a kernel convolution, some are nonlinear operators, and others impart histogram equalization within a neighborhood. In this section we present a set of established standard filters commonly used for enhancement. These can be easily extended to obtain slightly modified results by increasing the size of the neighborhood while maintaining the structure and function of the operator.

### 4.1 Noise Suppression by Mean Filtering

Mean filtering can be achieved by convolving the image with a (2K + 1x2L + 1) kernel where each coefficient has a value equal to the reciprocal of the number of coefficients in the kernel. For example, when L = K = l, we obtain

referred to as the 3x3 averaging kernel or mask. Typically, this type of smoothing reduces noise in the image, but at the expense of the sharpness of edges [4, 5, 12, 13]. Examples of the application of this kernel are seen in Fig. 4(a-d). Note that the size of the kernel is a critical factor in the successful application of this type of enhancement. Image details that are small relative to the size of the kernel are significantly suppressed, while image details significantly larger than the kernel size are affected moderately. The degree of noise suppression is related to the size of the kernel, with greater suppression achieved by larger kernels.

### 4.2 Noise Suppression by Median Filtering

Median filtering is a common nonlinear method for noise suppression that has unique characteristics. It does not use convolution to process the image with a kernel of coefficients. Rather, in each position of the kernel frame, a pixel of the input image contained in the frame is selected to become the output pixel located at the coordinates of the kernel center. The kernel frame is centered on each pixel (m, n) of the original image, and the median value of pixels within the kernel frame is computed. The pixel at the coordinates (m, n) of the output image is set to this median value. In general, median filters do not have the same smoothing characteristics as the mean filter [4, 5, 8, 9, 15]. Features that are smaller than half the size of the median filter kernel are completely removed by the filter. Large discontinuities such as edges and large changes in image intensity are not affected in terms of gray level intensity by the median filter, although their positions may be shifted by a few pixels. This nonlinear operation of the median filter allows significant reduction of specific types of noise. For example, "shot noise" may be removed completely from an image without attenuation of significant edges or image characteristics. Figure 5 presents typical results of median filtering.

### 4.3 Edge Enhancement

Edge enhancement in images is of unique importance because the human visual system uses edges as a key factor in the comprehension of the contents of an image [2, 4, 5, 10,13, 14]. Edges in different orientations can be selectively identified and

FIGURE 3 (a) Original image where gray levels are not uniformly distributed. Many image details are not well visualized in this image because of the low contrast. (b) Histogram of the original image in (a). Note the nonuniformity of the histogram. (c) Cumulative histogram of the original image in (a). (d) Histogram-equalized image. Contrast is enhanced so that subtle changes in intensity are more readily observable. This may allow earlier detection of pathological structures. (e) Histogram of the enhanced image in (d). Note that the distribution of intensity counts that are greater than the mean value have been distributed over a larger gray level range. (f) Cumulative histogram of the enhanced image in (d). (g) Original brain MRI image (courtesy of Dr. Christos Dzavatzikos, Johns Hopkins Radiology Department). (h) through (l) same steps as above for brain image.

FIGURE 3 (a) Original image where gray levels are not uniformly distributed. Many image details are not well visualized in this image because of the low contrast. (b) Histogram of the original image in (a). Note the nonuniformity of the histogram. (c) Cumulative histogram of the original image in (a). (d) Histogram-equalized image. Contrast is enhanced so that subtle changes in intensity are more readily observable. This may allow earlier detection of pathological structures. (e) Histogram of the enhanced image in (d). Note that the distribution of intensity counts that are greater than the mean value have been distributed over a larger gray level range. (f) Cumulative histogram of the enhanced image in (d). (g) Original brain MRI image (courtesy of Dr. Christos Dzavatzikos, Johns Hopkins Radiology Department). (h) through (l) same steps as above for brain image.

FIGURE 3 (Continued).
FIGURE 3 (Continued).

enhanced. The edge-enhanced images may be combined with the original image in order to preserve the context. Horizontal edges and lines are enhanced with

wH1(k, 0 = 4 o 0 M or wH2(k, 9 = < 000 1 1 1 111

and vertical edges and lines are enhanced with

0 0