Operations On Binary Images
A entire class of operations on binary images operates on a 3x3 window of the image. This contains nine pixels, so 512 possible values. Considering only the central pixel, it is possible to define whether it remains set or unset, based on the surrounding pixels. Examples of such operations are thinning, dilating, finding branchpoints and endpoints, removing isolated pixels, shifting the image a pixel in any direction, and breaking H-connections. Conway's Game of Life is also an example of a 3x3 window operation.
Another class of operations is based on the notion of filtering with a structuring element. The structuring element is binary image, usually small, which is passed over the target image, in a similar manner to a filter in greyscale image processing. Since the pixels can only have two values, the morphological operations are erosion (any unset pixels within the structuring element cause the pixel to be unset) and dilation (any set pixels within the structuring element cause the pixel to be set). Important operations are morphological opening and morphological closing which consist of erosion followed by dilation and dilation followed by erosion, respectively, using the same structuring element. Opening tends to enlarge small holes, remove small objects, and separate objects. Closing retains small objects, removes holes, and joins objects.
A very important characteristic of a binary image is the distance transform. This gives the distance of every set pixel from the nearest unset pixel. The distance transform can be efficiently calculated. It allows efficient computation of Voronoi diagrams, where each pixel in an image is assigned to the nearest of a set of points. It also allows skeletonization, which differs from thinning in that skeletons allow recovery of the original image. The distance transform is also useful for determining the centre of the object, and for matching in image recognition.
Another class of operations is gathering orientation-free metrics. This is often important in image recognition where the orientation of the camera needs to be removed. Orientation-free metrics of a group of connected or surrounded pixels include the Euler number, the perimeter, the area, the compactness, the area of holes, the minimum radius, the maximum radius.
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