A7.2. Thresholding

Thresholding of an image is a preprocessing technique that segments a grey level array into a binary array containing "object" and "background" areas. In order to convert the input data into a binary representation, a threshold value, T, must be chosen. All grey scale values in the original array whose intensities are less than T are assigned an output value of 0 (black), while those whose intensities are greater or equal to T are assigned a value of 255 (white). The effectiveness of this technique is heavily dependent on the scene; it is useful in situations where there is good contrast between the object of interest and background. It is not an effective method of segmenting a complex scene or one in which the objects of interest are specular [WESZK78].

Choosing a value T to use as a threshold value varies among images, and a histogram of the image is required to choose that value. A histogram is a graph of the frequencies with which each grey level in the image occurs. In many images, the objects of interest fall in one range of grey levels while the background falls in another range. By choosing the threshold between the two peaks, good segmentation results have been obtained [ROSEN82].

A7.3. Contrast Enhancement

Contrast enhancement is a method used to improve the clarity of details in an image. Because of variable lighting conditions, especially in the environment of the space station, camera data is usually compressed either at the low end of the histogram (dark image) or at the high end (light image) (fig. A2). Histogram equalization is a technique that stretches high concentrations of grey levels while compressing less populated grey levels (fig. A3). It creates a transformation that enhances contrasts and brings out details in poorly contrasted or heavily shadowed portions of the image. [BALLA82].

The result of this transformation is to spread the grey level intensities more evenly throughout the image, sharpening details. A potential disadvantage of contrast stretching is that a global property of the image, the histogram, is used to generate a local operation. Therefore, when there is a large variation in the grey level values of the background, the equalization transform will tend to stretch the un-interesting ranges [INTEG81].

A7.4. Smoothing

Smoothing data is a preprocessing technique for enhancing the appearance of images by diminishing the effects of noise. It is a form of spatial integration. Although there are many benefits to be gained by removing image noise, smoothing tends to blur the original image and therefore to de-emphasize sharp edges and contours [ROSEN82]. There are many methods used for smoothing data: neighborhood averaging, edge preserving smoothing, low pass filtering, shrinking and expanding, pyramiding, etc. [BALLA82, GONZA77, ROSEN82]. These methods are discussed in this section.

A7.4.1. Averaging

Averaging is a technique for reducing spurious noise in an image. It can be considered to be a special case of low-pass spatial filtering (see sec. 3.3.4). Averaging can be done as either temporal integration over successive images or as spatial integration in a single image [ROSEN82]. Processing in the temporal domain is useful when there are multiple instances of the same scene, i.e. a stationary scene, and where the noise values present in the images are independent of each other and have a mean value of 0. For example, if there are n images of a single scene, 11, 12, ... I, each pixel in the averaged output image G is computed as:

The noise values in the input images will be blurred (the degree of blurring depends on the number of input images averaged) while the objects in the image remain unchanged. Averaging images in a moving environment produces more blur.

Averaging in a single image involves a local operation over neighborhoods in the image.

A neighborhood of a point is defined as those points surrounding the point (fig. A4).

n = the total number of points in the neighborhood of f(x,y)

f¡(x,y) = grey level of all points in the eight neighborhood of f(x,y) [GONZA77].

Neighborhood averaging is an effective method of reducing fine-grained noise but, depending on the size of the neighborhood being averaged, can result in an image where boundaries, as well as noise, are blurred. Averaging over larger neighborhoods produces greater blurring. This blurring effect can be reduced by combining the averaging operation with a thresholding operation. A point which differs by less than a specified threshold T from its averaged neighbors is left unchanged. Thus

if (f(x,y)- (Σf(n,m))/M >T)

else

g(x,y) = (Sf(n,m))/M

g(x,y) = f(x,y) [GONZA77].

A7.4.2. Edge Preserving Smoothing

Edge preserving smoothing is a technique which performs a local blurring on an image to suppress noise without blurring any edges that might be present in the image [ROSEN82, SINGH87]. Noise values are suppressed only at selected points. Implementation of this scheme is based on detecting edges and determining edge directions in the image and then performing an averaging operation on only non-edge pixels. This operation can be iterated to weaken noise without affecting edges.

A7.4.3. Median Filtering

Another smoothing technique which does not blur or smooth edges is median filtering. Rather than averaging the points in a neighborhood around a point f(x,y), the output value

g(x,y) is set equal to the median value of the points in the neighborhood. Because edge points are not weakened by this operation, the operation can be iterated a fixed number of times to reduce noise values to an acceptable level.

A7.4.4. Low-Pass Filtering

Low-pass filtering is a technique that uses information from the frequency domain to enhance information in the spatial domain. In the frequency domain, an image is grouped into different frequency band widths, each of which contains unique information. The Fourier Transform maps the spatial domain onto the spatio-frequency domain. It is defined as:

and its inverse

I [f (x,y)] = ssf(x,y) exp[-j2Ã(ux + vy)] dx dy

3-1[F(u,v)] = SS F(u,v) exp[j2П(ux + vy)] du dv where

x,y=image coordinates

u = frequency in the x direction

v = frequency in the y direction

The primary advantage of frequency domain processing is that any arbitrary frequency response is easy to implement. Because of the reversibility of the transform, many properties that are inherent to the frequency domain can be used in the spatial domain which is a more natural and intuitive representation. In the image representation, local operators can be applied to the image to attenuate or completely suppress information in all other frequencies [GONZA77]. Since edges and other sharp transitions contribute heavily to the high frequency portion of an image's Fourier Transform, the smoothing operation can be performed by attenuating a specified range of high frequency components. A low-pass filter is one which filters out high frequency information (edges) and passes low frequency information. This results in a blurred or smoothed image. A Gaussian convolution applied over all points in the image is an example of a low-pass filter which reduces noise in those parts of an image where there are no strong edges. A side effect of this operation is that portions of the image containing a large intensity gradient are also blurred.

A7.4.5. Binary Edge Smoothing

Noise removal in a binary image is a more simple operation than grey scale image smoothing. Because a thresholded image consists only of objects and background values, noise can be misinterpreted as "object" and therefore must be removed. One method of noise removal involves a shrinking and expanding operation [ROSEN82]. The shrinking operation examines the neighborhood of each black point in the image and changes its value to white if any neighbors are white.

else

g(x,y) = black.

The expanding operation performs the reverse operation:

if (f(x,y): == white) && ( f(n,m)== black)

else

g(x,y) = black

g(x,y) = white.

This process completely removes any noise value that is smaller than two pixels wide, and the expanding step restores larger objects without restoring the noise.

Frame grabbers that convert grey scale information into binary information often contain additional hardware that can filter noise in an image as it is being digitized. The removal of noise and the width of the noise to be suppressed is a user option sent to the framegrabber when the image is to be read.

A7.4.6. Multi-Resolution Processing

Multi-resolution processing or image pyramids offer additional methods for image enhancement. A pyramid is an "image data structure consisting of the same image at several successively decreasing levels of resolution" [BALLA82]. The image at each level of the pyramid is formed by replacing each neighborhood at the nth level of the pyramid with a single pixel at the n+1 level (fig. A5). The resultant levels of images, each of which is one quarter the size of its next lower level, resemble a pyramid (fig. A6).

The multi-resolution method of smoothing an image involves averaging each 2 x 2 neighborhood of the image at level n and placing the value of the neighborhood average in the level n+1 image. This operation can be repeated for two or three levels of the pyramid. The smoothed image is restored to full resolution by expanding, i.e. mapping each pixel at level n+1 into four pixels at level n, and interpolating the results to remove "blocking" effects. This operation is repeated until the full resolution image is restored